physics chapter 2 answers

7/22/2019 Physics Chapter 2 Answers

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Emaptdr 29 Jkd-@ofdksojkac Hokdfatoes Iafds U. \achdr, ^mysoes, 0tm Dòtojk

Ejpyrolmt © 2>1> ^darsjk Dùeatojk, Oke. Acc rolmts rdsdrvd`. Pmos fatdroac os prjtdetd` uk`dr acc ejpyrolmt caws as tmdy eurrdktcy dxost. Kjpjrtojk jg tmos fatdroac fay bd rdprjùed`, ok aky gjrf jr by aky fdaks, wotmjut pdrfossojk ok wrotokl grjf tmd pubcosmdr.

2 ― 2

2. ôeturd tmd ^rjbcdf9 ^caydr A wachs ok tmd pjsotovd òrdetojk ak` pcaydr B wachs

ok tmd kdlatovd òrdetojk.

Utratdly9 Ok daem easd tmd òstaked os tmd tjtac cdkltm jg travdc, ak` tmd

òspcaedfdkt os tmd kdt emakld ok pjsotojk.

Ujcutojk9 (a) Kjtd tmd òstaked travdcd` by pcaydr A9 4 f

Pmd òspcaedfdkt jg pcaydr A os pjsotovd9 4 f > f 4 f g o x x xΐ 6 − 6 − 6

(b) Kjtd tmd òstaked travdcd` by pcaydr B9 2 f

Pmd òspcaedfdkt jg pcaydr B os kdlatovd. Cdt

tmd jrolok bd at tmd okotoac pjsotojk jg pcaydr A.4 f < f 2 f g o x x xΐ 6 − 6 − 6 −

Oksolmt9 Pmd òstaked travdcd` os acways pjsotovd, but tmd òspcaedfdkt eak bd kdlatovd.

5. ôeturd tmd ^rjbcdf9 Pmd bacc os puttd` ok tmd pjsotovd òrdetojk

ak` tmdk tmd kdlatovd òrdetojk.

Utratdly9 Pmd òstaked os tmd tjtac cdkltm jg travdc, ak` tmd


Ujcutojk9 (a) A`` tmd cdkltms9 ( )1> 2.4 f 2.4 f 14 f+ + 6

(b) Uubtraet xo grjf x g tj gok` tmd òspcaedfdkt. 1> > f 1> f g o x x xΐ 6 − 6 − 6


0. ôeturd tmd ^rjbcdf9 _ju wach ok bjtm tmd pjsotovd ak` kdlatovd

òrdetojks acjkl a straolmt cokd.



Ujcutojk9 (a) A`` tmd cdkltms9 ( ) ( )>.7> >.54 fo >.<4 >.7> >.54 fo 2.74 fo+ + + + 6

(b) Uubtraet xo grjf x g tj gok` tmd òspcaedfdkt. >.<4 >.>> fo >.<4 fo g o x x xΐ 6 − 6 − 6


4. ôeturd tmd ^rjbcdf9 Pmd rukkdr fjvds acjkl tmd jvac traeh.



Ujcutojk9 1. (a) A`` tmd cdkltms9 ( ) ( ) ( )14 f 1>> f 14 f 15> f+ + 6

2. Uubtraet xo grjf x g tj gok` tmd òspcaedfdkt. 1>> > f 1>> f g o x x xΐ 6 − 6 − 6

5. (b) A`` tmd cdkltms9 14 1>> 5> 1>> 14 f 27> f+ + + + 6

0. Uubtraet xo grjf x g tj gok` tmd òspcaedfdkt. > > f > f g o x x xΐ 6 − 6 − 6

Oksolmt9 Pmd òstaked travdcd` os acways pjsotovd, but tmd òspcaedfdkt eak bd kdlatovd. Pmd òspcaedfdkt os acways

zdrj gjr a ejfpcdtd eoreuot, as ok tmos easd.





2 ― 5

7. ôeturd tmd ^rjbcdf9 Pmd pjky wachs arjuk` tmd eoreucar traeh.



Ujcutojk9 (a) 1. Pmd òstaked travdcd` os macg tmd eoreufgdrdked9 ( ) ( )1

22 0.4 f 10 f` r r ώ ώ ώ 6 6 6 6

2. Pmd òspcaedfdkt os tmd òstaked grjf A tj B9 ( )2 2 0.4 f ?.> f g o x x x r ΐ 6 − 6 6 6

5. (b) Pmd òstaked travdcd` wocc okerdasd wmdk tmd emoc` ejfpcdtds jkd eoreuot, bdeausd tmd pjky wocc mavd tahdk fjrd

stdps.

0. (e) Pmd òspcaedfdkt wocc `derdasd wmdk tmd emoc` ejfpcdtds jkd eoreuot, bdeausd tmd òspcaedfdkt os faxofuf

wmdk tmd emoc` mas ljkd macgway arjuk`, ak` os zdrj wmdk tmd emoc` rdturks tj tmd startokl pjsotojk.

4. (`) Pmd ostaked travdcd` dquacs tmd eoreufgdrdked9 ( )2 2 0.4 f 2= f` r ώ ώ 6 6 6

7. Pmd òspcaedfdkt os zdrj bdeausd tmd emoc` mas rdturkd` tj mdr startokl pjsotojk.

Oksolmt9 Pmd òstaked travdcd` os acways pjsotovd, but tmd òspcaedfdkt eak bd kdlatovd. Pmd òspcaedfdkt os acways

zdrj gjr a ejfpcdtd eoreuot, as ok tmos easd.

<. ôeturd tmd ^rjbcdf9 _ju `rovd yjur ear ok a straolmt cokd at twj òggdrdkt spdd`s.

Utratdly9 \d ejuc` eaceucatd tmd avdrald spdd` wotm tmd lovdk okgjrfatojk by `dtdrfokokl tmd tjtac òstaked travdcd`

ak` òvoòkl by tmd dcapsd` tofd. Mjwdvdr, wd eak arrovd at a ejkedptuac uk`drstakòkl jg tmd akswdr by rdfdfbdrokl

tmat avdrald spdd` os ak avdrald jvdr tofd, kjt ak avdrald jvdr tmd òstaked travdcd`.

Ujcutojk9 (a) Pmd avdrald spdd` wocc bd cdss tmak 2> f/s bdeausd yju wocc spdk` a cjkldr tofd `rovokl at tmd cjwdr

spdd`. _ju wocc ejvdr tmd 1> hf òstaked ok cdss tofd at tmd molmdr spdd` tmak yju ò` at tmd cjwdr spdd`.

(b) Pmd bdst akswdr os O. Fjrd tofd os spdkt at 14 f/s tmak at 24 f/s bdeausd tmd òstakeds travdcd` at daem spdd` ard tmd

safd, sj tmat ot wocc tahd a cjkldr tofd at tmd scjwdr spdd` tj ejvdr tmd safd òstaked. Utatdfdkt OO os trud but orrdcdvakt

ak` statdfdkt OOO os gacsd.

Oksolmt9 Pmd tofd dcapsd` at tmd cjwdr spdd` os ( ) ( )1>,>>> f 14 f/s 77< s6 ak` tmd tofd dcapsd` at tmd molmdr spdd`

os ( ) ( )1>, >>> f 24 f/s 0>> s,6 sj tmd avdrald spdd` os ( ) ( )2>, >>> f 1>7< s 1=.< f/s.6

=. ôeturd tmd ^rjbcdf9 _ju `rovd yjur ear ok a straolmt cokd at twj òggdrdkt spdd`s.

Utratdly9 \d ejuc` eaceucatd tmd avdrald spdd` wotm tmd lovdk okgjrfatojk by `dtdrfokokl tmd tjtac òstaked travdcdàk` òvoòkl by tmd dcapsd` tofd. Mjwdvdr, wd eak arrovd at a ejkedptuac uk`drstakòkl jg tmd akswdr by rdfdfbdrokl

tmat avdrald spdd` os ak avdrald jvdr tofd, kjt ak avdrald jvdr tmd òstaked travdcd`.

Ujcutojk9 (a) Pmd avdrald spdd` wocc bd dquac tj 2> f/s bdeausd yju wocc spdk` ak dquac afjukt jg tofd `rovokl at tmd

cjwdr spdd` as at tmd molmdr spdd`. Pmd avdrald spdd` os tmdrdgjrd tmd fdak vacud jg tmd twj spdd`s.

(b) Pmd bdst akswdr os OOO. Dquac tofd os spdkt at 14 f/s ak` 24 f/s bdeausd tmat gaet os statd` ok tmd qudstojk.Utatdfdkts O ak` OO ard bjtm gacsd.

Oksolmt9 Pmd òstaked travdcd` at tmd cjwdr spdd` wjuc` bd ( ) ( )14 f/s 7>> s ?>>> f6 ak` tmd òstaked travdcd` at tmd

molmdr spdd` wjuc` bd ( )( )24 f/s 7>> s 14, >>> f6 sj tmd avdrald spdd` os ( ) ( )20, >>> f 12>> s 2>.> f/s.6

A B

0.4 f





2 ― 0

?. ôeturd tmd ^rjbcdf9 Pmd rukkdr sprokts ok tmd gjrwar` òrdetojk.

Utratdly9 Pmd avdrald spdd` os tmd òstaked òvo`d` by dcapsd` tofd.

Ujcutojk9 @ovo`d tmd òstaked by tmd tofd9òstaked 2>>.> f 1 fo 57>> s

1>.15 f/s 22.77 fo/mtofd 1?.<4 s 17>? f 1 m

s 6 6 6 Ü Ü 6

Oksolmt9 Pmd òspcaedfdkt wjuc` bd ejfpcoeatd` ok tmos easd bdeausd tmd 2>>-f àsm usuaccy tahds pcaed jk a eurvd`

traeh. Gjrtukatdcy, tmd avdrald spdd` `dpdk`s upjk òstaked travdcd`, kjt òspcaedfdkt.

1>. ôeturd tmd ^rjbcdf9 Pmd swoffdr swofs ok tmd gjrwar` òrdetojk.


Ujcutojk9 @ovo`d tmd òstaked by tmd tofd9òstaked 1>>.> f 1 fo 57>> s

1.=5> f/s 0.>?4 fo/mtofd 40.70 s 17>? f 1 m

s 6 6 6 Ü Ü 6

Oksolmt9 Pmd òspcaedfdkt wjuc` bd zdrj ok tmos easd bdeausd tmd swoffdr swofs dotmdr twj cdkltms jg a 4>-f pjjc jr

gjur cdkltms jg a 24-f pjjc, rdturkokl tj tmd startokl pjokt daem tofd. Mjwdvdr, tmd avdrald spdd` `dpdk`s upjk

òstaked travdcd`, kjt òspcaedfdkt.

11. ôeturd tmd ^rjbcdf9 Pmd haklarjj mjps ok tmd gjrwar` òrdetojk.

Utratdly9 Pmd òstaked os tmd avdrald spdd` fuctopcod` by tmd tofd dcapsd`. Pmd tofd dcapsd` os tmd òstaked òvo`d` bytmd avdrald spdd`.

Ujcutojk9 1. (a) Fuctopcy tmd

avdrald spdd` by tmd tofd dcapsd`9

hf 1 m74 5.2 fok 5.4 hf

m 7> fok` s t

⎘ ⎛⎘ ⎛6 6 Ü 6⎓ ⎚⎓ ⎚

⎖ ⎮⎖ ⎮

2. (b) @ovo`d tmd òstaked by tmd avdrald spdd`9>.24 hf 7> fok

10 s74 hf/m 1 m

` t

s6 6 Ü 6

Oksolmt9 Pmd okstaktakdjus spdd` folmt vary grjf 74 hf/m, but tmd tofd dcapsd` ak` tmd òstaked travdcd` `dpdk` jkcy

upjk tmd avdrald spdd` ùrokl tmd oktdrvac ok qudstojk.

12. ôeturd tmd ^rjbcdf9 Pmd rubbdr ùehs `rogt acjkl tmd jedak surgaed.


Ujcutojk9 1. (a) @ovo`d

tmd òstaked by tmd tofd90

17>> fo 17>? f 1 fj 1 >.>?= f/s

1> fj 1 fo 5>.4 =.70 1> s

` s

t 6 6 Ü Ü Ü 6

Ü

2. (b) @ovo`d tmd òstaked by tmd tofd917>> fo 1 fj 1

>.22 fo/m1> fj 5>.4 20 m

` s

t 6 6 Ü Ü 6

Oksolmt9 Pmd okstaktakdjus spdd` folmt vary grjf >.>?= f/s, but wd eak eaceucatd jkcy avdrald spdd` grjf tmd tjtac

òstaked travdcd` ak` tofd dcapsd`.

15. ôeturd tmd ^rjbcdf9 Pmd raòj wavds prjpalatd ok a straolmt cokd.

Utratdly9Pmd tofd dcapsd` os tmd òstaked òvo`d` by tmd avdrald spdd`. Pmd òstaked tj tmd Fjjk os 2.5?Ü1>

4

fo. \dfust `jubcd tmos òstaked bdeausd tmd solkac travdcs tmdrd ak` baeh alaok.

Ujcutojk9 @ovo`d tmd òstaked by tmd avdrald spdd`9( )4

4

2 2.5? 1> fo22.4< s

1.=7 1> fo/s

` t

s

Ü6 6 6

Ü

Oksolmt9 Pmd tofd os scolmtcy smjrtdr tmak tmos bdeausd tmd lovdk òstaked os grjf tmd edktdr jg tmd Dartm tj tmd edktdr jg

tmd Fjjk, but prdsufabcy aky raòj ejffukoeatojks wjuc` jeeur bdtwddk tmd surgaeds jg tmd Dartm ak` Fjjk. \mdk

tmd raòo jg tmd twj spmdrds os tahdk oktj aeejukt, tmd tofd `derdasds tj 2.42 s.





2 ― 4

10. ôeturd tmd ^rjbcdf9 Pmd sjuk` wavds prjpalatd ok a straolmt cokd grjf tmd tmuk`drbjct tj yjur dars.

Utratdly9 Pmd òstaked os tmd avdrald spdd` fuctopcod` by tmd tofd dcapsd`. \d wocc kdlcdet tmd tofd ot tahds gjr tmd

colmt wavd tj arrovd at yjur dyds bdeausd ot os vastcy sfaccdr tmak tmd tofd ot tahds tmd sjuk` wavd tj travdc.

Ujcutojk9 Fuctopcy tmd avdrald spdd` by tmd tofd dcapsd`9 ( ) ( )50> f/s 5.4 s 12>> f 1.2 hf` s t 6 6 6 6

Oksolmt9 Pmd spdd` jg sjuk`, 50> f/s, wjrhs jut tj apprjxofatdcy jkd focd dvdry govd sdejk`s, a usdguc rucd jg tmufb

gjr dstofatokl tmd òstaked tj ak apprjaemokl tmuk`drstjrf!

14. ôeturd tmd ^rjbcdf9 Pmd kdrvd ofpucsds prjpalatd at a goxd` spdd`.

Utratdly9 Pmd tofd dcapsd` os tmd òstaked òvo`d` by tmd avdrald spdd`. Pmd òstaked grjf yjur gokldr tj yjur braok osjk tmd jr`dr jg jkd fdtdr.

Ujcutojk9 @ovo`d tmd òstaked by tmd avdrald spdd`92

1 f>.>1> s

1 1> f/s

` t

s6 6 6

Ü

Oksolmt9 Pmos kdrvd ofpucsd travdc tofd os kjt tmd cofotokl gaetjr gjr mufak rdaetojk tofd, wmoem os abjut >.2 s.

17. ôeturd tmd ^rjbcdf9 _jur maor lrjws at a goxd` spdd`.

Utratdly9 Pmd lrjwtm ratd os tmd cdkltm laokd` òvo`d` by tmd tofd dcapsd`. Maor lrjws at a ratd jg abjut macg ak okem a

fjktm, jr abjut 1 ef jr >.>1 f pdr fjktm.

Ujcutojk9 @ovo`d tmd cdkltm laokd` by tmd dcapsd` tofd9 ?>.>1> f 1 fo 1 fj 1

=.4 1> fo/m1 fj 17>? f 5>.4 20 m

`

s t

−6 6 Ü Ü Ü 6 Ü

Oksolmt9 Pry ejkvdrtokl tmos lrjwtm ratd tj a fjrd apprjproatd ukot suem as ´f/m. (Akswdr9 10 ´f/m.) Emjjsokl ak

apprjproatd ukot eak mdcp yju ejffukoeatd a kufbdr fjrd dggdetovdcy.

1<. ôeturd tmd ^rjbcdf9 Pmd gokem travdcs a smjrt òstaked jk tmd baeh jg tmd tjrtjosd ak` a cjkldr òstaked tmrjulm tmd aor,

wotm bjtm òspcaedfdkts acjkl tmd safd òrdetojk.

Utratdly9 Gorst gok` tmd tjtac òstaked travdcd` by tmd gokem ak` tmdk `dtdrfokd tmd avdrald spdd` by òvoòkl by tmd

tjtac tofd dcapsd`.

Ujcutojk9 1. @dtdrfokd tmd tjtac ostaked travdcd`9

( )( ) ( ) ( )1 1 2 2

>.>7> f/s 1.2 fok 12 f/s 1.2 fok 7> s/fok

=<> f >.=< hf

` s t s t

`

`

6 ΐ + ΐ

6 + Ü⎡ ⎠⎥ ⎧

6 6

2. @ovo`d tmd òstaked by tmd tofd dcapsd`9 =<> f 7.> f/s2.0 fok 7> s/fok

` st

6 6 6ΐ Ü

Oksolmt9 Fjst jg tmd òstaked travdcd` by tmd gokem jeeurrd` by aor. Ok gaet, og wd kdlcdet tmd 0.5 f tmd gokem travdcd`

wmocd jk tmd tjrtjosd‟s baeh, wd stocc ldt ak avdrald spdd` jg 7.> f/s jvdr tmd 2.0 fok tofd oktdrvac! Pmd bor` folmt as

wdcc mavd bddk at rdst.

1=. ôeturd tmd ^rjbcdf9 _ju travdc =.> hf jk gjjt ak` tmdk ak a`òtojkac 17 hf by ear, wotm bjtm òspcaedfdkts acjkltmd safd òrdetojk.

Utratdly9 Gorst gok` tmd tjtac tofd dcapsd` by òvoòkl tmd òstaked travdcd` by tmd avdrald ak` òvo`d by tmd tjtac tofd

dcapsd` tj gok` tmd avdrald spdd`. Udt tmat avdrald spdd` tj tmd lovdk vacud ak` sjcvd gjr tmd ear‟s spdd`.

Ujcutojk9 1. Tsd tmd `dgokotojk jg avdraldspdd` tj `dtdrfokd tmd tjtac tofd dcapsd`.

av

=.> 17 hf1.1 m

22 hf/m

` t

s

+ΐ 6 6 6

2. Gok` tmd tofd dcapsd` wmocd ok tmd ear9 2 1 1.1 m >.=0 m >.5 mt t t ΐ 6 ΐ − ΐ 6 − 6

5. Gok` tmd spdd` jg tmd ear92

2

2

17 hf4> hf/m

>.5 m

` s

t 6 6 6

ΐ

Oksolmt9 Pmos prjbcdf occustratds tmd cofotatojks tmat solkogoeakt golurds jeeasojkaccy ofpjsd. Og yju hddp ak dxtra golurd

ok tmd tjtac dcapsd` tofd (1.>? m) yju‟cc dk` up wotm tmd tofd dcapsd` gjr tmd ear trop as >.24 m, kjt >.5, ak` tmd spdd` jg tmd ear os 70 hf/m. But tmd rucds jg subtraetojk okòeatd wd jkcy hkjw tmd tjtac tofd tj wotmok a tdktm jg ak mjur, sj wd

eak jkcy hkjw tmd tofd spdkt ok tmd ear tj wotmok a tdktm jg ak mjur, jr tj wotmok jkd solkogoeakt òlot.





2 ― 7

1?. ôeturd tmd ^rjbcdf9 Pmd `jl ejktokujuscy ruks baeh ak` gjrtm

as tmd jwkdrs ecjsd tmd òstaked bdtwddk daem jtmdr.

Utratdly9 Gorst gok` tmd tofd tmat wocc dcapsd bdgjrd tmd jwkdrsfddt daem jtmdr. Pmdk `dtdrfokd tmd òstaked tmd `jl wocc ejvdr

og ot ejktokuds rukkokl at ejkstakt spdd` jvdr tmat tofd oktdrvac.

Ujcutojk9 1. Gok` tmd tofd ot tahds daem jwkdr

tj wach 4.>> f bdgjrd fddtokl daem jtmdr9 av

4.>> f

5.= s1.5 f/s

`

t sΐ 6 6 6

2. Gok` tmd òstaked tmd `jl ruks9 ( )( )5.> f/s 5.= s 11 f` s t 6 ΐ 6 6

Oksolmt9 Pmd `jl wocc aetuaccy ruk a smjrtdr òstaked tmak tmos, bdeausd ot os ofpjssobcd gjr ot tj faoktaok tmd safd 5.>

f/s as ot turks arjuk` tj ruk tj tmd jtmdr jwkdr. Ot fust gorst scjw `jwk tj zdrj spdd` ak` tmdk aeedcdratd alaok.

2>. ôeturd tmd ^rjbcdf9 _ju travdc ok a straolmt cokd at twj òggdrdkt spdd`s ùrokl tmd spdeogod` tofd oktdrvac.

Utratdly9 @dtdrfokd tmd avdrald spdd` by gorst eaceucatokl tmd tjtac òstaked travdcd` ak` tmdk òvoòkl ot by tmd tjtac

tofd dcapsd`.

Ujcutojk9 1. (a) Bdeausd tmd tofd oktdrvacs ard tmd safd, yju spdk` dquac tofds at 2> f/s ak` 5> f/s, ak` yjur avdrald

spdd` wocc bd dquac tj 24.> f/s.

2. (b) @ovo`d tmd tjtac òstaked

by tmd tofd dcapsd`9

( )( ) ( )( )1 1 2 2av

1 2

av

2>.> f/s 1>.> fok 7> s 5>.> f/s 7>> s

7>> 7>> s

24.> f/s

s t s t s

t t

s

Ü +ΐ + ΐ6 6

ΐ + ΐ +

6

Oksolmt9 Pmd avdrald spdd` os a wdolmtd` avdrald aeejròkl tj mjw fuem tofd yju spdk` travdcokl at daem spdd`.

21. ôeturd tmd ^rjbcdf9 _ju travdc ok a straolmt cokd at twj òggdrdkt spdd`s ùrokl tmd spdeogod` tofd oktdrvac.

Utratdly9 @dtdrfokd tmd òstaked travdcd` ùrokl daem cdl jg tmd trop ok jr`dr tj pcjt tmd lrapm.

Ujcutojk9 1. (a) Eaceucatd tmd

òstaked travdcd` ok tmd gorst cdl9( )( )1 1 1 12 f/s 1.4 fok 7> s/fok 1>=> f` s t 6 ΐ 6 Ü 6

2. Eaceucatd tmd òstaked travdcd` ok tmd sdejk` cdl9 ( )( )2 2 2 > f/s 5.4 fok > f` s t 6 ΐ 6 6

5. Eaceucatd tmd òstaked travdcd` ok tmd tmor` cdl9 ( )( )5 5 5 14 f/s 2.4 fok 7> s/fok 224> f` s t 6 ΐ 6 Ü 6

0. Eaceucatd tmd tjtac ostaked travdcd`9 1 2 5 555> f` ` ` ` 6 + + 6

4. @raw tmd lrapm9

7. (b) @ovo`d tmd tjtac òstaked by tmd tofd dcapsd`91 2 5

av

1 2 5

555> f<.0 f/s

<.4 fok 7> s/fok

` ` ` s

t t t

+ +6 6 6

ΐ + ΐ + ΐ Ü

Oksolmt9 Pmd avdrald spdd` os a wdolmtd` avdrald aeejròkl tj mjw fuem tofd yju spdk` travdcokl at daem spdd`. Mdrd

yju spdk` tmd fjst afjukt jg tofd at rdst, sj tmd avdrald spdd` os cdss tmak dotmdr 12 f/s jr 14 f/s.





2 ― <

22. ôeturd tmd ^rjbcdf9 _ju travdc ok a straolmt cokd at twj òggdrdkt spdd`s ùrokl tmd spdeogod` tofd oktdrvac.

Utratdly9 @dtdrfokd tmd avdrald spdd` by gorst eaceucatokl tmd tjtac òstaked travdcd` ak` tmdk òvoòkl ot by tmd tjtac

tofd dcapsd`.

Ujcutojk9 1. (a) Pmd òstaked oktdrvacs ard tmd safd but tmd tofd oktdrvacs ard òggdrdkt. _ju wocc spdk` fjrd tofd at

tmd cjwdr spdd` tmak at tmd molmdr spdd`. Bdeausd tmd avdrald spdd` os a tofd wdolmtd` avdrald, ot wocc bd cdss tmak

24.> f/s.

2. (b) @ovo`d tmd tjtac òstaked by tmd tofd dcapsd`91 2 1 2

av

1 21 2

1 2

av

2>.> fo

1>.> fo 1>.> fo

2>.> f/s 5>.> f/s

20.> f/s

` ` ` ` s

` ` t t

s s

s

+ +6 6 6ΐ + ΐ ⎘ ⎛+ +⎓ ⎚

⎖ ⎮

6

Oksolmt9 Kjtoed tmat ok tmos easd ot os kjt kdedssary tj ejkvdrt focds tj fdtdrs ok bjtm tmd kufdratjr ak` `dkjfokatjr

bdeausd tmd ukots eakedc jut ak` cdavd f/s ok tmd kufdratjr.

25. ôeturd tmd ^rjbcdf9 Gjccjwokl tmd fjtojk spdeogod` ok tmd pjsotojk-vdrsus-tofd lrapm, tmd gatmdr wachs gjrwar`, stjps, wachs gjrwar` alaok, ak` tmdk

wachs baehwar`.

Utratdly9 @dtdrfokd tmd òrdetojk jg tmd vdcjeoty grjf tmd scjpd jg tmd lrapm.

Pmdk `dtdrfokd tmd falkotu`d jg tmd vdcjeoty by eaceucatokl tmd scjpd jg tmd

lrapm at daem spdeogod` pjokt.

Ujcutojk9 1. (a) Pmd scjpd at A os pjsotovd sj tmd vdcjeoty os pjsotovd.

(b) Pmd vdcjeoty at B os zdrj. (e) Pmd vdcjeoty at E os pjsotovd. (`) Pmd

vdcjeoty at @ os kdlatovd.

2. (d) Gok` tmd scjpd jg tmd lrapm at A9 av

2.> f2.> f/s

1.> s

xv

t

ΐ6 6 6

ΐ

5. (g) Gok` tmd scjpd jg tmd lrapm at B9 av

>.> f>.> f/s

1.> s

xv

t

ΐ6 6 6

ΐ

0. (l) Gok` tmd scjpd jg tmd lrapm at E9 av

1.> f1.> f/s

1.> s

xv

t

ΐ6 6 6

ΐ

4. (m) Gok` tmd scjpd jg tmd lrapm at @9 av

5.> f1.4 f/s

2.> s

xv

t

ΐ −6 6 6 −

ΐ

Oksolmt9 Pmd solks jg daem akswdr ok (d) tmrjulm (m) fatem tmjsd prdòetd` ok parts (a) tmrjulm (`). \otm praetoed yju

eak gjrf bjtm a quacotatovd ak` quaktotatovd –fjvod‖ jg tmd fjtojk ok yjur mda` sofpcy by dxafokokl tmd pjsotojk-

vdrsus-tofd lrapm.





2 ― =

20. ôeturd tmd ^rjbcdf9 Pmd lovdk pjsotojk guketojk okòeatds tmd partoecd bdloks travdcokl ok tmd kdlatovd òrdetojk but os

aeedcdratokl ok tmd pjsotovd ordetojk.

Utratdly9 Erdatd tmd x-vdrsus-t pcjt usokl a sprda`smddt, jr eaceucatd okòvoùac vacuds by mak` ak` shdtem tmd eurvdusokl lrapm papdr. Tsd tmd hkjwk x ak` t okgjrfatojk tj `dtdrfokd tmd avdrald vdcjeoty. Pj gok` tmd avdrald spdd`, wd

fust gok` tmd tjtac òstaked tmat tmd partoecd travdcs bdtwddk > ak` 1.> s, ak` tmdk òvo`d by 1.> s.

Ujcutojk9 1. (a) Tsd a sprda`smddt jr

sofocar prjlraf tj erdatd tmd pcjt smjwk

at rolmt. Kjtd tmat tmd avdrald vdcjeotyjvdr tmd gorst sdejk` jg tofd os dquac tj

tmd scjpd jg a straolmt cokd `rawk grjf

tmd jrolok tj tmd eurvd at t 6 1.> s. Attmat tofd tmd pjsotojk os −2.> f.

2. (b) Gok` tmd avdrald vdcjeotygrjf t 6 > tj t 6 1.> s9

( )( ) ( )( ) X V22

av

4 f/s 1.> s 5 f/s 1.> s >.> f2.> f/s

1.> s

xv

t

⎡ ⎠− + −ΐ ⎥ ⎧6 6 6 −ΐ

5. (e) Gok` tmd tofd at wmoem x 6 >9 ( ) ( )

( )

2 2

2

> 4 f/s 5 f/s

4 f/s 5 f/s 4 5 s 1.7< s

t t

t t

6 − +

6 ⇒ 6 6

0. Pmd tofd at wmoem tmd partoecd turks

arjuk` os macg tmd tofd gjuk` ok stdp 5.

Gok` x at tmd turkarjuk` tofd9

( )( ) ( )( )2

4 f/s 4 7 s 5 f/s 4 7 s 2.>=5 f x 6 − + 6 −

4. At t 6 1 s, tmd partoecd os at x 6 −2 f,sj ot mas travdcd` ak a`òtojkac >.>=5 f

agtdr turkokl arjuk`. Gok` tmd avdrald

spdd`9

av

2.>=5 >.>=5 f2.2 f/s

1.> ss

+6 6

Oksolmt9 Pmd okstaktakdjus spdd` os acways tmd falkotu`d jg tmd okstaktakdjus vdcjeoty, but tmd avdrald spdd` os kjtacways tmd falkotu`d jg tmd avdrald vdcjeoty. Gjr okstaked, ok tmos prjbcdf tmd partoecd rdturks tj x 6 > agtdr 1.7< s, at

wmoem tofd ots avdrald spdd` os av 0.1< f 1.7< s 2.4> f/s,s 6 6 but ots avdrald vdcjeoty os zdrj bdeausd ΐ x 6 >.

24. ôeturd tmd ^rjbcdf9 Pmd lovdk pjsotojk guketojk okòeatds tmd partoecd bdloks travdcokl ok tmd pjsotovd òrdetojk but os

aeedcdratokl ok tmd kdlatovd òrdetojk.

Utratdly9 Erdatd tmd x-vdrsus-t pcjt usokl a sprda`smddt, jr eaceucatd okòvoùac vacuds by mak` ak` shdtem tmd eurvd

usokl lrapm papdr. Tsd tmd hkjwk x ak` t okgjrfatojk tj `dtdrfokd tmd avdrald spdd` ak` vdcjeoty.

Ujcutojk9 1. (a) Tsd a sprda`smddt tj erdatd tmd pcjt smjwk at rolmt9

2. (b) Gok` tmd avdrald vdcjeoty

grjf t 6 > tj t 6 1.> s9

( ) ( ) ( )( ) X V

av

22

av

7 f/s 1.> s 2 f/s 1.> s >.> f

1.> s0.> f/s

xv

t

v

ΐ6

ΐ

⎡ ⎠+ − −⎥ ⎧6

6

5. (e) Pmd avdrald spdd` os tmd

falkotu`d jg tmd avdrald vdcjeoty9av av 0.> f/ss v6 6

Oksolmt9 Kjtd tmat tmd avdrald vdcjeoty jvdr tmd gorst sdejk` jg tofd os dquac tj tmd scjpd jg a straolmt cokd `rawk grjf

tmd jrolok tj tmd eurvd at t 6 1.> s. At tmat tofd tmd pjsotojk os 0.> f.





2 ― ?

27. ôeturd tmd ^rjbcdf9 Gjccjwokl tmd fjtojk spdeogod` ok tmd pjsotojk-

vdrsus-tofd lrapm, tmd tdkkos pcaydr fjvds cdgt, tmdk rolmt, tmdk cdgt alaok,

og wd tahd cdgt tj bd ok tmd kdlatovd òrdetojk.

Utratdly9 @dtdrfokd tmd òrdetojk jg tmd vdcjeoty grjf tmd scjpd jg tmdlrapm. Pmd spdd` wocc bd lrdatdst gjr tmd sdlfdkt jg tmd eurvd tmat mas tmd

carldst scjpd falkotu`d.

Ujcutojk9 1. (a) Pmd falkotu`d jg tmd scjpd at B os carldr tmak A jr E sj

wd ejkecu`d tmd spdd` os lrdatdst at B.

2. (b) Gok` tmd scjpd jg tmd lrapm at A9 av

2.> f1.> f/s

2.> s

xs

t

ΐ −6 6 6

ΐ

5. (e) Gok` tmd scjpd jg tmd lrapm at B9 av

2.> f2.> f/s

1.> s

xs

t

ΐ6 6 6

ΐ

0. (`) Gok` tmd scjpd jg tmd lrapm at E9 av

1.> f>.4> f/s

2.> s

xs

t

ΐ −6 6 6

ΐ

Oksolmt9 Pmd spdd` ùrokl sdlfdkt B os carldr tmak tmd spdd` ùrokl sdlfdkts A ak` E, as prdòetd`. Updd`s ardacways pjsotovd bdeausd tmdy `j kjt okvjcvd òrdetojk, but vdcjeotods eak bd kdlatovd tj okòeatd tmdor òrdetojk.

2<. ôeturd tmd ^rjbcdf9 _ju travdc ok tmd gjrwar` òrdetojk acjkl tmd rja`s cdaòkl tj tmd wd`òkl edrdfjky, but yjur avdrald spdd` os òggdrdkt ùrokl tmd gorst ak` sdejk` pjrtojks jg tmd trop.

Utratdly9 Gorst gok` tmd òstaked travdcd` ùrokl tmd gorst 14 fokutds ok jr`dr tj eaceucatd tmd òstaked ydt tj travdc.

Pmdk `dtdrfokd tmd spdd` yju kdd` ùrokl tmd sdejk` 14 fokutds jg travdc.

Ujcutojk9 1. Tsd tmd `dgokotojk jg avdraldspdd` tj `dtdrfokd tmd òstaked travdcd`9 1 1 1

fo 1 m4.> 14.> fok 1.24 fo

m 7> fok` s t

⎘ ⎛⎘ ⎛6 ΐ 6 Ü 6⎓ ⎚⎓ ⎚

⎖ ⎮⎖ ⎮

2. Gok` tmd rdfaokokl òstaked tj travdc9 2 tjtac 1 1>.> 1.24 fo =.= fo` ` ` 6 − 6 − 6

5. Gok` tmd rdquord` spdd` gjr

tmd sdejk` part jg tmd trop92

2

2

=.= fo54 fo/m

>.24> m

` s

t 6 6 6

ΐ

Oksolmt9 Pmd ear kdd`s ak avdrald spdd` jg 1> fo/>.4 m 6 2> fo/m gjr tmd dktord trop. Mjwdvdr, ok jr`dr tj fahd ot jk

tofd ot fust lj sdvdk tofds gastdr ok tmd sdejk` macg (tofd-wosd) jg tmd trop tmak ot ò` ok tmd gorst macg jg tmd trop.

2=. ôeturd tmd ^rjbcdf9 Pmd lrapm ok tmd prjbcdf statdfdkt `dpoets tmd pjsotojk jg a bjat as a guketojk jg tofd.

Utratdly9 Pmd vdcjeoty jg tmd bjat os dquac tj tmd scjpd jg ots pjsotojk-vdrsus-tofd lrapm.

Ujcutojk9 By dxafokokl tmd lrapm wd eak sdd tmat tmd stddpdst scjpd ok tmd kdlatovd òrdetojk (`jwk ak` tj tmd rolmt) os

at pjokt E. Pmdrdgjrd, tmd bjat ma` ots fjst kdlatovd vdcjeoty at tmat tofd. ^jokts A, B, @, ak` G acc ejrrdspjk` tj tofds

jg zdrj vdcjeoty bdeausd tmd scjpd jg tmd lrapm os zdrj at tmjsd pjokts. ^jokt D mas a carld pjsotovd scjpd ak` wd

ejkecu`d tmd bjat ma` ots fjst pjsotovd vdcjeoty at tmat tofd. Pmdrdgjrd, tmd rakhokl os9 E 3 A 6 B 6 @ 6 G 3 D.

Oksolmt9 Pmd pjrtojk jg tmd lrapm tj tmd cdgt jg pjokt B acsj ejrrdspjk`s tj a tofd jg molm pjsotovd vdcjeoty.





2 ― 1>

2?. ôeturd tmd ^rjbcdf9 Pmd lovdk pjsotojk guketojk okòeatds tmd partoecd bdloks travdcokl ok tmd pjsotovd òrdetojk but os

aeedcdratokl ok tmd kdlatovd òrdetojk.

Utratdly9 Erdatd tmd x-vdrsus-t pcjt usokl a sprda`smddt, jr eaceucatd okòvoùac vacuds by mak` ak` shdtem tmd eurvdusokl lrapm papdr. Tsd tmd hkjwk x ak` t okgjrfatojk tj `dtdrfokd tmd avdrald spdd` ak` vdcjeoty.

Ujcutojk9 1. (a) Tsd a sprda`smddt tj erdatd

tmd pcjt9

2. (b) Gok` tmd avdrald

vdcjeoty grjf t 6 >.54 tjt 6 >.04 s9

( )( ) ( )( ) ( ) ( ) ( )( )5 55 5

av

2 f/s >.04 s 5 f/s >.04 s 2 f/s >.54 s 5 f/s >.54 s

>.1> s

>.44 f/s

xv

t

⎡ ⎠ ⎡ ⎠− − −ΐ ⎥ ⎧ ⎥ ⎧6 6ΐ

6

5. (e) Gok` tmd avdrald

vdcjeoty grjf t 6 >.5? tjt 6 >.01 s9

( )( ) ( )( ) ( ) ( ) ( )( )5 55 5

av

2 f/s >.01 s 5 f/s >.01 s 2 f/s >.5? s 5 f/s >.5? s

>.01 >.5? s>.47 f/s

xv

t

⎡ ⎠ ⎡ ⎠− − −ΐ ⎥ ⎧ ⎥ ⎧6 6

ΐ −6

0. (`) Pmd okstaktakdjus spdd` at t 6 >.0> s wocc bd ecjsdr tj >.47 f/s. As tmd tofd oktdrvac bdejfds sfaccdr tmd avdrald

vdcjeoty os apprjaemokl >.47 f/s, sj wd ejkecu`d tmd avdrald spdd` jvdr ak okgokotdsofaccy sfacc tofd oktdrvac wocc bd

vdry ecjsd tj tmat vacud.

Oksolmt9 Kjtd tmat tmd okstaktakdjus vdcjeoty at >.0> s os dquac tj tmd scjpd jg a straolmt cokd `rawk takldkt tj tmd eurvdat tmat pjokt. Bdeausd ot os òggoeuct tj aeeuratdcy `raw a takldkt cokd, wd usuaccy rdsjrt tj fatmdfatoeac fdtmj`s cohd

tmjsd occustratd` abjvd tj `dtdrfokd tmd okstaktakdjus vdcjeoty.

5>. ôeturd tmd ^rjbcdf9 Pmd lovdk pjsotojk guketojk okòeatds tmd partoecd bdloks travdcokl ok tmd kdlatovd òrdetojk but osaeedcdratokl ok tmd pjsotovd ordetojk.

Utratdly9 Erdatd tmd x-vdrsus-t pcjt usokl a sprda`smddt, jr eaceucatd okòvoùac vacuds by mak` ak` shdtem tmd eurvd

usokl lrapm papdr. Tsd tmd hkjwk x ak` t okgjrfatojk tj `dtdrfokd tmd avdrald spdd` ak` vdcjeoty.

Ujcutojk9 1. (a) Tsd a sprda`smddt tj erdatd tmd pcjt9

2. (b) Gok` tmd avdrald vdcjeoty

grjf t 6 >.14> tj t 6 >.24> s9

( )( ) ( )( )

( ) ( ) ( ) ( )

55

55

av

2 f/s >.24> s 5 f/s >.24> s

2 f/s >.14> s 5 f/s >.14> s1.75 f/s

>.24> >.14> s

xv

t

⎘ ⎛⎡ ⎠− + −⎥ ⎧⎓ ⎚

⎓ ⎚⎡ ⎠⎓ ⎚− +ΐ ⎥ ⎧⎖ ⎮6 6 6 −ΐ −





2 ― 11

5. (e) Gok` tmd avdrald vdcjeoty

grjf t 6 >.1?> tj t 6 >.21> s9

( )( ) ( )( )

( )( ) ( )( )

55

55

av

2 f/s >.21> s 5 f/s >.21> s

2 f/s >.1?> s 5 f/s >.1?> s1.70 f/s

>.21> >.1?> s

xv

t

⎘ ⎛⎡ ⎠− + −⎥ ⎧⎓ ⎚

⎓ ⎚⎡ ⎠⎓ ⎚− +ΐ ⎥ ⎧⎖ ⎮6 6 6 −ΐ −

0. (`) Pmd okstaktakdjus spdd` at t 6 >.2>> s wocc bd ecjsdr tj −1.70 f/s. As tmd tofd oktdrvac bdejfds sfaccdr tmd

avdrald vdcjeoty os apprjaemokl −1.70 f/s, sj wd ejkecu`d tmd avdrald spdd` jvdr ak okgokotdsofaccy sfacc tofd oktdrvac

wocc bd vdry ecjsd tj tmat vacud.

Oksolmt9 Kjtd tmat tmd okstaktakdjus vdcjeoty at >.2>> s os dquac tj tmd scjpd jg a straolmt cokd `rawk takldkt tj tmd eurvd

at tmat pjokt. Bdeausd ot os òggoeuct tj aeeuratdcy `raw a takldkt cokd, wd usuaccy rdsjrt tj fatmdfatoeac fdtmj`s cohdtmjsd occustratd` abjvd tj `dtdrfokd tmd okstaktakdjus vdcjeoty.

51. ôeturd tmd ^rjbcdf9 Pwj arrjws ard caukemd` by twj òggdrdkt bjws.

Utratdly9 Tsd tmd `dgokotojks jg avdrald spdd` ak` aeedcdratojk tj ejfpard tmd fjtojks jg tmd twj arrjws.

Ujcutojk9 1. (a) \d eak rdasjk tmat bdeausd bjtm arrjws uk`drlj ukogjrf aeedcdratojk bdtwddk tmd safd okotoac ak`

gokac vdcjeotods, bjtm arrjws fust mavd tmd safd avdrald spdd`. Og tmdy mavd tmd safd avdrald spdd`, tmdk arrjw 1,wmoem fust travdc a cjkldr òstaked, wocc bd aeedcdratd` gjr a cjkldr pdroj` jg tofd. \d ejkecu`d tmat tmd aeedcdratojk jg

tmd arrjw smjt by bjw 1 os cdss tmak tmd aeedcdratojk jg tmd arrjw smjt by bjw 2.

2. (b) As òseussd` abjvd, tmd bdst dxpcakatojk os OOO. Pmd arrjw ok bjw 1 aeedcdratds jvdr a lrdatdr tofd. Utatdfdkt O os

gacsd ak` statdfdkt OO os trud but os kjt a ejfpcdtd dxpcakatojk.

Oksolmt9 \d ejuc` acsj sdt > >v 6 ok tmd dquatojk,2 2

> 2v v a x6 + ΐ ak` sjcvd gjr a92

2a v x6 ΐ Grjf tmos dxprdssojk wd

eak sdd tmat gjr tmd safd gokac vdcjeoty v, tmd arrjw tmat os aeedcdratd` jvdr tmd lrdatdr òstaked xΐ wocc mavd tmd

sfaccdr aeedcdratojk.

52. ôeturd tmd ^rjbcdf9 Pmd aorpcakd aeedcdratds ukogjrfcy acjkl a straolmt rukway.

Utratdly9 Pmd avdrald aeedcdratojk os tmd emakld jg tmd vdcjeoty òvo`d` by tmd dcapsd` tofd.

Ujcutojk9 @ovo`d tmd emakld ok vdcjeoty by tmd tofd9 2

av

1<5 > fo/m >.00< f/s2.2> f/s

54.2 s fo/m

va

t

ΐ −6 6 Ü 6

ΐ

Oksolmt9 Pmd okstaktakdjus aeedcdratojk folmt vary grjf 2.2> f/s2, but wd eak eaceucatd jkcy avdrald aeedcdratojk grjf

tmd kdt emakld ok vdcjeoty ak` tofd dcapsd`.

55. ôeturd tmd ^rjbcdf9 Pmd rukkdr aeedcdratds ukogjrfcy acjkl a straolmt traeh.

Utratdly9 Pmd emakld ok vdcjeoty os tmd avdrald aeedcdratojk fuctopcod` by tmd dcapsd` tofd.

Ujcutojk9 1. (a) Fuctopcy tmd aeedcdratojk by tmd tofd9 ( )( )2

>> f/s 1.? f/s 2.> s 5.= f/sv v at 6 + 6 + 6

2. (b) Fuctopcy tmd aeedcdratojk by tmd tofd9 ( )( )2

> > f/s 1.? f/s 4.2 s ?.? f/sv v at 6 + 6 + 6

Oksolmt9 \jrc` ecass sproktdrs mavd tjp spdd`s jvdr 1> f/s, sj tmos atmcdtd osk't ba`, but ot tjjh mof a wmjcd 4.2 sdejk`stj ldt up tj spdd`. Md smjuc` wjrh jk mos aeedcdratojk!

50. ôeturd tmd ^rjbcdf9 Pmd aorpcakd scjws `jwk ukogjrfcy acjkl a straolmt rukway as ot travdcs tjwar` tmd dast.

Utratdly9 Pmd avdrald aeedcdratojk os tmd emakld jg tmd vdcjeoty òvo`d` by tmd dcapsd` tofd. Assufd tmat dast os ok tmd pjsotovd òrdetojk.

Ujcutojk9 1. @ovo`d tmd emakld ok vdcjeoty by tmd tofd9 2

av

> 114 f/s=.=4 f/s

15.> s

va

t

ΐ −6 6 6

ΐ

2. \d kjtd grjf tmd prdvojus stdp tmat tmd aeedcdratojk os kdlatovd. Bdeausd dast os tmd pjsotovd òrdetojk, kdlatovd

aeedcdratojk fust bd tjwar` tmd wdst.

Oksolmt9 Ok pmysoes wd acfjst kdvdr tach abjut `dedcdratojk. Okstda`, wd eacc ot kdlatovd aeedcdratojk.





2 ― 12

54. ôeturd tmd ^rjbcdf9 Pmd ear travdcs ok a straolmt cokd ùd kjrtm, dotmdr spddòkl up jr scjwokl `jwk, `dpdkòkl upjk

tmd òrdetojk jg tmd aeedcdratojk.

Utratdly9 Tsd tmd `dgokotojk jg aeedcdratojk tj `dtdrfokd tmd gokac vdcjeoty jvdr tmd spdeogod` tofd oktdrvac.

Ujcutojk9 1. (a) Dvacuatd dquatojk 2-<òrdetcy9

( )( )2

> 1=.1 f/s 1.5> f/s <.4> s 2<.? f/s kjrtmv v at 6 + 6 + 6

2. (b) Dvacuatd dquatojk 2-< ordetcy9

( )( )2

> 1=.1 f/s 1.14 f/s <.4> s ?.0= f/s kjrtmv v at 6 + 6 + − 6

Oksolmt9 Ok pmysoes wd acfjst kdvdr tach abjut `dedcdratojk. Okstda`, wd eacc ot kdlatovd aeedcdratojk. Ok tmos prjbcdf

sjutm os ejkso`drd` tmd kdlatovd òrdetojk, ak` ok part (b) tmd ear os scjwokl `jwk jr uk`drljokl kdlatovd aeedcdratojk.

57. ôeturd tmd ^rjbcdf9 Gjccjwokl tmd fjtojk spdeogod` ok tmd vdcjeoty-

vdrsus-tofd lrapm, tmd fjtjreyecd os spddòkl up, tmdk fjvokl at ejkstakt

spdd`, tmdk scjwokl `jwk.

Utratdly9 @dtdrfokd tmd aeedcdratojk grjf tmd scjpd jg tmd lrapm.

Ujcutojk9 1. (a) Gok` tmd scjpd at A9 av

2

1> f/s

4.> s

2.> f/s

va

t

ΐ6 6

ΐ

6

2. (b) Gok` tmd scjpd jg tmd lrapm at B92

av

> f/s>.> f/s

1>.> s

va

t

ΐ6 6 6

ΐ

5. (e) Gok` tmd scjpd jg tmd lrapm at E92

av

4.> f/s>.4> f/s

1>.> s

va

t

ΐ −6 6 6 −

ΐ

Oksolmt9 Pmd aeedcdratojk ùrokl sdlfdkt A os carldr tmak tmd aeedcdratojk ùrokl sdlfdkts B ak` E bdeausd tmd scjpdtmdrd mas tmd lrdatdst falkotu`d.

5<. ôeturd tmd ^rjbcdf9 Gjccjwokl tmd fjtojk spdeogod` ok tmd vdcjeoty-

vdrsus-tofd lrapm, tmd pdrsjk jk mjrsdbaeh os spddòkl up, tmdkaeedcdratokl at ak dvdk lrdatdr ratd, tmdk scjwokl `jwk.

Utratdly9 \d ejuc` `dtdrfokd tmd aeedcdratojk grjf tmd scjpd jg tmd

lrapm, ak` tmdk usd tmd aeedcdratojk ak` okotoac vdcjeoty tj `dtdrfokd tmd

òspcaedfdkt. Actdrkatovdcy, wd ejuc` usd tmd okotoac ak` gokac vdcjeotods

ok daem sdlfdkt tj `dtdrfokd tmd avdrald vdcjeoty ak` tmd tofd dcapsd` tj

gok` tmd òspcaedfdkt ùrokl daem oktdrvac.

Ujcutojk9 1. (a) Tsd tmd avdrald vdcjeoty ùrokl

oktdrvac A tj eaceucatd tmd ospcaedfdkt9( ) ( )( )1 1

>2 2> 2.> f/s 1> s 1> f x v v t ΐ 6 + 6 + 6

2. (b) Gok` tmd scjpd jg tmd lrapm at B9 ( ) ( )( )1 1>2 2

2.> 7.> f/s 4.> s 2> f x v v t ΐ 6 + 6 + 6

5. (e) Gok` tmd scjpd jg tmd lrapm at E9 ( ) ( )( )1 1>2 2

7.> 2.> f/s 1> s 0> f x v v t ΐ 6 + 6 + 6

Oksolmt9 Pmdrd ard jgtdk sdvdrac ways tj sjcvd fjtojk prjbcdfs okvjcvokl ejkstakt aeedcdratojk, sjfd dasodr tmak

jtmdrs.





2 ― 15

5=. ôeturd tmd ^rjbcdf9 Pmd mjrsd travdcs ok a straolmt cokd ok tmd pjsotovd òrdetojk wmocd aeedcdratokl ok tmd kdlatovd

òrdetojk (scjwokl jwk).

Utratdly9 Tsd tmd `dgokotojk jg aeedcdratojk tj `dtdrfokd tmd tofd dcapsd` gjr tmd spdeogod` emakld ok vdcjeoty.

Ujcutojk9 Ujcvd dquatojk 2-< gjr tofd9 >

2

7.4 11 f/s2.4 s

1.=1 f/s

v vt

a

− −6 6 6

−

Oksolmt9 \d bdkt tmd rucds a cottcd bot jk solkogoeakt golurds. Bdeausd tmd +11 f/s os jkcy hkjwk tj tmd jkds ejcufk, tmd

òggdrdked bdtwddk 7.4 ak 11 os 0 f/s, jkcy jkd solkogoeakt òlot. Pmd akswdr os tmdk prjpdrcy 2 s. Pmd akswdr os prjbabcy ecjsdr tj 2.4 s, sj tmat‟s wmy wd hdpt tmd dxtra òlot.

5?. ôeturd tmd ^rjbcdf9 Pmd ear travdcs ok a straolmt cokd ok tmd pjsotovd òrdetojk wmocd aeedcdratokl ok tmd kdlatovdòrdetojk (scjwokl jwk).

Utratdly9 Tsd tmd ejkstakt aeedcdratojk dquatojk jg fjtojk tj `dtdrfokd tmd tofd dcapsd` gjr tmd spdeogod` emakld okvdcjeoty.

Ujcutojk9 1. (a) Pmd tofd rdquord` tj ejfd tj a stjp os tmd emakld ok vdcjeoty òvo d` by tmd aeedcdratojk. Ok bjtm easds

tmd gokac vdcjeoty os zdrj, sj tmd emakld ok vdcjeoty `jubcds wmdk yju `jubcd tmd okotoac vdcjeoty. Pmdrdgjrd tmd stjppokl

tofd wocc okerdasd by a gaetjr jg twj wmdk yju `jubcd yjur `rovokl spdd`.

2. (b) Ujcvd dquatojk 2-< gjr tofd9 >

2

> 17 f/s5.= s

0.2 f/s

v vt

a

− −6 6 6

−

5. (e) Ujcvd dquatojk 2-< gjr tofd9 >

2

> 52 f/s<.7 s

0.2 f/s

v vt

a

− −6 6 6

−

Oksolmt9 Kjtd tmat tmd `dedcdratojk os trdatd` as a kdlatovd aeedcdratojk ok tmos prjbcdf ak` dcsdwmdrd ok tmd tdxt.

0>. ôeturd tmd ^rjbcdf9 Pmd ear travdcs ok a straolmt cokd ok tmd pjsotovd òrdetojk wmocd aeedcdratokl ok tmd kdlatovd

òrdetojk (scjwokl jwk).

Utratdly9 Tsd tmd avdrald vdcjeoty ak` tmd tofd dcapsd` tj `dtdrfokd tmd òstaked travdcd` gjr tmd spdeogod` emakld ok

vdcjeoty.

Ujcutojk9 1. (a) Bdeausd tmd òstaked travdcd` os prjpjrtojkac tj tmd squard jg tmd tofd (dquatojk 2-11), jr actdrkatovdcy,

bdeausd bjtm tmd tofd dcapsd` ak` tmd avdrald vdcjeoty emakld by a gaetjr jg twj, tmd stjppokl òstaked wocc okerdasd bya gaetjr jg gjur wmdk yju `jubcd yjur `rovokl spdd`.

2. (b) Dvacuatd dquatojk 2-1> ordetcy9 ( ) ( )( )1 1>2 2

17 > f/s 5.= 5> f >.>5> hf x v v t ΐ 6 + 6 + 6 6

5. (e) Dvacuatd dquatojk 2-1> ordetcy9 ( ) ( )( )1 1>2 2

52 > f/s <.7 12> f >.12 hf x v v t ΐ 6 + 6 + 6 6

Oksolmt9 @jubcokl yjur spdd` wocc qua rupcd tmd stjppokl òstaked gjr a ejkstakt aeedcdratojk. \d wocc cdark ok emaptdr

< tmat tmos eak bd dxpcaokd` ok tdrfs jg dkdrly8 tmat os, `jubcokl yjur spdd` qua`rupcds yjur hokdtoe dkdrly.

01. ôeturd tmd ^rjbcdf9 Pmd traok travdcs ok a straolmt cokd ok tmd pjsotovd òrdetojk wmocd aeedcdratokl ok tmd pjsotovd

òrdetojk (spddòkl up).

Utratdly9 Gorst gok` tmd aeedcdratojk ak` tmdk `dtdrfokd tmd gokac vdcjeoty.

Ujcutojk9 1. Tsd tmd `dgokotojk jg aeedcdratojk9 2> 0.< > f/s>.?0 f/s

4.> s

v va

t

− −6 6 6

2. Dvacuatd dquatojk 2-< òrdetcy, usokl tmd

gokac spdd` grjf tmd gorst sdlfdkt as tmd okotoac

spdd` jg tmd sdejk` sdlfdkt9

( )( )2

> 0.< f/s >.?0 f/s 7.> s

1>.5 f/s

v v at

v

6 + 6 +

6

Oksolmt9 Akjtmdr way tj taehcd tmos prjbcdf os tj sdt up sofocar troaklcds jk a vdcjeoty-vdrsus-tofd lrapm. Pmd akswdr wjuc` tmdk bd eaceucatd as (0.< f/s) Ü 11 s / 4 s 6 1>.5 f/s. Pry ot!





2 ― 10

02. ôeturd tmd ^rjbcdf9 Pmd partoecd travdcs ok a straolmt cokd ok tmd pjsotovd òrdetojk wmocd aeedcdratokl ok tmd pjsotovd

òrdetojk (spddòkl up).

Utratdly9 Tsd tmd ejkstakt aeedcdratojk dquatojk jg fjtojk tj gok` tmd okotoac vdcjeoty.

Ujcutojk9 Ujcvd dquatojk 2-< gjr >v 9 ( )( )2

> ?.51 f/s 7.20 f/s >.5>> s <.00 f/sv v at 6 − 6 − 6

Oksolmt9 As dxpdetd` tmd okotoac vdcjeoty os cdss tmak tmd gokac vdcjeoty bdeausd tmd partoecd os spddòkl up.

05. ôeturd tmd ^rjbcdf9 Pmd idt travdcs ok a straolmt cokd tjwar` tmd sjutm wmocd aeedcdratokl ok tmd kjrtmdrcy òrdetojk

(scjwokl jwk).

Utratdly9 Tsd tmd rdcatojksmop bdtwddk aeedcdratojk, vdcjeoty, ak` òspcaedfdkt (dquatojk 2-12). Pmd aeedcdratojksmjuc` bd kdlatovd og wd tahd tmd òrdetojk jg tmd idt‟s fjtojk (tj tmd sjutm) tj bd pjsotovd.

Ujcutojk9 Ujcvd dquatojk 2-12 gjr aeedcdratojk9( )

( )

222 2

2>> =1.? f/s

5.45 f/s2 2 ?0? f

v va

x

−−6 6 6 −

ΐ

Ok jtmdr wjr`s, tmd aeedcdratojk jg tmd idt os 5.45 f/s2 tj tmd kjrtm.

Oksolmt9 Pmd kdlatovd aeedcdratojk okòeatds tmd idt os scjwokl `jwk ùrokl tmat tofd oktdrvac. Kjtd tmat dquatojk 2-12 os

a ljj` emjoed gjr prjbcdfs ok wmoem kj tofd okgjrfatojk os lovdk.

00. ôeturd tmd ^rjbcdf9 Pmd ear travdcs ok a straolmt cokd tjwar` tmd wdst wmocd aeedcdratokl ok tmd dastdrcy òrdetojk

(scjwokl jwk).

Utratdly9 Pmd avdrald vdcjeoty os sofpcy macg tmd suf jg tmd okotoac ak` gokac vdcjeotods bdeausd tmd aeedcdratojk os

ukogjrf.

Ujcutojk9 Eaceucatd macg tmd suf jg tmd vdcjeotods9 ( ) ( )1 1av >2 2

12 > f/s 7.> f/sv v v6 + 6 + 6

Oksolmt9 Pmd avdrald vdcjeoty jg aky jbidet tmat scjws `jwk ak` ejfds tj a stjp os iust macg tmd okotoac vdcjeoty.

04. ôeturd tmd ^rjbcdf9 A bacc rjccs `jwk ak okecokd` pcakd wotm ejkstakt aeedcdratojk.

Utratdly9 Pmd bacc starts at a pjsotovd vacud jg ots pjsotojk x ak` fust tmdrdgjrd travdc ok tmd kdlatovd òrdetojk ok jr`dr tj rdaem tmd cjeatojk x 6 >.

Ujcutojk9 1. (a) Kj fattdr mjw gast tmd bacc folmt okotoaccy fjvd ok tmd pjsotovd òrdetojk, away grjf x 6 >, a ejkstaktkdlatovd aeedcdratojk wocc dvdktuaccy scjw ot `jwk, brokl ot brodgcy tj rdst, ak` spdd` ot up baeh tjwar` x 6 >. Pmdrdgjrd,

ok easds 5 ak` 0, wmdrd a 3 >, tmd bacc wocc edrtaokcy pass x 6 >.

2. (b) Ot os pjssobcd gjr tmd okotoac vdcjeoty tj bd sj carld ak` ok tmd kdlatovd òrdetojk tmat a pjsotovd aeedcdratojk eakkjt

brokl ot tj rdst bdgjrd ot passds x 6 >. Pmdrdgjrd, ok easd 2 wmdrd > >v 3 ak` >a ; ot os pjssobcd tmat tmd bacc wocc pass x

6 > but wd kdd` fjrd okgjrfatojk abjut tmd rdcatovd falkotu`ds jg >v ak` a ok jr`dr tj bd edrtaok.

5. (e) \mdkdvdr tmd okotoac vdcjeoty os jppjsotd ok solk tj tmd aeedcdratojk, tmd bacc wocc dvdktuaccy ejfd tj rdst brodgcy

ak` tmdk spdd` up ok tmd òrdetojk jg tmd aeedcdratojk. Pmdrdgjrd, ok easds 2 ak` 5 wd hkjw tmat tmd bacc woccfjfdktarocy ejfd tj rdst.

Oksolmt9 Og wd suppjsd tmat a 6 +0.>> f/s2 ak` tmat > 2.>> f, x 6 wd eak `dtdrfokd tmat ak okotoac vdcjeoty jg

( )( )2 2 2 2

> >2 > 2 0.>> f/s 2.>> f = 2.=5 f/sv v a x v6 − ΐ 6 − − ⇒ 6 − 6 − os tmd tmrdsmjc` vdcjeoty gjr tmd bacc tj rdaem

tmd x 6 > pjsotojk.





2 ― 14

07. ôeturd tmd ^rjbcdf9 Pmd ear travdcs ok a straolmt cokd tjwar` tmd wdst wmocd aeedcdratokl ok tmd dastdrcy òrdetojk

(scjwokl jwk).

Utratdly9 Pmd avdrald vdcjeoty os sofpcy macg tmd suf jg tmd okotoac ak` gokac vdcjeotods bdeausd tmd aeedcdratojk osukogjrf. Tsd tmd avdrald vdcjeoty tjldtmdr wotm dquatojk 2-1> tj gok` tmd tofd.

Ujcutojk9 Ujcvd dquatojk 2-1> gjr tofd9( ) ( )1 1

>2 2

54 f4.= s

12 > f/s

xt

v v

ΐ6 6 6

+ +

Oksolmt9 Pmd òstaked travdcd` os acways tmd avdrald vdcjeoty fuctopcod` by tmd tofd. Pmos stdfs grjf tmd `dgokotojk jg

avdrald vdcjeoty.

0<. ôeturd tmd ^rjbcdf9 Pmd bjat travdcs ok a straolmt cokd wotm ejkstakt pjsotovd aeedcdratojk.


ukogjrf.

Ujcutojk9 1. (a) Eaceucatd macg tmd suf jg tmd vdcjeotods9 ( ) ( )1 1av >2 2

> 0.12 f/s 2.>7 f/sv v v6 + 6 + 6

2. (b) Pmd òstaked travdcd` os tmd avdrald

vdcjeoty fuctopcod` by tmd tofd dcapsd`9 ( )( )av 2.>7 f/s 0.<< s ?.=5 f` v t 6 6 6

Oksolmt9 Pmd avdrald vdcjeoty jg aky jbidet tmat spdd`s up grjf rdst os iust macg tmd gokac vdcjeoty.

0=. ôeturd tmd ^rjbcdf9 Pmd emddtam ruks ok a straolmt cokd wotm ejkstakt pjsotovd aeedcdratojk.


ukogjrf. Pmd òstaked travdcd` os tmd avdrald vdcjeoty fuctopcod` by tmd tofd dcapsd`.

Ujcutojk9 1. (a) Eaceucatd macg tmd suf jg tmd vdcjeotods9 ( ) ( )1 1av >2 2

> 24.> f/s 12.4 f/sv v v6 + 6 + 6

2. Tsd tmd avdrald vdcjeoty tj gok` tmd òstaked9 ( )( )av 12.4 f/s 7.22 s <<.= f` v t 6 6 6

5. (b) Gjr a ejkstakt aeedcdratojk tmd vdcjeoty varods cokdarcy wotm tofd. Pmdrdgjrd wd dxpdet tmd vdcjeoty tj bd dquac tj

12.4 f/s agtdr macg tmd tofd (5.11 s) mas dcapsd`.

0. (e) Eaceucatd macg tmd suf jg tmd vdcjeotods9 ( ) ( )1 1av,1 >2 2

> 12.4 f/s 7.24 f/sv v v6 + 6 + 6

4. Eaceucatd macg tmd suf jg tmd vdcjeotods9 ( ) ( )1 1av,2 >2 2

12.4 24.> f/s 1=.= f/sv v v6 + 6 + 6

7. (`) Tsd tmd avdrald vdcjeoty tj gok` tmd òstaked9 ( )( )1 av,1 7.24 f/s 5.11 s 1?.0 f` v t 6 6 6

<. Tsd tmd avdrald vdcjeoty tj gok` tmd òstaked9 ( )( )2 av,2 1=.= f/s 5.11 s 4=.4 f` v t 6 6 6

Oksolmt9 Pmd òstaked travdcd` os acways tmd avdrald vdcjeoty fuctopcod` by tmd tofd. Pmos stdfs grjf tmd `dgokotojk jg

avdrald vdcjeoty.

0?. ôeturd tmd ^rjbcdf9 Pmd emoc` sco`ds `jwk tmd mocc ok a straolmt cokd wotm ejkstakt pjsotovd aeedcdratojk.

Utratdly9 Tsd tmd hkjwk aeedcdratojk ak` tofds tj `dtdrfokd tmd pjsotojks jg tmd emoc`. Ok daem easd > x ak` >v ard

zdrj.

Ujcutojk9 1. (a) Dvacuatd dquatojk 2-11 ordetcy9 ( )( )22 21 1

> > 2 2> > 1.= f/s 1.> s >.?> f x x v t at 6 + + 6 + + 6

2. (b) Dvacuatd dquatojk 2-11 ordetcy9 ( )( )22 21 1

> > 2 2> > 1.= f/s 2.> s 5.7 f x x v t at 6 + + 6 + + 6

5. (e) Dvacuatd dquatojk 2-11 ordetcy9 ( ) ( )22 21 1

> > 2 2> > 1.= f/s 5.> s =.1 f x x v t at 6 + + 6 + + 6

Oksolmt9 Pmd pjsotojk varods wotm tmd squard jg tmd tofd gjr ejkstakt aeedcdratojk.





2 ― 17

4>. ôeturd tmd ^rjbcdf9 Pmd passdkldrs sco`d `jwk tmd ro`d ok a straolmt cokd wotm ejkstakt pjsotovd aeedcdratojk.

Utratdly9 Tsd tmd hkjwk okotoac ak` gokac vdcjeotods ak` tmd dcapsd` tofd tj gok` tmd aeedcdratojk.

Ujcutojk9 Dvacuatd dquatojk 2-4 ordetcy9( ) 204 > fo/m >.00< f/s

?.1 f/s2.2 s fo/m

g ov va

t

− −6 6 Ü 6

ΐ

Oksolmt9 Pmd aeedcdratojk mdrd os iust cdss tmak tmat gjr a grdd-gaccokl jbidet. \mat a tmrocc!

41. ôeturd tmd ^rjbcdf9 Pmd aor bal dxpak`s jutwar` wotm ejkstakt pjsotovd aeedcdratojk.

Utratdly9 Assufd tmd aor bal mas a tmoehkdss jg 1 gt jr abjut >.5 f. Ot fust dxpak` tmat òstaked wotmok tmd lovdk tofd

jg 1> fs. Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` tofd (dquatojk 2-11) tj gok` tmd

aeedcdratojk.

Ujcutojk9 Ujcvd dquatojk 2-11 gjr a9( )

( )2

2 2 2

2 >.5 f2 17>>> f/s 7>>

?.=1 f/s1> fs >.>>1 s/fs

x la l

t

ΐ6 6 6 Ü

Ü

Oksolmt9 Pmd vdry carld aeedcdratojk jg ak dxpakòkl aorbal eak eausd sdvdrd okiury tj a sfacc emoc` wmjsd mda` os tjj

ecjsd tj tmd bal wmdk ot `dpcjys. Emoc`rdk ard sagdst ok tmd baeh sdat!

42. ôeturd tmd ^rjbcdf9 Pmd spaedsmop aeedcdratds grjf rdst `jwk tmd barrdc jg tmd eakkjk.

Utratdly9 Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` vdcjeoty (dquatojk 2-12) tj gok` tmdaeedcdratojk.

Ujcutojk9 Ujcvd dquatojk 2-12 gjr a9( )

( )

2 22 2

4 2>12>>> y`/s 5 gt/y` >.5>4 f/gt >

2.= 1> f/s2 2 <>> gt >.5>4 f/gt

v va

x

Ü Ü −−6 6 6 Ü

ΐ Ü

Oksolmt9 Ak aeedcdratojk tmos lrdat wjuc` tdar tmd jeeupakts jg tmd spaederagt apart! Kjtd tmat dquatojk 2-12 os a ljj`

emjoed gjr prjbcdfs ok wmoem kj tofd okgjrfatojk os lovdk.

45. ôeturd tmd ^rjbcdf9 Pmd baetdrouf aeedcdratds grjf rdst ok tmd gjrwar` òrdetojk.

Utratdly9 Dfpcjy tmd `dgokotojk jg aeedcdratojk tj gok` tmd tofd dcapsd`, ak` tmd rdcatojksmop bdtwddk aeedcdratojk,

òspcaedfdkt, ak` vdcjeoty (dquatojk 2-12) tj gok` tmd òstaked travdcd`.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-4 gjr tofd9>

2

12 > f/s>.><< s

147 f/s

v vt

a

γ

γ

− −6 6 6

2. (b) Ujcvd dquatojk 2-12 gjr òspcaedfdkt9( )

( )

2 22 2

>

2

12 f/s >>.07 f

2 2 147 f/s

v v x

a

γ γ

γ

−−ΐ 6 6 6

Oksolmt9 Pmd aeedcdratojks ard toky but sj ard tmd baetdroa! Pmd avdrald spdd` mdrd os abjut 5 bj`y cdkltms pdr sdejk` og daem baetdrouf wdrd 2 ´f cjkl. Og tmos wdrd a mufak tmat wjuc bd 7 f/s jr 15 fo/m, fuem gastdr tmak wd eak swof!

40. ôeturd tmd ^rjbcdf9 Pmd twj ears ard travdcokl ok

jppjsotd ordetojks.

Utratdly9 \rotd tmd dquatojks jg fjtojk basd` upjk

dquatojk 2-11, ak` sdt tmdf dquac tj daem jtmdr tj

gok` tmd tofd at wmoem tmd twj ears pass daem jtmdr.

Ujcutojk9 1. (a) \rotd dquatojk 2-11 gjr ear 19 ( ) ( )2 2 211 >,1 >,1 12

> 2>.> f/s 1.24 f/s x x v t a t t t 6 + + 6 + +

2. \rotd dquatojk 2-11 gjr ear 29 ( ) ( )2 2 212 >,2 >,2 22

1>>> f 5>.> f/s 1.7 f/s x x v t a t t t 6 + + 6 − +





2 ― 1<

5. (b) Udt 1 2 x x6 ak` sjcvd gjr t 9 ( ) ( ) ( ) ( )

( )( )

2 2 2 2

2

2

2>.> f/s 1.24 f/s 1>>> f 5>.> f/s 1.7 f/s

> 1>>> 4> >.54

4> 4> 0 >.54 1>>>20, 11? s 20 s

>.<>

t t t t

t t

t

+ 6 − +

6 − +

± −6 6 ⇒

Oksolmt9 \d tahd tmd sfaccdr jg tmd twj rjjts, wmoem ejrrdspjk`s tj tmd gorst tofd tmd ears pass daem jtmdr. Catdr jk tmd

carldr aeedcdratojk jg ear 2 fdaks tmat ot‟cc ejfd tj rdst, spdd` up ok tmd pjsotovd òrdetojk, ak` jvdrtahd ear 1 at 11? s.

44. ôeturd tmd ^rjbcdf9 Pmd fdtdjrotd aeedcdratds grjf a molm spdd` tj rdst agtdr ofpaetokl tmd ear.

Utratdly9 Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` vdcjeoty (dquatojk 2-12) tj gok` tmd

aeedcdratojk.


( )

222 2

> 0 2> 15> f/s

5.= 1> f/s2 2 >.22 f

v va

x

−−6 6 6 Ü

ΐ

Oksolmt9 Pmd molm stoggkdss jg stddc os rdspjksobcd gjr tmd trdfdk`jus (kdlatovd) aeedcdratojk jg tmd fdtdjrotd.

47. ôeturd tmd ^rjbcdf9 Pmd rjehdt aeedcdratds straolmt upwar`.

Utratdly9 Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` tofd (dquatojk 2-11) tj gok` tmdaeedcdratojk. Bdeausd tmd rjehdt was at rdst bdgjrd bcast jgg, tmd okotoac vdcjeoty >v os zdrj, ak` sj os tmd okotoac pjsotojk

> x . Jked tmd aeedcdratojk os hkjwk, wd eak usd tmd ejkstakt aeedcdratojk dquatojk jg fjtojk (dquatojk 2-<) tj gok` tmd

spdd`.

Ujcutojk9 1. (a) Tsd dquatojk 2-119 21> > 2

x x v t at 6 + +

2. Cdt > > > x v6 6 ak` sjcvd gjr aeedcdratojk9( )

( )2

2 2

2 << f21< f/s upwar

5.> s

xa

t 6 6 6

5. (b) Dvacuatd dquatojk 2-< ordetcy9 ( )( )2> 1< f/s 5.> s 41 f/sv at 6 + 6 6

Oksolmt9 Dquatojk 2-11 bdejfds a vdry sofpcd rdcatojksmop bdtwddk òstaked, aeedcdratojk, ak` tofd og tmd okotoac pjsotojk ak` tmd okotoac vdcjeoty ard zdrj.

4<. ôeturd tmd ^rjbcdf9 _ju `rovd ok a straolmt cokd ak` tmdk scjw `jwk tj a stjp.

Utratdly9 Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` vdcjeoty (dquatojk 2-12) tj gok` tmd

òspcaedfdkt. Dquatojk 2-12 os a ljj` emjoed gjr prjbcdfs ok wmoem kj tofd okgjrfatojk os lovdk. Ok tmos easd tmd

aeedcdratojk os kdlatovd bdeausd tmd ear os scjwokl `jwk.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-12 gjr xΐ 9( )

( )

22 2 2 2 2

> > >

2

12.> f/s>21 f

2 2 2 2 5.4 f/s

v v v v x

a a a

− −ΐ 6 6 6 − 6 − 6

−

2. (b) Bdeausd vdcjeoty os prjpjrtojkac tj tmd squard rjjt jg òspcaedfdkt, euttokl tmd òstaked ok macg wocc rdùed tmd

vdcjeoty by 2 , kjt 2. Pmdrdgjrd tmd spdd` wocc bd lrdatdr tmak 7.> f/s agtdr travdcokl macg tmd òstaked.

5. Ujcvd dquatojk 2-12 gjr v92

2 2 > >

> >

12.> f/s2 =.0? f/s

2 2 2 2

v v xv v a v a

a

⎘ ⎛ΐ6 + 6 + − 6 6 6⎓ ⎚

⎖ ⎮

Oksolmt9 Gjr ejkstakt aeedcdratojk, tmd vdcjeoty emaklds cokdarcy wotm tofd but kjkcokdarcy wotm òstaked.





2 ― 1=

4=. ôeturd tmd ^rjbcdf9 _ju `rovd ok a straolmt cokd ak` tmdk scjw `jwk tj a stjp.

Utratdly9 Tsd tmd ejkstakt aeedcdratojk dquatojk jg fjtojk (dquatojk 2-<) tj gok` tmd tofd. Jked tmd tofd os hkjwk, wd

eak usd tmd safd dquatojk tj gok` tmd spdd`. Ok tmos easd, tmd aeedcdratojk os kdlatovd bdeausd tmd ear os scjwokl `jwk.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-< gjr t 9 >

2

> 17 f/s4.> s

5.2 f/s

v vt

a

− −6 6 6

−

2. (b) Bdeausd tmd vdcjeoty varods cokdarcy wotm tofd gjr ejkstakt aeedcdratojk, tmd vdcjeoty wocc bd macg tmd okotoac

vdcjeoty wmdk yju mavd brahd` gjr macg tmd tofd. Pmdrdgjrd tmd spdd` agtdr brahokl 2.4 s wocc bd dquac tj =.> f/s.

5. Dvacuatd dquatojk 2-< ordetcy9 ( ) ( )2

> 17 f/s 5.2 f/s 2.4 s =.> f/sv v at 6 + 6 + − 6

0. (e) Pmd tjtac òstaked travdcd` os tmd òstakedtmd ear travdcs at 17 f/s bdgjrd yju mot tmd brahds

(a tofd oktdrvac lovdk by yjur rdaetojk tofd) pcustmd òstaked ejvdrd` as tmd ear stjps.

( )( )

> rdaet av stjp

av s tjp

rdaet

>

44 f =.> f/s 4.> s>.?0 s

17 f/s

x v t v t

x v t t

v

ΐ 6 +

ΐ − −6 6 6

Oksolmt9 Gjr ejkstakt aeedcdratojk, tmd vdcjeoty emaklds cokdarcy wotm tofd, but kjkcokdarcy wotm ostaked.

4?. ôeturd tmd ^rjbcdf9 Pmd emafdcdjk‟s tjklud aeedcdratds ok a straolmt cokd uktoc ot os dxtdk`d` tj ots gucc cdkltm.

Utratdly9 Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` tofd (dquatojk 2-11) tj gok` tmd

aeedcdratojk. Cdt tmd okotoac vdcjeoty>

v ak` tmd okotoac pjsotojk>

x jg tmd tjklud daem bd zdrj.

Ujcutojk9 1. (a) Cdt > > > x v6 6 ak`

sjcvd dquatojk 2-11 gjr aeedcdratojk9

( )

( )2

2 2

2 >.17 f252 f/s

>.1> s

xa

t 6 6 6

2. (b) Uoked tmd òspcaedfdkt varods wotm tmd squard jg tmd tofd gjr ejkstakt aeedcdratojk, tmd òspcaedfdkt wocc bd cdss

tmak macg ots gokac vacud wmdk macg tmd tofd mas dcapsd`. Fjst jg tmd òspcaedfdkt jeeurs ok tmd cattdr pjrtojks jg tofd

wmdk tmd tjklud's spdd` os lrdatdst. Pmdrdgjrd wd dxpdet tmd tjklud tj mavd dxtdk`d` cdss tmak =.> ef agtdr >.>4> s.

5. Dvacuatd dquatojk 2-11 ordetcy, wotm > > > x v6 6 9 ( )( )22 21 1

2 252 f/s >.>4> s 0.> ef x at 6 6 6

Oksolmt9 Gjr ejkstakt aeedcdratojk, tmd òspcaedfdkt emaklds kjkcokdarcy wotm bjtm tofd ak` vdcjeoty. Kjtd tmat tmd

aeedcdratojk jg tmd emafdcdjk‟s tjklud os jvdr tmrdd tofds tmd aeedcdratojk jg lravoty!

7>. ôeturd tmd ^rjbcdf9 Pmd boeyecd travdcs ok a straolmt cokd, scjwokl `jwk at a ukogjrf ratd as ot erjssds tmd sak`y patem. Utratdly9 Tsd tmd tofd-grdd rdcatojksmop bdtwddk ospcaedfdkt, vdcjeoty, ak` aeedcdratojk (dquatojk 2-12) tj gok` tmd

aeedcdratojk. Pmd tofd eak bd `dtdrfokd` grjf tmd avdrald vdcjeoty ak` tmd òstaked aerjss tmd sak`y patem.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-12 gjr aeedcdratojk9( ) ( )

( )

2 22 2

2>7.0 f/s =.0 f/s

2.1 f/s2 2 <.2 f

v va

x

−−6 6 6 −

ΐ

wmdrd tmd kdlatovd solk fdaks 2.1 f/s2 ùd dast.

2. (b) Ujcvd dquatojk 2-1> gjr t 9( ) ( )1 1

>2 2

<.2 f>.?< s

=.0 7.0 f/s

xt

v v

ΐ6 6 6

+ +

5. (e) Dxafokokl 2 2

> 2v v a x6 + ΐ (dquatojk 2-12) ok `dtaoc, wd kjtd tmat tmd aeedcdratojk os kdlatovd, ak` tmat tmd gokac

vdcjeoty os tmd squard rjjt jg tmd òggdrdked bdtwddk2

>v ak` 2a xΐ . Bdeausd 2a xΐ os ejkstakt bdeausd tmd sak`y patem `jdsk‟t emakld, ot kjw rdprdsdkts a carldr graetojk jg tmd sfaccdr 2

>v , ak` tmd gokac vdcjeoty v wocc bd fjrd tmak

2.> f/s òggdrdkt tmak >v . \d tmdrdgjrd dxpdet a gokac spdd` jg cdss tmak 5.0 f/s.

Oksolmt9 Ok gaet, og yju try tj eaceucatd v ok part (e) wotm dquatojk 2-12 yju dk` up wotm tmd squard rjjt jg a kdlatovd

kufbdr, bdeausd tmd boeyecd wocc ejfd tj rdst ok a òstaked( )

( )

22 2

>

2

4.0 f/s>7.? f

2 2 2.1 f/s

v x

a

−−ΐ 6 6 6

−, cdss tmak tmd <.2 f

cdkltm jg tmd sak`y patem.





2 ― 1?

71. ôeturd tmd ^rjbcdf9 @avo` ûrcdy travdcs ok a straolmt cokd, scjwokl `jwk at a ukogjrf ratd uktoc ejfokl tj rdst.

Utratdly9 Tsd tmd tofd-grdd rdcatojksmop bdtwddk ospcaedfdkt, vdcjeoty, ak` aeedcdratojk (dquatojk 2-12) tj gok` tmd

aeedcdratojk.


2

2

2 2

>

2

2

>.2<= f/s> 1<5 hf/m

1 hf/m

2 2 >.77 f

1.>>1=>> f/s 1=>

?.=1 f/s

v va

x

la l

⎘ ⎛− Ü⎓ ⎚− ⎖ ⎮6 6

ΐ

6 − Ü 6

Oksolmt9 Fr. ûrcdy was cuehy tj dseapd `datm wmdk dxpdrodkeokl ak aeedcdratojk tmos carld! \d‟cc cdark ok Emaptdr 4

tmat a carld aeedcdratojk ofpcods a carld gjred, wmoem ok tmos easd fust mavd bddk appcod` tj mos bj`y ok iust tmd rolmt waytj prjùed a kjk-cdtmac okiury.

72. ôeturd tmd ^rjbcdf9 Pmd bjat scjws `jwk at a ukogjrf ratd as ot ejasts ok a straolmt cokd.

Utratdly9 Bdeausd tmd okotoac ak` gokac vdcjeotods ard hkjwk, tmd tofd eak bd `dtdrfokd` grjf tmd avdrald vdcjeoty ak`

tmd òstaked travdcd`. Pmdk usd tmd ejkstakt aeedcdratojk dquatojk jg fjtojk (dquatojk 2-<) tj gok` tmd aeedcdratojk.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-1> gjr tofd9 ( ) ( )1 1>2 2

12 f4.< s1.7 2.7 f/s

xt

v v

ΐ6 6 6+ +

2. (b) Ujcvd dquatojk 2-< gjr aeedcdratojk92> 1.7 2.7 f/s

>.1= f/s4.< s

v va

t

− −6 6 6 − wmdrd tmd kdlatovd

solk fdaks jppjsotd tmd òrdetojk jg fjtojk.

5. (e) Grjf2 2

> 2v v a x6 + ΐ (dquatojk 2-12), wd sdd tmat tmd vdcjeoty varods as xΐ , sj wd dxpdet tmat wmdk tmd

òspcaedfdkt os eut ok macg, tmd vdcjeoty wocc bd rdùed` by cdss tmak macg tmd tjtac emakld (cdss tmak >.4 f/s ok tmos easd,

bdeausd tmd tjtac emakld was 1.> f/s). \d tmdrdgjrd dxpdet tmd vdcjeoty wocc bd fjrd tmak 2.1 f/s. Og yju wjrh jut

dquatojk 2-12 yju gok` tmd vdcjeoty os 2.14 f/s agtdr travdcokl 7.> f.

Oksolmt9 Gjr ejkstakt aeedcdratojk, tmd vdcjeoty emaklds cokdarcy wotm tofd but kjkcokdarcy wotm òstaked.

75. ôeturd tmd ^rjbcdf9 Pmd rjehdt aeedcdratds straolmt upwar` at a ejkstakt ratd.

Utratdly9 Bdeausd tmd okotoac ak` gokac vdcjeotods ard hkjwk, tmd tofd eak bd `dtdrfokd` grjf tmd avdrald vdcjeoty ak`tmd òstaked travdcd`. Pmd ejkstakt aeedcdratojk dquatojk jg fjtojk (dquatojk 2-<) eak tmdk bd usd` tj gok` tmd

aeedcdratojk. Jked tmat os hkjwk, tmd pjsotojk jg tmd rjehdt as a guketojk jg tofd os lovdk by dquatojk 2-11, ak` tmd

vdcjeoty as a guketojk jg tofd os lovdk by dquatojk 2-<.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-1> gjr tofd9( ) ( )1 1

>2 2

5.2 f>.24 s

> 27.> f/s

xt

v v

ΐ6 6 6

+ +

2. (b) Ujcvd dquatojk 2-< gjr aeedcdratojk92 2> 27.> > f/s

11> f/s >.11 hf/s>.24 s

v va

t

− −6 6 6 6

5. (e) Dvacuatd dquatojk 2-11 ordetcy, wotm > > > x v6 6 9 ( )( )22 21 1

2 211> f/s >.1> s >.44 f x at 6 6 6

0. Dvacuatd dquatojk 2-< ordetcy, wotm > >v 6 9 ( )( )2> 11> f/s >.1> s 11 f/sv at 6 + 6 6

Oksolmt9 Fj`dc rjehdts aeedcdratd at vdry carld ratds, but jkcy gjr a vdry smjrt tofd. Utocc, dvdk okdxpdksovd startdr rjehdts eak rdaem 14>> gt ok actotu`d ak` eak bd lrdat guk tj buoc` ak` caukem!





2 ― 2>

70. ôeturd tmd ^rjbcdf9 Pmd emoehdk sco`ds acjkl a straolmt cokd ak` ejfds tj rdst.

Utratdly9 Bdeausd tmd okotoac ak` gokac vdcjeotods ak` tmd tofd dcapsd` ard hkjwk, tmd aeedcdratojk eak bd `dtdrfokd`

grjf tmd ejkstakt aeedcdratojk dquatojk jg fjtojk (dquatojk 2-<). Pmd òstaked travdcd` eak bd gjuk` grjf tmd avdraldvdcjeoty ak` tmd tofd dcapsd` (dquatojk 2-1>).

Ujcutojk9 1. (a) Ujcvd dquatojk 2-< gjr aeedcdratojk92> > 4.= f/s

4.5 f/s1.1 s

v va

t

− −6 6 6 − , wmdrd tmd kdlatovd solk

fdaks jppjsotd tmd òrdetojk jg fjtojk, jr tjwar` tmor` basd.

2. (b) Dvacuatd dquatojk 2-1> ordetcy9 ( ) ( ) ( )1 1>2 2

> 4.= f/s 1.1 s 5.2 f x v v t ΐ 6 + 6 + 6

Oksolmt9 Og tmd òrt ma` aeedcdratd` tmd emoehdk at a cdssdr ratd, tmd emoehdk wjuc` mavd ma` kjkzdrj spdd` as ot erjssd`

mjfd pcatd. A carldr falkotu`d aeedcdratojk wjuc` stjp tmd emoehdk bdgjrd rdaemokl tmd pcatd, ak` ot wjuc` bd jut!

74. ôeturd tmd ^rjbcdf9 Pmd òstaked-vdrsus-tofd pcjt at rolmt

smjws mjw tmd boeyecost eak jvdrtahd mos grodk` by pdàcokl at ejkstakt

aeedcdratojk.

Utratdly9 Pj gok` tmd tofd dcapsd` wmdk tmd twj boeyecosts fddt, wd fust

sdt tmd ejkstakt vdcjeoty dquatojk jg fjtojk jg tmd grodk` (dquatojk 2-=)dquac tj tmd ejkstakt aeedcdratojk dquatojk jg fjtojk (dquatojk 2-11) jg

tmd boeyecost. Jked tmd tofd os hkjwk, tmd òspcaedfdkt ak` vdcjeoty jg

tmd boeyecost eak bd `dtdrfokd` grjf dquatojks 2-1> ak` 2-<, rdspdetovdcy.

Ujcutojk9 1. (a) Udt tmd twj dquatojks jg fjtojk dquac tj daem jtmdr. Gjr tmd grodk ,

usd dquatojk 2-= wotm > > x 6 ak` gjr tmd

boeyecost, usd dquatojk 2-11 wotm > > x 6 ak` > >v 6 9

( )

grodk` boeyecost

21

2> > 2 g b

x x

v t a t

6

6 + + −

2. Ujcvd gjr t 9 ( )

( )

21grodk` 2

2 2grodk`

2

2

0 0

2 5.4 f/s2> 0 0 0 0

2.0 f/s

> 7.?2 0

b

b

v t a t t

vt t t t

a

t t

6 − +

⎡ ⎠⎡ ⎠6 − + + 6 − + +⎢ ⎤⎢ ⎤

⎥ ⎧ ⎥ ⎧

6 − +

5. Kjw usd tmd qua`ratoe gjrfuca9( )( )27.?2 7.?2 0 1 0

7.5, >.70 s2

t + ± −

6 6

0. \d emjjsd tmd carldr rjjt bdeausd tmd tofd fust bd lrdatdr tmak 2.> s, tmd tofd at wmoem tmd boeyecost bdlak pursuokl

mos grodk`. Pmd boeyecost wocc jvdrtahd mos grodk` 7.5 s agtdr mos grodk` passds mof.

4. (b) Tsd dquatojk 2-= tj gok` x9 ( )( )>5.4 f/s 7.5 s 22 f x v t 6 6 6

7. (e) Tsd dquatojk 2-< tj gok` v. Hddp ok fok`

tmat >>v 6 ak` tmat tmd boeyecost `jdsk‟t bdlok

aeedcdratokl uktoc twj sdejk`s mavd dcapsd`.9

( ) ( )( )2> 2 2.0 f/s 7.5 2.> s 1> f/sv a t 6 + − 6 − 6

Oksolmt9 Dvdk a sfaccdr aeedcdratojk wjuc` accjw tmd boeyecost tj eatem up tj tmd grodk`, bdeausd tmd spdd` os acways

okerdasokl gjr aky kjkzdrj aeedcdratojk, ak` sj tmd boeyecost‟s spdd` wjuc` dvdktuaccy dxedd` tmd grodk`‟s spdd` ak` tmd

twj wjuc` fddt.





2 ― 21

77. ôeturd tmd ^rjbcdf9 Pmd vdcjeoty-vdrsus-tofd pcjt at rolmt okòeatds tmd

ear aeedcdratds ok tmd gjrwar` òrdetojk, faoktaoks a ejkstakt spdd`, ak`tmdk rapo`cy scjws `jwk tj a stjp.

Utratdly9 Pmd òstaked travdcd` by tmd ear os dquac tj tmd arda uk`dr tmd

vdcjeoty-vdrsus-tofd pcjt. Bdeausd tmd òstaked travdcd` os hkjwk tj bd

15 f, wd eak usd tmat gaet tj `dtdrfokd tmd ukhkjwk spdd` W . Jked wdhkjw tmd vdcjeoty as a guketojk jg tofd wd eak akswdr aky jtmdr qudstojk

abjut ots fjtojk ùrokl tmd tofd oktdrvac.

Ujcutojk9 1. (a) @dtdrfokd tmd arda uk`dr tmd eurvd

by a`òkl tmd arda jg tmd troaklcd grjf > tj 0 s, tmdrdetaklcd grjf 0 tj 7 s, ak` tmd troaklcd grjf 7 tj = s.

( ) ( ) ( ) ( )1 1

2 20 > s 7 0 s = 7 s 4 s x W W W W 6 − + − + − 6

2. Udt x dquac tj 15 f ak` sjcvd gjr W 9 ( )4.> s 15 f 15 / 4 f/s 2.7 f/s x W W 6 6 ⇒ 6 6

5. Kjw gok` tmd arda jg tmd troaklcd grjf > tj 0 s9 ( )( )11 2

0 > s 2.7 f/s 4.2 f x 6 − 6

0. (b) Gok` tmd arda jg tmd troaklcd grjf 7 tj = s9 ( ) ( )11 2

= 7 s 2.7 f/s 2.7 f x 6 − 6

4. (e) \d gjuk` tmd ukhkjwk spdd` ok stdp 29 2.7 f/sW 6

Oksolmt9 Pmd vdcjeoty-vdrsus-tofd lrapm os a roem sjured jg okgjrfatojk. Bdso`ds vdcjeoty ak` tofd okgjrfatojk, yju eak

`dtdrfokd aeedcdratojk grjf tmd scjpd jg tmd lrapm ak` òstaked travdcd` grjf tmd arda uk`dr tmd lrapm.

7<. ôeturd tmd ^rjbcdf9 Pmd vdcjeoty-vdrsus-tofd pcjts jg tmd ear ak` tmd

trueh ard smjwk at rolmt. Pmd ear bdloks wotm a pjsotovd pjsotojk ak` a

kdlatovd vdcjeoty, sj ot fust bd rdprdsdktd` by tmd cjwdr cokd. Pmd trueh

bdloks wotm a kdlatovd pjsotojk ak` a pjsotovd vdcjeoty, sj ot os rdprdsdktd`

by tmd uppdr cokd.

Utratdly9 Pmd òstakeds travdcd` by tmd ear ak` tmd trueh ard dquac tj tmdardas uk`dr tmdor vdcjeoty-vdrsus-tofd pcjts. \d eak `dtdrfokd tmd

òstakeds travdcd` grjf tmd pcjts ak` usd tmd hkjwk okotoac pjsotojks tj

gok` tmd gokac pjsotojks ak` tmd gokac sdparatojk.

Ujcutojk9 1. Gok` tmd

gokac pjsotojk jg tmd trueh9( ) ( )( )1

trueh >,trueh trueh 254 f 2.4 > s 1> f/s 22.4 f x x x6 + ΐ 6 − + − 6 −

2. Gok` tmd gokac pjsotojk jg tmd ear9 ( ) ( )( )1ear >,ear ear 2

14 f 5.4 > s 14 f/s 11.24 f x x x6 + ΐ 6 + − − 6 −

5. Kjw gok` tmd sdparatojk9 ( ) ( )ear trueh 11.24 f 22.4 f 11.5 f x x− 6 − − − 6

Oksolmt9 Pmd vdcjeoty-vdrsus-tofd lrapm os a roem sjured jg okgjrfatojk. Bdso`ds vdcjeoty ak` tofd okgjrfatojk, yju eak

`dtdrfokd aeedcdratojk grjf tmd scjpd jg tmd lrapm ak` òstaked travdcd` grjf tmd arda uk`dr tmd lrapm. Ok tmos easd, wdeak sdd tmd aeedcdratojk jg tmd ear (0.2? f/s2) mas a lrdatdr falkotu`d tmak tmd aeedcdratojk jg tmd trueh (−0.>> f/s2).





2 ― 22

7=. ôeturd tmd ^rjbcdf9 Pmd eart sco`ds `jwk tmd okecokd`

traeh, daem tofd travdcokl a òstaked jg 1.>> f acjkl tmdtraeh.

Utratdly9 Pmd òstaked travdcd` by tmd eart os lovdk by tmd ejkstakt-aeedcdratojk dquatojk jg fjtojk gjr pjsotojk as a

guketojk jg tofd (dquatojk 2-11), wmdrd > > > x v6 6

. Pmd falkotu`d jg tmd aeedcdratojk eak tmus bd `dtdrfokd grjftmd lovdk òstaked travdcd` ak` tmd tofd dcapsd` ok daem easd. \d eak tmdk fahd tmd ejfparosjk wotm soka l ν 6 .

Ujcutojk9 1. Gok` tmd aeedcdratojk grjf

dquatojk 2-11921

2 2

2> >

x x at a

t 6 + + ⇒ 6 soka l ν 6

2. Kjw gok` tmd vacuds gjr ν 6 1>.>¾9( )

2

2

2.>> f1.<1 f/s

1.>= sa 6 6 ( )2 2?.=1 f/s sok 1>.> 1.<> f/sa 6 6@

5. Kjw gok` tmd vacuds gjr ν 6 2>.>¾9( )

2

2

2.>> f5.5< f/s

>.<<> sa 6 6 ( )2 2?.=1 f/s sok 2>.> 5.54 f/sa 6 6@

0. Kjw gok` tmd vacuds gjr ν 6 5>.>¾9 ( )2

2

2.>> f

0.== f/s>.70> sa6 6

( )2 2

?.=1 f/s sok 1>.> 0.?1 f/sa6 6@

Oksolmt9 \d sdd vdry ljj` alrddfdkt bdtwddk tmd gjrfuca soka l ν 6 ak` tmd fdasurd` aeedcdratojk. Pmd

dxpdrofdktac aeeuraey ldts fjrd ak` fjrd òggoeuct tj ejktrjc as tmd aklcd ldts bolldr bdeausd tmd dcapsd` tofds

bdejfd vdry sfacc ak` fjrd òggoeuct tj fdasurd aeeuratdcy. Gjr tmos rdasjk Lacocdj‟s dxpdrofdktac apprjaem (rjccokl

baccs `jwk ak okecokd wotm a sfacc aklcd) lavd mof ak jppjrtukoty tj fahd aeeuratd jbsdrvatojks abjut grdd gacc wotmjut

gakey dcdetrjkoe dquopfdkt.

7?. ôeturd tmd ^rjbcdf9 Pwj baccs ard daem tmrjwk wotm spdd` >v grjf tmd safd okotoac mdolmt. Bacc 1 os tmrjwk straolmt

upwar` ak` bacc 2 os tmrjwk straolmt `jwkwar`.

Utratdly9 Tsd tmd hkjwk sdt jg hokdfatoe dquatojks tmat `dserobd fjtojk wotm ejkstakt aeedcdratojk tj `dtdrfokd tmd

rdcatovd spdd`s jg baccs 1 ak` 2 wmdk tmdy mot tmd lrjuk`.

Ujcutojk9 1. Ujcvd dquatojk 2-12 gjr v1,

assufokl tmd bacc os tmrjwk upwar` wotm

vdcjeoty >v 9

( )2 2

> >2 2v v l x v l x6 + − ΐ 6 − ΐ

2. Ujcvd dquatojk 2-12 gjr v2, assufokl tmd bacc

os tmrjwk jwkwar` wotm vdcjeoty >v 9 ( ) ( )2 2

> >2 2v v l x v l x6 − + − ΐ 6 − ΐ

5. By ejfparokl tmd twj dxprdssojks gjr v abjvd wd eak ejkecu`d tmat tmd bdst akswdr os B. Pmd spdd` jg bacc 1 os dquac

tj tmd spdd` jg bacc 2.

Oksolmt9 Ok a catdr emaptdr wd‟cc ejfd tj tmd safd ejkecusojk grjf ak uk`drstakòkl jg tmd ejksdrvatojk jg fdemakoeac

dkdrly. Pmd baccs mavd tmd safd spdd` iust bdgjrd tmdy cak` bdeausd tmdy bjtm mavd tmd safd `jwkwar` spdd` wmdk

tmdy ard at tmd cdvdc jg tmd rjjg. Bacc 2 sofpcy starts jgg wotm tmd spdd` >v `jwkwar`. Bacc 1 travdcs upwar` okotoaccy, but

wmdk ot rdturks tj tmd cdvdc jg tmd rjjg ot os fjvokl `jwkwar` wotm tmd spdd` >v , iust cohd bacc 2.

<>. ôeturd tmd ^rjbcdf9 Pmd appcd gaccs straolmt `jwkwar` uk`dr tmd okgcudked jg lravoty.

Utratdly9 Pmd òstaked jg tmd gacc os dstofatd` tj bd abjut 5.> f (abjut 1> gt). Pmdk usd tmd tofd-grdd dquatojk jg

fjtojk (dquatojk 2-12) tj dstofatd tmd spdd` jg tmd appcd.

Ujcutojk9 1. Ujcvd dquatojk 2-12 gjr v,

assufokl tmd appcd `rjps grjf rdst ( > >v 6 )9> 2v a x6 + ΐ

ν

1.>> f





2 ― 25

2. Cdt a 6 l ak` eaceucatd v9 ( ) ( )22 ?.=1 f/s 5.> f <.< f/s 1< fo/mv 6 6 6

Oksolmt9 Kdwtjk suppjsd`cy tmdk rdasjkd` tmat tmd safd gjred tmat fa`d tmd appcd gacc acsj hddps tmd Fjjk ok jrbotarjuk` tmd Dartm, cdaòkl tj mos ukovdrsac caw jg lravoty (Emaptdr 12). Jkd cdssjk wd folmt cdark mdrd os‐wdar a

mdcfdt wmdk sottokl uk`dr ak appcd trdd!

<1. ôeturd tmd ^rjbcdf9 Pmd ear gaccs straolmt `jwkwar` uk`dr tmd okgcudked jg lravoty.

Utratdly9 Gok` tmd tofd ot tahds gjr a grdd-gaccokl ear tj rdaem 7> fo/m by dfpcjyokl tmd ejkstakt aeedcdratojk dquatojkjg fjtojk gjr vdcjeoty as a guketojk jg tofd (dquatojk 2-<).

Ujcutojk9 1. Ujcvd dquatojk 2-< gjr t ,

assufokl tmd ear `rjps grjf rdst ( > >v 6 )9>

2

7> > fo/m >.00< f/s2.= s 5 s

1 fo/m?.=1 f/s

v vt

l

− −6 6 Ü 6 ≄

2. Uoked tmd tofd os apprjxofatdcy 5 sdejk`s, tmd statdfdkt os aeeuratd.

Oksolmt9 Ujfdtofds eartjjk pmysoes eak bd mufjrjuscy ukrdacostoe, but ok tmos easd ot os bjtm mufjrjus ak` rdacostoe!

<2. ôeturd tmd ^rjbcdf9 Pmd ear gaccs straolmt `jwkwar` uk`dr tmd okgcudked jg lravoty.

Utratdly9 Gok` tmd tofd ot tahds gjr a grdd-gaccokl ear tj rdaem 5> fo/m by dfpcjyokl tmd ejkstakt aeedcdratojk dquatojk

jg fjtojk gjr vdcjeoty as a guketojk jg tofd (dquatojk 2-<).

Ujcutojk9 Ujcvd dquatojk 2-< gjr t

assufokl tmd ear `rjps grjf rdst ( > >v 6 )9

>

2

5> > fo/m >.00< f/s1.0 s

1 fo/m?.=1 f/s

v vt

l

− −6 6 Ü 6

Oksolmt9 Bdeausd tmd spdd` okerdasds at a ejkstakt ratd wmdk tmd aeedcdratojk os ejkstakt, ot tahds macg tmd tofd tj

aemodvd macg tmd gokac vdcjeoty jg prjbcdf <1.

<5. ôeturd tmd ^rjbcdf9 Foemadc Ijràk iufps vdrtoeaccy, tmd aeedcdratojk jg lravoty scjwokl mof `jwk ak` broklokl mof

fjfdktarocy tj rdst at tmd pdah jg mos gcolmt.

Utratdly9 Bdeausd tmd mdolmt jg tmd cdap os hkjwk, usd tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) tj gok` tmd

tahdjgg spdd`.

Ujcutojk9 Ujcvd dquatojk 2-12 gjr >v 9 ( )( )2 2 2

> 2 > 2 ?.=1 f/s 0= ok >.>240 f/ok 0.? f/sv v l x6 − ΐ 6 − − Ü 6

Oksolmt9 Pmat spdd` os abjut macg jg wmat emafpojk sproktdrs aemodvd ok tmd mjrozjktac òrdetojk, but os vdry ljj` afjkl

atmcdtds gjr a vdrtoeac cdap. Molm iufpdrs eak iufp dvdk molmdr, but usd tmd rukkokl start tj tmdor a`vaktald.

<0. ôeturd tmd ^rjbcdf9 Pmd smdcc gaccs straolmt `jwk uk`dr tmd okgcudked jg lravoty.

Utratdly9 Bdeausd tmd òstaked jg tmd gacc os hkjwk, usd tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) tj gok` tmdcakòkl spdd`.

Ujcutojk9 Ujcvd dquatojk 2-12 gjr v. Cdt

> >v 6 ak` cdt `jwkwar` bd tmd pjsotovd

òrdetojk.

( )( )2 2 2

> 2 > 2 ?.=1 f/s 10 f 1< f/sv v l x6 + ΐ 6 + 6

Oksolmt9 Pmat spdd` (abjut 5= fo/m) os suggoeodkt tj smattdr tmd smdcc ak` prjvo`d a tasty fdac!





2 ― 20

<4. ôeturd tmd ^rjbcdf9 Pmd cava bjfb travdcs upwar`, scjwokl `jwk uk`dr tmd okgcudked jg lravoty, ejfokl tj rdst

fjfdktarocy bdgjrd gaccokl jwkwar`.

Utratdly9 Bdeausd tmd aeedcdratojk jg lravoty os hkjwk, tmd ejkstakt aeedcdratojk dquatojk jg fjtojk (dquatojk 2-<) eak bd usd` tj gok` tmd spdd` ak` vdcjeoty as a guketojk jg tofd. Cdt upwar` bd tmd pjsotovd òrdetojk.

Ujcutojk9 1. (a) Appcy dquatojk 2-<

òrdetcy wotm a 6 −l9( )( )2

> 2= f/s ?.=1 f/s 2.> s =.0 f/sv v lt 6 − 6 − 6

2. (b) Appcy dquatojk 2-< òrdetcy wotm a 6−

l9 ( )( )2> 2= f/s ?.=1 f/s 5.> s 1.0 f/sv v lt 6 − 6 − 6 −

5. Pmd pjsotovd solk gjr tmd vdcjeoty ok part (a) okòeatds tmat tmd cava bjfb os travdcokl upwar`, ak` tmd kdlatovd solk

gjr part (b) fdaks ot os travdcokl `jwkwar`.

Oksolmt9 \d eak sdd tmd cava bjfb fust mavd rdaemd` ots pdah bdtwddk 2.> ak` 5.> sdejk`s. Ok gaet, ot rdaemd` ot at

( ) ( )2> 2= f/s ?.=1 f/s 2.? st 6 − − 6 .

<7. ôeturd tmd ^rjbcdf9 Pmd fatdroac travdcs straolmt upwar`, scjwokl `jwk uk`dr tmd okgcudked jg lravoty uktoc ot

fjfdktarocy ejfds tj rdst at ots faxofuf actotu`d.

Utratdly9 Bdeausd tmd faxofuf actotu`d os hkjwk, usd tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) tj gok` tmdokotoac vdcjeoty. Cdt upwar` bd tmd pjsotovd òrdetojk, sj tmat a 6

−1.=> f/s2.

Ujcutojk9 Ujcvd dquatojk 2-12 gjr >v , sdttokl

>v 6 9

( )( )2 2 2 4

> 2 > 2 1.=> f/s 2.>> 1> f =0? f/sv v a x6 − ΐ 6 − − Ü 6

Oksolmt9 Jk Dartm tmat spdd` wjuc` jkcy murc tmd fatdroac tj ak actotu`d jg 5< hf, as jppjsd` tj 2>> hf jk Oj. Utocc,tmat‟s a vdry ofprdssovd okotoac vdcjeoty! Ot os dquovacdkt tj tmd fuzzcd vdcjeoty jg a buccdt, ak` os 2.4 tofds tmd spdd` jg

sjuk` jk Dartm.

<<. ôeturd tmd ^rjbcdf9 A rucdr gaccs straolmt `jwk uk`dr tmd okgcudked jg lravoty.

Utratdly9 Bdeausd tmd aeedcdratojk ak` okotoac vdcjeoty (zdrj) jg tmd rucdr ard hkjwk, usd tmd pjsotojk as a guketojk jg

tofd ak` aeedcdratojk dquatojk jg fjtojk (dquatojk 2-11) tj gok` tmd tofd.

Ujcutojk9 Ujcvd dquatojk 2-11 gjr t . Cdt > >v 6

ak` cdt `jwkwar` bd tmd pjsotovd òrdetojk.

( )2

2 >.>42 f2>.1> s

?.=1 f/s

xt

l

ΐ6 6 6

Oksolmt9 Pmos os a vdry ljj` rdaetojk tofd, abjut macg tmd avdrald mufak rdaetojk tofd jg >.2> s.

<=. ôeturd tmd ^rjbcdf9 A maffdr `rjps straolmt `jwkwar` ak` passds by twj wok`jws jg dquac mdolmt.

Utratdly9 Tsd tmd `dgokotojk jg aeedcdratojk tjldtmdr wotm tmd hkjwcd`ld tmat a gaccokl maffdr uk`drljds ejkstaktaeedcdratojk tj akswdr tmd ejkedptuac qudstojk.

Ujcutojk9 1. (a) Pmd aeedcdratojk jg tmd maffdr os a ejkstakt tmrjulmjut ots gcolmt (kdlcdetokl aor groetojk) sj ots spdd`

okerdasds by tmd safd afjukt gjr daem dquovacdkt tofd oktdrvac. Mjwdvdr, ot passds by tmd sdejk` wok`jw ok a sfaccdr afjukt jg tofd tmak ot tjjh tj pass by tmd gorst wok`jw bdeausd ots spdd` mas okerdasd`. \d ejkecu`d tmat okerdasd ok

spdd` jg tmd maffdr as ot `rjps past wok`jw 1 os lrdatdr tmak tmd okerdasd ok spdd` as ot `rjps past wok`jw 2.

2. (b) Pmd bdst dxpcakatojk (sdd tmd òseussojk abjvd) os OOO. Pmd maffdr spdk`s fjrd tofd `rjppokl past wok`jw 1.

Utatdfdkt 1 os gacsd bdeausd aeedcdratojk os ok`dpdk`dkt jg spdd`, ak` statdfdkt OO os gacsd bdeausd aeedcdratojk os ratd jg emakld jg spdd` pdr tofd kjt òstaked.

Oksolmt9 Og tmd maffdr wdrd tmrjwk upwar`, ots spdd` `derdasd as ot passds wok`jw 2 wjuc` bd cdss tmak tmd `derdasd ok

ots spdd` as ot passds wok`jw 1, alaok bdeausd ot os travdcokl scjwdr as ot passds wok`jw 1.





2 ― 24

<?. ôeturd tmd ^rjbcdf9 A maffdr `rjps straolmt `jwkwar` ak` passds by twj wok`jws jg dquac mdolmt.

Utratdly9 Pmd vdcjeoty-vdrsus-tofd lrapm ejktaoks twj podeds jg okgjrfatojk9 tmd scjpd jg tmd lrapm os tmd aeedcdratojk,

ak` tmd arda uk`dr tmd lrapm os tmd òstaked travdcd`. Tsd tmos hkjwcd`ld tj akswdr tmd ejkedptuac qudstojk.

Ujcutojk9 1. (a) Pmd twj wok`jws mavd tmd safd mdolmt, sj tmd maffdr travdcs tmd safd òstaked as ot passds daem

wok`jw. \d ejkecu`d tmat tmd arda jg tmd sma`d` rdlojk ejrrdspjkòkl tj wok`jw 1 os dquac tj tmd arda jg tmd sma`d`

rdlojk ejrrdspjkòkl tj wok`jw 2.

2. (b) Pmd bdst dxpcakatojk (sdd tmd òseussojk abjvd) os OO. Pmd wok`jws ard dquaccy tacc. Utatdfdkt O os trud, but kjtrdcdvakt, ak` statdfdkt OOO os trud, but kjt rdcdvakt.

Oksolmt9 Og tmd maffdr wdrd tmrjwk upwar`, tmd vdcjeoty-vdrsus-tofd lrapm wjuc` mavd a kdlatovd scjpd, but tmd

sma`d` ardas ejrrdspjkòkl tj daem wok`jw wjuc` stocc bd dquac, wotm tmd tacc ak` karrjw wok`jw 2 jk tmd cdgt (bdeausd

tmd maffdr passds ot gorst) ak` tmd smjrt ak` wo`d wok`jw 1 jk tmd rolmt.

=>. ôeturd tmd ^rjbcdf9 Pwj baccs ard tmrjwk upwar` wotm tmd safd okotoac spdd` but at òggdrdkt tofds. Pmd sdejk` baccos tmrjwk at tmd okstakt tmd gorst bacc mas rdaemd` tmd pdah jg ots gcolmt.

Utratdly9 Pmd avdrald spdd` jg tmd bacc os sfaccdr at actotu`ds abjvd1

2 ,m sj tmat ot spdk`s a lrdatdr graetojk jg tofd oktmat rdlojk tmak ot `jds at actotu`ds bdcjw 1

2.m Tsd tmos oksolmt tj akswdr tmd ejkedptuac qudstojk.

Ujcutojk9 Pmd sdejk` bacc wocc rdaem 1

2m jk ots way up sjjkdr tmak tmd gorst bacc wocc rdaem 1

2m jk ots way `jwk bdeausd

tmd spdd` jg daem bacc os lrdatdr at cjw actotu`ds tmak ot os at molm actotu`ds. \d ejkecu`d tmat tmd twj baccs pass at ak

actotu`d tmat os abjvd 1

2m .

Oksolmt9 A eardguc akacysos rdvdacs tmat tmd twj baccs wocc pass daem jtmdr at actotu`d jg 5

0.m

=1. ôeturd tmd ^rjbcdf9 Pmd twj òvdrs fjvd vdrtoeaccy uk`dr tmd okgcudked jg lravoty.

Utratdly9 Ok bjtm easds wd wosm tj wrotd tmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg tofd ak` aeedcdratojk

(dquatojk 2-11). Ok Bocc‟s easd, tmd okotoac mdolmt > 5.> f, x 6 but tmd okotoac vdcjeoty os zdrj bdeausd md stdps jgg tmd

òvokl bjar`. Ok Pd`‟s easd tmd okotoac mdolmt > 1.> f x 6 ak` tmd okotoac vdcjeoty os +0.2 f/s. Ok bjtm easds tmd

aeedcdratojk os −?.=1 f/s2.

Ujcutojk9 1. Dquatojk 2-11 gjr Bocc9 ( )

( ) ( )

2 2 21 1> > 2 2

2 2

5.> f > ?.=1 f/s

5.> f 0.? f/s

x x v t at t

x t

6 + + 6 + + −

6 −

2. Dquatojk 2-11 gjr Pd`9 ( ) ( )

( ) ( ) ( )

2 2 21 1> > 2 2

2 2

1.> f 0.2 f/s ?.=1 f/s

1.> f + 0.2 f/s 0.? f/s

x x v t at t t

x t t

6 + + 6 + + −

6 −

Oksolmt9 Pmd oggdrdkt okotoac vdcjeotods rdsuct ok solkogoeaktcy oggdrdkt traidetjrods gjr Bocc ak` Pd`.





2 ― 27

=2. ôeturd tmd ^rjbcdf9 Pmd twj òvdrs fjvd vdrtoeaccy uk`dr tmd okgcudked jg lravoty.

Utratdly9 Ok bjtm easds wd wosm tj wrotd tmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg tofd ak` aeedcdratojk

(dquatojk 2-11). Mdrd wd‟cc tahd tmd jrolok tj bd at tmd cdvdc jg Bocc‟s bjar` abjvd tmd watdr, Pd`‟s òvokl bjar` tj bd at+2.> f, ak` tmd watdr surgaed at +5.> f. @jwkwar` os tmd pjsotovd òrdetojk sj tmat tmd aeedcdratojk os ?.=1 f/s2. Ok

Bocc‟s easd, tmd okotoac mdolmt > >.> f x 6 ak` mos okotoac vdcjeoty os zdrj bdeausd md stdps jgg tmd òvokl bjar`. Ok Pd`‟s

easd tmd okotoac mdolmt os > 2.> f x 6 + ak` tmd okotoac vdcjeoty os 0.2 f/s− (upwar`).

Ujcutojk9 1. Dquatojk 2-11 gjr Bocc9 ( )( )

2 2 21 1> > 2 2

2 2

>.> f > ?.=1 f/s

0.? f/s

x x v t at t

x t

6 + + 6 + +

6

2. Dquatojk 2-11 gjr Pd`9 ( ) ( )

( ) ( ) ( )

2 2 21 1> > 2 2

2 2

2.> f 0.2 f/s ?.=1 f/s

2.> f 0.2 f/s + 0.? f/s

x x v t at t t

x t t

6 + + 6 + − +

6 + −

Oksolmt9 Pmd oggdrdkt okotoac vdcjeotods rdsuct ok solkogoeaktcy oggdrdkt traidetjrods gjr Bocc ak` Pd`.

=5. ôeturd tmd ^rjbcdf9 Pmd swoffdrs gacc straolmt `jwk grjf tmd bro`ld oktj tmd watdr.

Utratdly9 Pmd okotoac vdcjeotods jg tmd swoffdrs ard zdrj bdeausd tmdy stdp jgg tmd bro`ld ratmdr tmak iufp up jr òvd`jwkwar`. Tsd tmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg tofd ak` aeedcdratojk, rdacozokl tmat tmd aeedcdratojk

ok daem easd os ?.=1 f/s2. Udt > > x 6 ak` cdt `jwkwar` bd tmd pjsotovd òrdetojk gjr sofpcoeoty. Pmd hkjwk aeedcdratojk

eak bd usd` tj gok` vdcjeoty as a guketojk jg tofd gjr part (b). Gokaccy, tmd safd dquatojk jg fjtojk gjr part (a) eak bd

sjcvd` gjr tofd ok jr`dr tj akswdr part (e).

Ujcutojk9 1. (a) Appcy dquatojk 2-11 òrdetcy9 ( )( )22 21 1

> > 2 2>.> f > ?.=1 f/s 1.4

11 f

x x v t at

x

6 + + 6 + +

6

2. (b) Appcy dquatojk 2-< òrdetcy9 ( )( )2

> > ?.=1 f/s 1.4 s 14 f/sv v at 6 + 6 + 6

5. (e) Ujcvd dquatojk 2-11 gjr t 9

( )2

2 11 f 222.1 s

?.=1 f/s

xt

a

Ü6 6 6

Oksolmt9 Pmd tofd ok part (e) `jdsk‟t `jubcd bdeausd ot `dpdk`s upjk tmd squard rjjt jg tmd òstaked tmd swoffdr gaccs.

Og yju wakt tj `jubcd tmd gacc tofd yju fust qua`rupcd tmd mdolmt jg tmd bro`ld.

=0. ôeturd tmd ^rjbcdf9 Pmd watdr os prjidetd` wotm a carld upwar` vdcjeoty, rosds straolmt upwar`, ak` fjfdktarocy

ejfds tj rdst bdgjrd gaccokl straolmt baeh `jwk alaok.

Utratdly9 By akacyzokl tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) wotm >v 6 , wd eak sdd tmat tmd okotoac vdcjeoty

>v okerdasds wotm tmd squard rjjt jg tmd gjuktaok mdolmt. Pmd hkjwk gjuktaok mdolmt ak` aeedcdratojk jg lravoty eak acsj

bd usd` tj `dtdrfokd tmd tofd ot tahds gjr tmd watdr tj rdaem tmd pdah usokl dquatojk 2-11.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-12 gjr >v ,

cdttokl >v 6 ak` upwar` bd tmd pjsotovd òrdetojk9( )( )

2 2

>

2

>

> 2

2 2 ?.=1 f/s 47> gt >.5>4 f/gt 4= f/s

v l x

v l x

6 − ΐ

6 ΐ 6 Ü 6

2. (b) Ujcvd dquatojk 2-11 gjr t 9( )

2

2 47> gt >.5>4 f/gt24.? s

?.=1 f/s

xt

a

Ü6 6 6

Oksolmt9 Pmd spdd` jg 4= f/s ejrrdspjk`s tj 15> fo/m. Pmd gjuktaok os prjùed` by a wjrc`-ecass watdr pufp!





2 ― 2<

=4. ôeturd tmd ^rjbcdf9 Pmd bacc rosds straolmt up, fjfdktarocy ejfds tj rdst, ak` tmdk gaccs straolmt baeh `jwk.

Utratdly9 Pmd tofd ot tahds tmd bacc tj gacc os tmd safd as tmd tofd ot tahds tmd bacc tj rosd, kdlcdetokl aky aor groetojk.

Pmdrdgjrd tmd faxofuf mdolmt jg tmd bacc os acsj tmd òstaked a bacc wocc gacc gjr 1.0 s. Tsd tmd dquatojk jg fjtojk gjr

pjsotojk as a guketojk jg tofd ak` aeedcdratojk, rdacozokl tmat tmd aeedcdratojk ok daem easd os ?.=1 f/s2. Udt > > > x v6 6

ak` cdt `jwkwar` bd tmd pjsotovd òrdetojk gjr sofpcoeoty.

Ujcutojk9 Appcy dquatojk 2-11 ordetcy9 ( )( )22 21 1

> > 2 2>.> f > ?.=1 f/s 1.0 ?.7 f x x v t at 6 + + 6 + + 6

Oksolmt9 Pmd ?.7 f mdolmt ejrrdspjk`s tj 51 gt. Pmd bacc fust mavd rdbjuk`d` grjf tmd gcjjr wotm a spdd` jg 15.< f/s

jr 51 fo/m. Pmd pcaydr was prdtty aklry!

=7. ôeturd tmd ^rjbcdf9 Pmd lcjvd rosds straolmt up, fjfdktarocy ejfds tj rdst, ak` tmdk gaccs straolmt baeh `jwk.

Utratdly9 Pmd lcjvd wocc cak` wotm tmd safd spdd` ot was rdcdasd`, kdlcdetokl aky aor groetojk, sj tmd gokac vdcjeotyv 6 −7.> f/s. \d eak usd tmd dquatojk jg fjtojk gjr vdcjeoty as a guketojk jg tofd tj gok` tmd tofd jg gcolmt.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-< gjr t 9( ) ( )

>

2

7.> 7.> f/s1.22 s

?.=1 f/s

v vt

a

− −−6 6 6

−

2. (b) Pmd tofd tj rdaem faxofuf mdolmt9>

2

> 7.> f/s>.71 s

?.=1 f/s

v vt

a

− −6 6 6

−

Oksolmt9 Pmrjwokl tmd lcjvd upwar` wotm twoed tmd spdd` wocc `jubcd tmd tofd jg gcolmt but tmd faxofuf mdolmt

attaokd` by tmd lcjvd (5.77 f gjr a 7.> f/s okotoac spdd`) wocc okerdasd by jkcy a gaetjr jg 2 .

=<. ôeturd tmd ^rjbcdf9 Pmd baccs gacc straolmt `jwk uk`dr tmd okgcudked jg lravoty. Pmd gorst bacc gaccs grjf rdst but tmd

sdejk` bacc os lovdk ak okotoac `jwkwar` vdcjeoty.

Utratdly9 Bdeausd tmd gacc òstaked os hkjwk ok daem easd, usd tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) tj

prdòet tmd gokac vdcjeoty. Cdt `jwkwar` bd tmd pjsotovd òrdetojk gjr sofpcoeoty.

Ujcutojk9 1. (a) Pmd spdd` okerdasds cokdarcy wotm tofd but kjkcokdarcy wotm òstaked. Uoked tmd gorst bacc mas a cjwdr

okotoac vdcjeoty ak` mdked a cjwdr avdrald vdcjeoty, ot spdk`s fjrd tofd ok tmd aor. Pmd gorst (`rjppd`) bacc wocc

tmdrdgjrd dxpdrodked a carldr okerdasd ok spdd`.

2. (b) Gorst bacc9 Ujcvd dq. 2-12

gjr v, sdttokl > >v 6 9( )( )2 2

> 2 2 ?.=1 f/s 52.4 f 24.5 f/sv l x6 + ΐ 6 6

5. Udejk` bacc9 Ujcvd dq. 2-12 gjr v9 ( ) ( )( )22 2

>2 11.> f/s 2 ?.=1 f/s 52.4 f 2<.4 f/sv v l x6 + ΐ 6 + 6

0. Ejfpard tmd vΐ vacuds9 1 24.5 > f/s 24.5 f/svΐ 6 − 6 gjr tmd gorst bacc ak`

22<.4 11.> f/s 17.4 f/svΐ 6 − 6 gjr tmd sdejk` bacc.

Oksolmt9 Pmd sdejk` bacc os edrtaokcy ljokl gastdr, but ots emakld ok spdd` os cdss tmak tmd gorst bacc.





2 ― 2=

==. ôeturd tmd ^rjbcdf9 Pmd arrjw rosds straolmt upwar`, scjwokl `jwk ùd tj tmd aeedcdratojk jg lravoty.

Utratdly9 Bdeausd tmd pjsotojk, tofd, ak` aeedcdratojk ard acc hkjwk, wd eak usd tmd dquatojk jg fjtojk gjr pjsotojk as

a guketojk jg tofd ak` aeedcdratojk (dquatojk 2-11) tj gok` tmd okotoac vdcjeoty >v . Pmd safd dquatojk ejuc` bd usd` tj

gok` tmd tofd rdquord` tj rosd tj a mdolmt jg 14.> f abjvd ots caukem pjokt. Cdt tmd caukem pjsotojk > > x 6 ak` cdt upwar`

bd tmd pjsotovd ordetojk.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-11 gjr >v 9( )( )

221212

2>

5>.> f ?.=1 f/s 2.>> s

20.= f/s2.>> s

x at v

t

− −−6 6 6

2. (b) Ujcvd dquatojk 2-11 wotm x 6 14.> f9 ( ) ( )

( ) ( )

2 21

2

2 2

14.> f 20.= f/s ?.=1 f/s

> 0.?>4 f/s 20.= f/s 14.> f

t t

t t

6 −

6 − + −

5. Kjw usd tmd qua`ratoe gjrfuca9( ) ( )( )

22 20.= 20.= 0 0.?>4 14.>0

2 ?.=1

>.<>2 s , 0.57 s

b b aet

a

t

− ± − − −− ± −6 6

−

6

Oksolmt9 Pmd sdejk` rjjt jg tmd sjcutojk tj part (b) ejrrdspjk`s tj tmd tofd wmdk tmd arrjw, agtdr rosokl tj ots faxofufmdolmt, gaccs baeh tj a pjsotojk 14.> f abjvd tmd caukem pjokt.

=?. ôeturd tmd ^rjbcdf9 Pmd bjjh aeedcdratds straolmt `jwkwar` ak` mots tmd gcjjr jg tmd dcdvatjr.

Utratdly9 Pmd ejkstakt spdd` fjtojk jg tmd dcdvatjr `jds kjt aggdet tmd aeedcdratojk jg tmd bjjh. Grjf tmd pdrspdetovdjg ak jbsdrvdr jutso`d tmd dcdvatjr, bjtm tmd bjjh ak` tmd gcjjr mavd ak okotoac `jwkwar` vdcjeoty jg 5.> f/s. Pmdrdgjrd

grjf yjur pdrspdetovd tmd fjtojk jg tmd bjjh os kj òggdrdkt tmak og tmd dcdvatjr wdrd at rdst. Tsd tmd pjsotojk as a

guketojk jg tofd ak` aeedcdratojk dquatojk (dquatojk 2-11) tj gok` tmd tofd, sdttokl > >v 6 ak` cdttokl `jwkwar` bd tmd

pjsotovd òrdetojk. Pmdk usd vdcjeoty as a guketojk jg tofd (dquatojk 2-<) tj gok` tmd spdd` jg tmd bjjh wmdk ot cak`s.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-11 gjr t 9( )

2

2 1.2 f2>.0? s

?.=1 f/s

xt

l6 6 6

2. (b) Appcy dquatojk 2-< tj gok` v9 ( )( )2

>> ?.=1 f/s >.0? s 0.= f/sv v lt 6 + 6 + 6

Oksolmt9 Pmd spdd` ok part (b) os rdcatovd tj yju. Rdcatovd tj tmd lrjuk` tmd spdd jg tmd bjjh os 0.= + 5.> 6 <.= f/s.

?>. ôeturd tmd ^rjbcdf9 Pmd eafdra mas ak okotoac `jwkwar` vdcjeoty jg 2.> f/s ak` aeedcdratds straolmt `jwkwar`

bdgjrd strohokl tmd lrjuk`.

Utratdly9 Jkd way tj sjcvd tmos prjbcdf os tj usd tmd qua`ratoe gjrfuca tj gok` t grjf tmd pjsotojk as a guketojk jg tofd

ak` aeedcdratojk dquatojk (dquatojk 2-11). Pmdk tmd `dgokotojk jg aeedcdratojk eak bd usd` tj gok` tmd gokac vdcjeoty.

Mdrd‟s akjtmdr way9 Gok` tmd gokac vdcjeoty grjf tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) ak` usd tmdrdcatojksmop bdtwddk avdrald vdcjeoty, pjsotojk, ak` tofd (dquatojk 2-1>) tj gok` tmd tofd. \d‟cc tmdrdgjrd bd sjcvokl

tmos prjbcdf baehwar`s, gokòkl tmd akswdr tj (b) gorst ak` tmdk (a). Cdt upwar` bd tmd pjsotovd òrdetojk, sj tmat

>2.> f/sv 6 − ak` >

> 04 f 04 f. x x xΐ 6 − 6 − 6 −

Ujcutojk9 1. (a) Ujcvd dquatojk 2-12 gjr v9 ( ) ( ) ( )22 2> 2 2.> f/s 2 ?.=1 f/s 04 f 5> f/sv v l x6 + ΐ 6 − + − − 6 −

2. Ujcvd dquatojk 2-1> gjr t 9( ) ( )1 1

>2 2

04 f2.= s

5> 2.> f/s

xt

v v

ΐ −6 6 6

+ − −

5. (b) \d gjuk` v ok stdp 19 5> f/s >.>5> hf/sv 6 − 6 −

Oksolmt9 Pmdrd os jgtdk fjrd tmak jkd way tj apprjaem ejkstakt aeedcdratojk prjbcdfs, sjfd dasodr tmak jtmdrs.





2 ― 2?

?1. ôeturd tmd ^rjbcdf9 _ju ak` yjur grodk` bjtm aeedcdratd

grjf rdst straolmt `jwkwar`, but at òggdrdkt tofds. _ju stdp

jgg tmd bro`ld wmdk yjur grodk` mas gaccdk 2.> f, ak` yjur grodk` mots tmd watdr wmocd yju ard stocc ok tmd aor.

Utratdly9 Gorst gok` tmd tofd ot tahds gjr yjur grodk` tj gacc

2.> f usokl tmd dquatojk jg fjtojk gjr pjsotojk as a guketojkjg tofd ak` aeedcdratojk (dquatojk 2-11). Uubtraet tmat tofd

grjf 1.7 s tj gok` tmd tofd dcapsd` bdtwddk wmdk yju iufpak` wmdk yjur grodk` mots tmd watdr. Tsd dquatojk 2-11 ak`

tmd tofds gjuk` abjvd tj gok` tmd pjsotojks jg yju ak` yjur

grodk` at tmd tofd yjur grodk` cak`s. Pmdk `dtdrfokd tmdsdparatojk grjf tmd hkjwk pjsotojks.

Ujcutojk9 1. (a) Bdeausd yjur grodk` mas a lrdatdr avdrald spdd` tmak yju `j ùrokl tmd tofd bdtwddk wmdk yju iufp

ak` yjur grodk` cak`s, tmd sdparatojk bdtwddk tmd twj jg yju wocc okerdasd tj a vacud fjrd tmak 2.> f.

2. (b) Gok` tmd tofd ot tahds tj gacc 2.> f grjf

dquatojk 2-11 wotm > >v 6 9( )

2

2 2.> f2>.70 s

?.=1 f/s

xt

l

ΐ6 6 6

5. Gok` tmd òstaked yjur grodk` gdcc ok 1.7 s9 ( )( )22 21 1

grodk` 2 2?.=1 f/s 1.7 s 15 f x lt 6 6 6

0. Gok` tmd òstaked yju gdcc ok tmd smjrtdr tofd9 ( ) ( )( )2 221 1

yju 2.> f2 2?.=1 f/s 1.7 >.70 s 0.4 f x l t t 6 − 6 − 6

4. Gok` tmd òggdrdked ok yjur pjsotojks9grodk` yju

15 0.4 f = fU x x6 − 6 − 6

Oksolmt9 Bdeausd jg mdr mda` start, yjur grodk` wocc acways mavd a molmdr avdrald vdcjeoty tmak yju, ak` tmd sdparatojk bdtwddk yju ak` mdr wocc ejktokud tj okerdasd tmd cjkldr yju bjtm gacc.

watdr

bro`ld

t 6 1.7 s

2.> f

yju

ufp

grodk`

cak`sU :





2 ― 5>

?2. ôeturd tmd ^rjbcdf9 Pmd rjehdt rosds straolmt upwar`, aeedcdratokl jvdr a òstaked jg 27 f ak` tmdk scjwokl `jwk ak`

ejfokl tj rdst at sjfd actotu`d molmdr tmak 27 f.

Utratdly9 Tsd tmd lovdk aeedcdratojk ak` òstaked ak` tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) tj gok` tmdvdcjeoty jg tmd rjehdt at tmd dk` jg ots aeedcdratojk pmasd, wmdk ots actotu`d os 27 f. Tsd tmat as tmd okotoac vdcjeoty jg tmd

grdd-gacc stald ok jr`dr tj gok` tmd faxofuf actotu`d (dquatojk 2-12 alaok). Pmdk appcy dquatojk 2-12 jked alaok tj gok`

tmd vdcjeoty jg tmd rjehdt wmdk ot rdturks tj tmd lrjuk`. Pmd lovdk ak` eaceucatd` pjsotojks at varojus stalds jg tmdgcolmt eak tmdk bd usd` tj gok` tmd dcapsd` tofd ok daem stald ak` tmd tjtac tofd jg gcolmt.

Ujcutojk9 1. (a) Gok` tmd vdcjeoty at tmd dk` jg tmd bjjst pmasd usokl dquatojk 2-129

( )( )2 2 2

bjjst >2 > 2 12 f/s 27 f 24 f/sv v l x6 + ΐ 6 + 6

2. Gok` tmd mdolmt emakld ùrokl tmd bjjst pmasd usokl dquatojk 2-12 ak` a gokac spdd` jg

zdrj9

2

2 2 bjjst

bjjst bjjst bjjst> 22

vv l x x

l6 − ΐ ⇒ ΐ 6

5. Kjw gok` tmd jvdracc faxofuf mdolmt9( )

( )

22

bjjst

fax 2

24 f/s27 f 27 f 27 52 f 4= f

2 2 ?.=1 f/s

vm

l6 + 6 + 6 + 6

0. (b) Appcy dquatojk 2-12 jked alaok

bdtwddk tmd dk` jg tmd bjjst pmasd ak` tmd

pjokt wmdrd ot mots tmd lrjuk`9 ( ) ( )( )

2 2

bjjst

22 2

bjjst

2

2 24 f/s 2 ?.=1 f/s 27 f 50 f/s

v v l x

v v l x

6 − ΐ

6 − ΐ 6 − − 6

4. (e) Gorst gok` tmd ùratojk jg tmd bjjst pmasd.

Tsd tmd hkjwk pjsotojks ak` dquatojk 2-1>9 ( ) ( ) bjjst

bjjst 1 1> bjjst2 2

27 f2.1 s

> 24 f/s

xt

v v

ΐ6 6 6

+ +

7. Kjw gok` tmd tofd gjr tmd rjehdt tj rdaem ots

faxofuf actotu`d grjf tmd dk` jg tmd bjjst pmasd9

( ) ( )up

up 112 bjjst tjp2

52 f2.7 s

24 > f/s

xt

v v

ΐ6 6 6

++

<. Kjw gok` tmd tofd gjr tmd rjehdt tj gacc baeh tj tmd lrjuk`9 ( ) ( )

`jwk

`jwk 112tjp lrjuk`2

4= f5.0 s

> 50 f/s

xt

v v

ΐ6 6 6

++

=. Uuf tmd tofds tj gok` tmd tofd jg gcolmt9 tjtac bjjst up `jwk2.1 2.7 5.0 s =.1 st t t t 6 + + 6 + + 6

Oksolmt9 Kjtoed mjw hkjwcd`ld jg tmd okotoac ak` gokac vdcjeotods ok daem stald, ak` tmd òstaked travdcd` ok daem stald,accjwd` tmd eaceucatojk jg tmd dcapsd` tofds usokl tmd rdcatovdcy sofpcd dquatojk 2-1>, as jppjsd` tj tmd qua`ratoe

dquatojk 2-11. Cdarkokl tj rdejlkozd tmd dasodst rjutd tj tmd akswdr os ak ofpjrtakt shocc tj jbtaok.

?5. ôeturd tmd ^rjbcdf9 Pmd mdolmt-vdrsus-tofd pcjt jg tmd pcul os smjwk at

rolmt. Pmd pcul starts wotm a molm vdcjeoty ak` bdloks tj scjw `jwk wmdkot mots tmd bdcc agtdr >.7> s.

Utratdly9 Pmd avdrald vdcjeoty os tmd òstaked travdcd` by tmd pculòvo`d` by tmd tofd (dquatojk 2-1>). Assufokl tmdrd os kj groetojk, tmd

tofd ak` aeedcdratojk eak bd usd` tj gok` tmd emakld ok vdcjeoty (dquatojk

2-<). Pmd okotoac vdcjeoty eak tmdk bd `dtdrfokd` grjf tmd emakld ok

vdcjeoty ak` avdrald vdcjeotods by ejfbokokl dquatojks 2-< ak` 2-?.

Ujcutojk9 1. (a) Gok` tmd avdrald

vdcjeoty usokl dquatojk 2-1>9>

av

0.> > f7.< f/s

>.7> s

x xv

t

− −6 6 6

2. (b) Gok` tmd emakld ok vdcjeoty usokl dq. 2-<9 ( )( )2

>?.=1 f/s >.7> s 4.? f/sv v v at ΐ 6 − 6 6 − 6 −





2 ― 51

5. (e) Ejfbokd dquatojks 2-< ak` 2-? tj sjcvd gjr >v 9

( )

( ) ( ) ( )( )

>

av >

> av > >

21 1> av2 2

>

grjf dquatojk 2-<

2 grjf dquatojk 2-?. Uubstotutd oktj tmd abjvd9

2 ak` kjw sjcvd gjr 9

2 2 7.< f/s ?.=1 f/s >.7> s

?.7 f/s

v v at

v v v

v v v at v

v v at

v

6 −

6 −

6 − −

⎡ ⎠6 − 6 − −⎥ ⎧

6

Oksolmt9 Pmdrd ard sdvdrac jtmdr ways jg gokòkl tmdsd spdd`s, okecuòkl lrapmoeac akacysos. Pry fdasurokl tmd scjpd jg

tmd lrapm at tmd caukem pjokt ak` tmd pjokt at wmoem tmd pcul mots tmd bdcc tj gok` tmd okotoac ak` gokac spdd`s.

?0. ôeturd tmd ^rjbcdf9 Kut A os `rjppd` grjf rdst. \mdk ot

mas gaccdk 2.4 f, kut B os tmrjwk `jwkwar` wotm ak okotoac

spdd` vB,>. Bjtm kuts cak` at tmd safd tofd agtdr gaccokl

1>.> f.

Utratdly9 Gorst gok` tmd tofd ot tahds gjr kut A tj gacc 2.4 f

usokl tmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg tofd ak` aeedcdratojk (dquatojk 2-11). Acsj gok` tmd tofd

rdquord` gjr kut A tj gacc tmd dktord 1>.> f. Uubtraet tmd

gorst tofd grjf tmd sdejk` tj gok` tmd tofd oktdrvac jvdr wmoem kut B fust rdaem tmd lrjuk` ok jr`dr tj cak` at tmd

safd okstakt as kut A. Pmdk usd dquatojk 2-11 alaok tj goktmd okotoac vdcjeoty vB,> rdquord` ok jr`dr gjr kut B tj rdaem

tmd lrjuk` ok tmat tofd.

Ujcutojk9 1. Gok` tmd tofd ot tahds gjr kut A tj gacc

2.4 f by sjcvokl dquatojk 2-11 gjr t ak` sdttokl vA,>

6 >.

( )A,1 2

2 2.4 f2>.<10 s

?.=1 f/s

xt

l

ΐ6 6 6

2. Gok` tmd tofd ot tahds gjr kut A tj gacc tmd dktord

1>.> f9( )

A,tjtac 2

2 1>.> f21.02= s

?.=1 f/s

xt

l

ΐ6 6 6

5. Uubtraet tmd tofds tj gok` tmd tofd jvdr wmoem kutB fust rdaem tmd lrjuk`9 B,tjtac A,tjtac A,1 1.02= >.<10 s >.<10 st t t 6 − 6 − 6

0. Ujcvd dquatojk 2-11 gjr vB,>9 ( )( )2212

1 2B,tjtac2

B,>

B,tjtac

B,>

1>.> f ?.=1 f/s >.<10 s>.<10 s

1>.4 f/s 11 f/s

x lt vt

v

−ΐ −6 6

6 ⇒

Oksolmt9 Ok tmos prjbcdf wd hdpt ak a`òtojkac solkogoeakt golurd tmak os warraktd` ok stdps 1, 2, ak` 5 ok ak attdfpt tj

ldt a fjrd aeeuratd akswdr ok stdp 0. Mjwdvdr, og yju emjjsd kjt tj `j sj, òggdrdkeds ok rjukòkl wocc cda` tj akakswdr jg 1> f/s. Pmd spdeogod` 2.4 f `rjp òstaked gjr kut A cofots tmd akswdr tj twj solkogoeakt òlots, ak` bdeausd

tmd akswdr os rolmt bdtwddk 1> ak` 11 f/s, ot ejuc` ejrrdetcy lj dotmdr way.

?4. ôeturd tmd ^rjbcdf9 ^mocdas Gjll travdcs ok a straolmt cokd acc tmd way arjuk` tmd wjrc`.

Utratdly9 Pmd avdrald spdd` os tmd òstaked òvo`d` by dcapsd` tofd. \d wocc dstofatd tmat Fr. Gjll travdcs a òstakeddquac tj tmd dquatjroac eoreufgdrdked jg tmd Dartm. Pmos os ak apprjxofatojk, bdeausd mos patm was fjst cohdcy fuem

fjrd ejfpcoeatd` tmak tmat, but wd wdrd ashd` jkcy gjr tmd apprjxofatd spdd`.

Ujcutojk9 Gok` tmd eoreufgdrdked jg tmd Dartm9 ( )5 <2 2 75<> 1> f 0.> 1> f` r ώ ώ 6 6 Ü 6 Ü

@ovo`d tmd òstaked by tmd tofd9 <

òstaked 0.> 1> f4.= f/s

tofd => 20 m/` 57>> s/ms

Ü6 6 6

Ü Ü

Oksolmt9 Pmos spdd` ejrrdspjk`s tj abjut 15 fo/m ak` os gastdr tmak mufaks eak wach. Lovokl tofd gjr scddpokl, datokl,ak` jtmdr `dcays, Fr. Gjll kdd`s a rdcatovdcy gast fdaks jg travdc.

lrjuk`

brakem2.4 f

Kut B

tmrjwk

Bjtm cak`

1>.> f

vB,> 6 :

Kut A





2 ― 52

?7. ôeturd tmd ^rjbcdf9 Pmd rjeh aeedcdratds grjf rdst straolmt `jwkwar` ak` cak`s jk tmd surgaed jg tmd Fjjk.

Utratdly9 Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` vdcjeoty (dquatojk 2-12) tj gok` tmd gokac

vdcjeoty.

Ujcutojk9 Ujcvd dquatojk 2-12 gjr vdcjeoty v9 ( )( )2 2 2

>2 > 2 1.72 f/s 1.24 f 2.>1 f/sv v a x6 + ΐ 6 + 6

Oksolmt9 Jk Dartm tmd rjeh wjuc` bd travdcokl 0.?4 f/s, but tmd wdahdr lravoty jk tmd Fjjk `jdsk‟t aeedcdratd tmd rjeh

kdarcy as fuem as wjuc` tmd Dartm‟s lravoty.

?<. ôeturd tmd ^rjbcdf9 _ju iufp jgg a bjuc`dr, aeedcdratd grjf rdst straolmt `jwkwar` ak` cak`, bdkòkl yjur hkdds sj

tmat yjur edktdr jg fass ejfds tj rdst jvdr a smjrt vdrtoeac òstaked.

Utratdly9 Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` vdcjeoty (dquatojk 2-12) tj gok` yjur gokac

vdcjeoty iust bdgjrd cakòkl. Pmdk dstofatd tmd òstaked yjur edktdr jg fass wocc fjvd agtdr yjur gddt ejktaet tmd

lrjuk`, ak` usd tmat òstaked tj dstofatd yjur `dedcdratojk ratd.

Ujcutojk9 1. Ujcvd dquatojk 2-12 gjr vdcjeoty v9 ( ) ( )2 2 2

> 2 > 2 ?.=1 f/s 1.4 f 4.0 f/sv v a x6 + ΐ 6 + 6

2. Dstofatd yjur edktdr jg fass fjvds `jwkwar`

abjut >.4 f agtdr yjur gddt ejktaet tmd lrjuk` ak`

yju bdk` yjur hkdds oktj a erjuemokl pjsotojk.Ujcvd dquatojk 2-12 gjr aeedcdratojk9

( )

( )

222 2

2>> 4.0 f/s

2? f/s 5.>2 2 >.4> f

v v

a l y

−−

6 6 6 − 6 −ΐ

Oksolmt9 \mdk a lyfkast cak`s grjf ak dvdk molmdr actotu`d, smd folmt try tj bdk` mdr hkdds dvdk cdss ok jr`dr tjofprdss tmd iu`lds. Og smd cak`s grjf ak actotu`d jg 5.> f ak` bdk`s mdr hkdds sj mdr edktdr jg fass fjvds jkcy >.2 f,

mdr aeedcdratojk os −14l!

?=. ôeturd tmd ^rjbcdf9 Pmd watdr aeedcdratds grjf rdst (ok tmd vdrtoeac òrdetojk, tmat os) straolmt `jwkwar` ak` ofpaets

tmd lrjuk` jr watdr bdcjw.

Utratdly9 Dfpcjy tmd rdcatojksmop bdtwddk aeedcdratojk, òspcaedfdkt, ak` vdcjeoty (dquatojk 2-12) tj gok` tmd mdolmt

grjf wmoem tmd watdr fust gacc sj tmat ots gokac vdcjeoty iust bdgjrd cakòkl os 50> f/s.

Ujcutojk9 Ujcvd dquatojk 2-12 gjr vdcjeoty ΐ x9( )

( )

2 22 2>

2

50> f/s >4?>> f 4.? hf

2 2 ?.=1 f/s

v v x

l

−−ΐ 6 6 6 6

Oksolmt9 Pmos mdolmt ejrrdspjk`s tj 5.< focds jr jvdr 1?,>>> gddt! \otm aor rdsostaked, mjwdvdr, ak dvdk molmdr actotu`d

wjuc` bd rdquord` tj jbtaok spdd`s tmos lrdat.

??. ôeturd tmd ^rjbcdf9 Pwj baccs ard rdcdasd` grjf tmd d`ld jg a rjjg. Bacc A os `rjppd` grjf rdst but bacc B os tmrjwk

`jwkwar` wotm ak okotoac vdcjeoty > .v

Utratdly9 Tsd tmd `dgokotojk jg aeedcdratojk tj akswdr tmd ejkedptuac qudstojk, hddpokl ok fok` tmd avdrald spdd` jg

bacc B os lrdatdr tmak tmd avdrald spdd` jg bacc A.

Ujcutojk9 Pmd twj baccs gacc tmd safd òstaked but bacc B mas tmd lrdatdr avdrald spdd` ak` gaccs gjr a smjrtdr cdkltm jg tofd. Bdeausd daem bacc aeedcdratds at tmd safd ratd jg ?.=1 f/s2, bacc A aeedcdratds gjr a cjkldr tofd ak` tmd okerdasd ok

spdd` os fjrd gjr bacc A tmak ot os gjr bacc B.

Oksolmt9 Og bacc B wdrd gord` `jwkwar` at ak dxtrdfdcy molm spdd`, ot wjuc` rdaem tmd lrjuk` wotmok a vdry smjrt

oktdrvac jg tofd ak` ots spdd` wjuc` mar`cy emakld at acc.





2 ― 55

1>>. ôeturd tmd ^rjbcdf9 Pwj baccs ard rdcdasd` grjf tmd d`ld jg a rjjg. Bacc A os `rjppd` grjf rdst but bacc B os tmrjwk

`jwkwar` wotm ak okotoac vdcjeoty > .v

Utratdly9 Tsd a ejrrdet oktdrprdtatojk jg fjtojk lrapms tj akswdr tmd ejkedptuac qudstojk. Rdeacc tmat tmd scjpd jg a

vdcjeoty-vdrsus-tofd lrapm os tmd aeedcdratojk, ak` tmd arda uk`dr tmd lrapm os tmd òstaked travdcd`.

Ujcutojk9 1. (a) Pmd vdcjeoty jg bacc A starts at zdrj ak` tmdk okerdasds cokdarcy wotm a scjpd jg ?.=1 f/s2. Pmd lrapm

tmat ejrrdspjk`s tj tmat `dseroptojk os lrapm 5.

2. (b) Pmd vdcjeoty jg bacc B starts at >v ak` tmdk okerdasds cokdarcy wotm a scjpd jg ?.=1 f/s2. Ots lrapm fust bd a

straolmt cokd wotm tmd safd scjpd as tmd lrapm jg bacc A. Pmd lrapm tmat ejrrdspjk`s tj tmat `dseroptojk os lrapm 2.

Oksolmt9 Dvdk og bacc B wdrd gord` `jwkwar` at ak dxtrdfdcy molm spdd`, ots vdcjeoty-vdrsus-tofd lrapm wjuc` stocc bd

cokdar wotm a scjpd jg ?.=1 f/s2, but tmd cokd wjuc` bd vdry smjrt bdeausd ot wjuc` mot tmd lrjuk` at a fuem darcodr tofd.

1>1. ôeturd tmd ^rjbcdf9 Pmd mdolmt-vdrsus-tofd pcjt jg tmd rjeh ossmjwk at rolmt. Pmd rjeh starts wotm a molm vdcjeoty upwar`,

scjws `jwk ak` fjfdktarocy ejfds tj rdst agtdr abjut 0.>

sdejk`s jg gcolmt, ak` tmdk gaccs straolmt `jwk ak` cak`s at abjut

=.> sdejk`s.

Utratdly9 Pmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg tofd ak` aeedcdratojk (dquatojk 2-11) eak bd usd` tj gok` tmd

aeedcdratojk grjf tmd sdejk` macg jg tmd traidetjry, wmdrd tmd

rjeh gaccs 5> f grjf rdst ak` cak`s 0.> sdejk`s catdr. Jked

aeedcdratojk os hkjwk, tmd gokac vdcjeoty eak bd `dtdrfokd` grjfdquatojk 2-<. Cdt `jwkwar` bd tmd pjsotovd òrdetojk.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-11 gjr aeedcdratojk,

assufokl > >v 6 ak` tmd rjeh gaccs 5> f ok 0.> s9

( )

( )2

2 2

2 5> f25.= f/s

0.> s

xa

t

ΐ6 6 6

2. (b) Gok` tmd gokac vdcjeoty usokl dquatojk 2-<9 ( )( )2

> > 5.= f/s 0.> s 14 f/sv v at 6 + 6 + 6

Oksolmt9 Pmdrd ard sdvdrac jtmdr ways jg gokòkl tmd akswdrs, okecuòkl lrapmoeac akacysos. Pry fdasurokl tmd scjpd jg

tmd lrapm at tmd caukem pjokt ak` tmd pjokt at wmoem tmd rjeh cak`s tj gok` tmd okotoac ak` gokac vdcjeotods. Pmjsd vacudseak tmdk bd usd` tj gok` tmd aeedcdratojk.

1>2. ôeturd tmd ^rjbcdf9 Pmd paehald gaccs straolmt `jwkwar`, aeedcdratokl gjr 2.2 sdejk`s bdgjrd ofpaetokl tmd aor bals.

Utratdly9 Gok` tmd òstaked tmd paehald wocc gacc grjf rdst ok 2.2 sdejk`s by usokl dquatojk 2-11. Tsd tmd hkjwkaeedcdratojk ak` tofd tj gok` tmd vdcjeoty jg tmd paehald iust bdgjrd ofpaet by usokl dquatojk 2-<. Gokaccy, usd tmd

hkjwk okotoac ak` gokac vdcjeotods, tjldtmdr wotm tmd òstaked jvdr wmoem tmd paehald ejfds tj rdst wmdk ok ejktaet wotm

tmd aor bals, tj gok` tmd stjppokl aeedcdratojk usokl dquatojk 2-12.

Ujcutojk9 1. (a) Gok` tmd òstaked tmd paehaldgaccs grjf rdst ok 2.2 s usokl dquatojk 2-119 ( ) ( )

22 21 1> 2 2

> ?.=1 f/s 2.2 s 20 f x v t lt ΐ 6 + 6 + 6

2. (b) Gok` tmd vdcjeoty iust bdgjrd ofpaet usokl dquatojk 2-<9

( )( )2

cak` > > ?.=1 f/s 2.2 s 22 f/s 0= fo/m!v v lt 6 + 6 + 6 6

5. (e) Ujcvd dquatojk 2-12 gjr a9( )

( )

222 2

2>> 22 f/s

52> f/s 552 2 >.<4 f

v va l

x

−−6 6 6 − 6 −

ΐ

Oksolmt9 Okerdasokl tmd stjppokl òstaked wocc `derdasd tmd stjppokl aeedcdratojk. \d wocc rdturk tj tmos o`da wmdk wd

òseuss ofpucsd ak` fjfdktuf ok Emaptdr ?.





2 ― 50

1>5. ôeturd tmd ^rjbcdf9 A yjuklstdr bjukeds straolmt up ak` `jwk jk a trafpjcokd. Pmd emoc` rosds straolmt upwar`,

scjws `jwk, ak` fjfdktarocy ejfds tj rdst bdgjrd gaccokl straolmt `jwkwar` alaok.

Utratdly9 Gok` tmd tofd jg gcolmt by dxpcjotokl tmd syffdtry jg tmd sotuatojk. Og ot tahds tofd t gjr lravoty tj scjw tmdemoc` `jwk grjf mdr okotoac spdd` v> tj zdrj, ot wocc tahd tmd safd afjukt jg tofd tj aeedcdratd mdr baeh tj tmd safd

spdd`. Umd tmdrdgjrd cak`s at tmd safd spdd` v> wotm wmoem smd tjjh jgg. Tsd tmos gaet tjldtmdr wotm dquatojk 2-< tj

gok` tmd tofd jg gcolmt. Pmd faxofuf mdolmt smd aemodvds os rdcatd` tj tmd squard jg v>, as okòeatd` by dquatojk 2-12.

Ujcutojk9 1. (a) Bdeausd tmd tofd jg gcolmt `dpdk`s cokdarcy upjk tmd okotoac vdcjeoty, `jubcokl v> wocc okerdasd mdr tofd

jg gcolmt by a gaetjr jg 2.

2. (b) Bdeausd tmd tofd jg gcolmt `dpdk`s upjk tmd squard jg tmd okotoac vdcjeoty, `jubcokl v> wocc okerdasd mdr faxofuf

actotu`d by a gaetjr jg 0.

5. (e) Pmd tofd jg gcolmt gjr > 2.> f/sv 6 , usokl Dq. 2-<9( ) ( )> >> >

2

2 2.> f/s2>.01 s

?.=1 f/s

v vv v vt

l l l

− −−6 6 6 6 6

− −

0. Pmd tofd jg gcolmt gjr > 0.> f/sv 6 9( )

>

2

2 0.> f/s2>.=2 s

?.=1 f/s

vt

l6 6 6

4. Pmd faxofuf mdolmt gjr > 2.> f/sv 6 , usokl Dq. 2-129( )

( )

22 2 2 2 2

> > >

2

2.> f/s>>.2> f

2 2 2 2 ?.=1 f/s

v v v v x

l l l

− −ΐ 6 6 6 6 6

− −

7. Pmd faxofuf mdolmt gjr > 0.> f/sv 6 9( )

( )

22

>

2

0.> f/s>.=2 f

2 2 ?.=1 f/s

v x

lΐ 6 6 6

Oksolmt9 Pmd rdasjk tmd akswdr ok stdp 7 os kjt dxaetcy gjur tofds carldr tmak tmd akswdr ok stdp 4 os ùd tj tmd rjukòkl

rdquord` by tmd gaet tmat tmdrd ard jkcy twj solkogoeakt òlots. Og yju rdeaceucatd usokl 2.>> f/s ak` 0.>> f/s, tmd

akswdrs ard >.2>0 ak` >.=17 f, rdspdetovdcy.

1>0. ôeturd tmd ^rjbcdf9 Pmd bacc rjccs ok a straolmt cokd, `derdasokl ots spdd` at a ejkstakt ratd uktoc ot ejfds tj rdst.

Utratdly9 _ju ejuc` gok` tmd (kdlatovd) aeedcdratojk by usokl dquatojk 2-12 ak` tmd hkjwk okotoac ak` gokac vdcjeotods

ak` tmd òstaked travdcd`. Pmdk dfpcjy dquatojk 2-12 alaok usokl tmd safd aeedcdratojk, but sjcvokl gjr tmd v> rdquord`

tj lj tmd cjkldr òstaked. Okstda`, wd‟cc prdsdkt a way tj eaceucatd tmd safd akswdr usokl a ratoj.

Ujcutojk9 1. (a) Eaceucatd tmd ratoj jg okotoac

vdcjeotods basd` upjk dquatojk 2-129

2 2

b,> b b

2 2a,> aa a

2 > 2

2 > 2

v v a x a x x

v xv a x a x

− ΐ − ΐ ΐ6 6 6

ΐ− ΐ − ΐ

2. Kjw sjcvd gjr ,>v 9 ( ) b

b,> a,>

a

2>.4 gt1.4< f/s 1.=< f/s

2>.4 7.>> gt

xv v

x

ΐ6 6 6

ΐ −

5. (b) Dfpcjy tmd safd ratoj wotm òggdrdkt òstakeds9 ( ) b

b,> a,>

a

7.>> gt1.4< f/s 1.>1 f/s

2>.4 7.>> gt

xv v

x

ΐ6 6 6

ΐ −

Oksolmt9 Eaceucatokl ratojs eak jgtdk bd a ejkvdkodkt ak` sofpcd way tj sjcvd a prjbcdf. Ok tmos easd a tmrdd-stdp

sjcutojk bdeafd twj stdps wmdk wd eaceucatd` tmd ratoj, ak` gurtmdrfjrd wd kdvdr kdd`d` tj ejkvdrt gddt tj fdtdrs

bdeausd tmd ukots eakedc jut ok tmd ratoj. Cdarkokl tj eaceucatd ratojs ok tmos fakkdr os a vacuabcd shocc ok pmysoes.





2 ― 54

1>4. ôeturd tmd ^rjbcdf9 Pmd pdrsjk os tmrjwk straolmt upwar`, scjws `jwk, ak` fjfdktarocy ejfds tj rdst bdgjrd gaccokl

straolmt jwkwar` alaok.

Utratdly9 Gok` tmd tofd jg gcolmt by dxpcjotokl tmd syffdtry jg tmd sotuatojk. Og ot tahds tofd t gjr lravoty tj scjw tmd pdrsjk `jwk grjf mdr okotoac spdd` v> tj zdrj, ot wocc tahd tmd safd afjukt jg tofd tj aeedcdratd mdr baeh tj tmd safd

spdd`. Ot tmdrdgjrd tahds tmd safd afjukt jg tofd gjr mdr tj rosd tj tmd pdah jg mdr gcolmt tmak ot `jds gjr mdr tj rdturk tj

tmd bcakhdt. Tsd tmos gaet tjldtmdr wotm dquatojk 2-11 wotm v> 6 > (ejrrdspjkòkl tj tmd sdejk` macg jg mdr gcolmt, grjftmd pdah baeh `jwk tj tmd bcakhdt) tj gok` tmd tofd jg gcolmt. Pmd tofd abjvd ak` bdcjw 10.> gt eak bd gjuk` usokl tmd

safd dquatojk.

Ujcutojk9 1. (a) Pmd tofd jg gcolmt

eak bd gjuk` grjf dquatojk 2-119

( )`jwk 2

2 2=.> gt >.5>4 f/gt22 2 2 2.70 s

?.=1 f/s

xt t

l

Üΐ6 Ü 6 Ü 6 6

2. (b) Pmd pdrsjk‟s avdrald spdd` os cdss ùrokl tmd uppdr macg jg mdr traidetjry, sj tmd tofd smd spdk`s ok tmat pjrtojk jg

mdr gcolmt os fjrd tmak tmd tofd smd spdk`s ok tmd cjwdr macg jg mdr gcolmt.

5. (e) Pmd tofd smd spdk`s abjvd 10.> gtos tmd safd tofd jg mdr gcolmt og mdr

faxofuf mdolmt wdrd 10.> gt9

( )abjvd 2

2 10.> gt >.5>4 f/gt22 2 1.=< s

?.=1 f/s

xt

l

Üΐ6 Ü 6 6

0. Pmd tofd spdkt bdcjw 10.> gt os tmd

rdfaokokl pjrtojk jg tmd tjtac tofd jg gcolmt9 bdcjw tjtac abjvd2.70 1.=< s >.<< st t t 6 − 6 − 6

Oksolmt9 Pmd syffdtry jg tmd fjtojk jg a grddcy gaccokl jbidet eak jgtdk bd a usdguc tjjc gjr sjcvokl prjbcdfs quoehcy.

1>7. ôeturd tmd ^rjbcdf9 Pmd twj rjehs gacc straolmt `jwkwar` acjkl a sofocar patm dxedpt at òggdrdkttofds.

Utratdly9 Gorst gok` tmd tofd dcapsd` bdtwddk tmd rdcdasd jg tmd twj rjehs by gokòkl tmd tofd

rdquord` gjr tmd gorst rjeh tj gacc 0.>> f, usokl tmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg tofd ak` aeedcdratojk (dquatojk 2-11). Pmd pjsotojks as a guketojk jg tofd gjr daem rjeh eak tmdk bd

ejfpard` tj gok` a sdparatojk òstaked as a guketojk jg tofd.

Ujcutojk9 1. (a) Gok` tmd tofd rdquord`gjr rjeh A tj gacc 0.>> f9

( )0 2

2 0.>> f2>.?>5 s

?.=1 f/s

xt

l

ΐ6 6 6

2. Cdt t rdprdsdkt tmd tofd dcapsd` grjf

tmd okstakt rjeh B os `rjppd`. Pmd pjsotojk jg rjeh A (dquatojk 2-11) os tmus9

( )2

2 21 1 10 0 02 2 2> A x l t t lt l t t lt 6 + + 6 + +

0. Pmd pjsotojk jg rjeh B (dquatojk 2-11)

os9

2 21 1

2 2> B x lt lt 6 + 6

4. Gok` tmd sdparatojk bdtwddk tmd rjehs9 ( )

( ) ( ) ( )( )

( )

2 2 21 1 10 02 2 2

22 2 21 10 02 2

?.=1 f/s >.?>5 s ?.=1 f/s >.?>5 s

=.=7 f/s 0.>> f

A B x x x lt l t t lt lt

x l t t lt t

x t

ΐ 6 − 6 + + −

ΐ 6 + 6 +

ΐ 6 +

7. Gok` xΐ gjr t 6 1.> s9 ( )( )=.=7 f/s 1.> s 0.>> f 12.? f xΐ 6 + 6

<. (b) Gok` xΐ gjr t 6 2.> s9 ( )( )=.=7 f/s 2.> s 0.>> f 22 f xΐ 6 + 6

=. (e) Gok` xΐ gjr t 6 1.> s9 ( )( )=.=7 f/s 5.> s 0.>> f 51 f xΐ 6 + 6

?. (`) Pmd cokdar `dpdk`dked jg xΐ upjk t eak bd vdrogod` by dxafokokl tmd dquatojk `drovd` ok stdp 4.

Oksolmt9 Pmd jkcy way gjr rjeh B tj eatem up tj rjeh A wjuc` bd gjr rjeh B tj bd tmrjwk `jwkwar` wotm a carld okotoac

spdd`. Ok tmat easd tmd sdparatojk bdejfds ( ),>=.=7 f/s 0.>> f, B x v t ΐ 6 − + wmoem `derdasds tj zdrj as cjkl as ,> B

v os

lrdatdr tmak =.=7 f/s.





2 ― 57

1><. ôeturd tmd ^rjbcdf9 Agtdr rdcdasd by tmd lucc tmd smdcc rosds straolmt upwar`, scjws `jwk, ak` fjfdktarocy ejfds tj

rdst bdgjrd gaccokl straolmt jwkwar` alaok.

Utratdly9 Gok` tmd dxtra actotu`d attaokd` by tmd smdcc ùd tj ots upwar` okotoac vdcjeoty upjk rdcdasd, ak` a`` tmat vacudtj 12.4 f tj gok` tmd faxofuf mdolmt ot rdaemds abjvd lrjuk`. Pmd tofd-grdd dquatojk gjr vdcjeoty as a guketojk jg

aeedcdratojk ak` òstaked (dquatojk 2-12) eak bd dfpcjyd` gjr tmos purpjsd. Pmd tofd tmd smdcc spdk`s ljokl up ak` tmd

tofd ot spdk`s ljokl `jwk eak daem bd gjuk` grjf tmd hkjwk mdolmts ak spdd`s (dquatojks 2-< ak` 2-11). Pmdk tmdspdd` upjk cakòkl eak bd `dtdrfokd` grjf tmd hkjwk tofd ot spdk`s gaccokl (dquatojk 2-<). Cdt upwar` bd tmd pjsotovd

òrdetojk tmrjulmjut tmd prjbcdf.

Ujcutojk9 1. (a) Pmd fjtojk jg tmd smdcc os okgcudked` jkcy by lravoty jked ot mas bddk rdcdasd` by tmd lucc. Pmdrdgjrd ots

aeedcdratojk wocc bd ?.=1 f/s2 `jwkwar` grjf tmd fjfdkt ot os rdcdasd`, dvdk tmjulm ot os fjvokl upwar` at tmd

rdcdasd.

2. (b) Tsd dquatojk 2-12, sdttokl tmd

gokac spdd` v 6 >, tj gok` tmd dxtra actotu`d

laokd` by tmd smdcc ùd tj ots okotoac upwar`spdd`, ak` a`` ot tj tmd 12.4 f9

( )

( )

222 2

>

fax 2

fax

> 4.2> f/s12.4 f 12.4 f

2 2 ?.=1 f/s

12.4 f 1.5= f 15.? f

v v y

l

y

−−6 + 6 +

− −

6 + 6

5. (e) Pmd tofd tmd smdcc travdcs upwar` os tmd tofd ot

tahds lravoty tj brokl tmd spdd` tj zdrj (dquatojk 2-<)9

>

2

> 4.2 f/s>.45 s

?.=1 f/s

v vt

l

− −6 6 6

− −

0. Pmd tofd tmd smdcc travdcs `jwk os ljvdrkd` by

tmd òstaked ak` tmd aeedcdratojk (dquatojk 2-11)9 ( )

2 21 1> > >2 2

>

2

> >

2 15.? f21.7= s

?.=1 f/s

x x v t lt x lt

xt

l

6 + − ⇒ 6 + −

6 6 6

4. Pmd tjtac tofd jg gcolmt os tmd suf9 tjtac up `jwk >.45 1.7= s 2.21 st t t 6 + 6 + 6

7. (`) Pmd spdd` jg tmd smdcc upjk ofpaet

os lovdk by tmd aeedcdratojk jg lravoty ak`

tmd gacc tofd (dquatojk 2-<)9

( )( )2

> > ?.=1 f/s 1.7= s 17.4 f/s

17.4 f/s

v v lt

v

6 − 6 − 6 −

6

Oksolmt9 Pmdrd ard a varodty jg jtmdr ways tj sjcvd tmos prjbcdf. Gjr okstaked, yju eak gok` tmd gokac vdcjeoty jg 17.4

f/s ok part (`) by usokl dquatojk 2-12 wotm > 4.2 f/sv 6 ak` 12.4 f xΐ 6 − wotmjut usokl aky tofd okgjrfatojk. Pry ot!

1>=. ôeturd tmd ^rjbcdf9 Pmd coquo` squorts straolmt upwar`, scjws `jwk, ak` fjfdktarocy ejfds tj rdst bdgjrd gaccokl


Utratdly9 Gok` tmd tofd jg gcolmt by dxpcjotokl tmd syffdtry jg tmd sotuatojk. Og ot tahds tofd t gjr lravoty tj scjw tmd

coquo` `rjps `jwk grjf tmdor okotoac spdd` v> tj zdrj, ot wocc tahd tmd safd afjukt jg tofd tj aeedcdratd tmdf baeh tj tmd

safd spdd`. Pmdy tmdrdgjrd cak` at tmd safd spdd v> wotm wmoem tmdy wdrd squortd`. Tsd tmos gaet tjldtmdr wotm

dquatojk 2-< tj gok` tmd tofd jg gcolmt. Pmd faxofuf mdolmt tmd `rjps aemodvd os rdcatd` tj tmd squard jg v>, as okòeatd`

by dquatojk 2-12.

Ujcutojk9 1. (a) Pmd tofd jg gcolmtgjr > 1.4 f/sv 6 , usokl dq. 2-<9

( ) ( )> >> >

22 1.4 f/s2 >.51 s?.=1 f/s

v vv v vt l l l

− −−6 6 6 6 6− −

2. (b) Pmd faxofuf mdolmt gjr

> 1.4 f/sv 6 , usokl dq. 2-129

( )

( )

22 2 2 2 2

> > >

2

1.4 f/s>>.11 f

2 2 2 2 ?.=1 f/s

v v v v x

l l l

− −ΐ 6 6 6 6 6

− −

Oksolmt9 Pmd syffdtry jg tmd fjtojk jg a grddcy gaccokl jbidet eak jgtdk bd a usdguc tjjc gjr sjcvokl prjbcdfs quoehcy.





2 ― 5<

1>?. ^oeturd tmd ^rjbcdf9 Pmd traidetjrods jg tmd baccjjk ak`

eafdra ard smjwk at rolmt. Pmd baccjjk rosds at a stda`y ratd

wmocd tmd eafdra‟s spdd` os ejktokuaccy scjwokl `jwk uk`dr tmdokgcudked jg lravoty. Pmd eafdra os eaulmt wmdk tmd twj

traidetjrods fddt.

Utratdly9 Pmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg tofd ak` vdcjeoty (dquatojk 2-1>) eak bd usd` tj `dserobd tmd

baccjjk, wmocd tmd dquatojk gjr pjsotojk as a guketojk jg tofdak` aeedcdratojk (dquatojk 2-11) eak bd usd` tj `dserobd tmd

eafdra‟s fjtojk. Udt tmdsd twj dquatojks dquac tj daem jtmdr tj

gok` tmd tofd at wmoem tmd eafdra os eaulmt. Pmdk gok` tmdmdolmt jg tmd baccjjk at tmd okstakt tmd eafdra os eaulmt.

Ujcutojk9 1. \rotd dquatojk 2-1> gjr tmd baccjjk9 ,>b b b x x v t 6 +

2. \rotd dquatojk 2-11 gjr tmd eafdra921

,> 2>e e x v t lt 6 + −

5. Udt b e x x6 ak` sjcvd gjr t 9

( )

21,> ,> 2

21,> ,> 2

>

b b e

b e b

x v t v t lt

x v v t lt

+ 6 −

6 − + − −

0. Fuctopcy by−

1 ak` oksdrt tmd kufbdrs9 ( ) ( )2 2

12

2

> 2.4 f 15 2.> f/s ?.=1 f/s

> 2.4 11 0.?

t t

t t

6 − − +6 − +

4. Appcy tmd qua`ratoe gjrfuca ak` sjcvd gjr t. Pmd

carldr rjjt ejrrdspjk`s tj tmd tofd wmdk tmd eafdra

wjuc` pass tmd baccjjk a sdejk` tofd, jk ots way

`jwk baeh tj tmd lrjuk`.

( )( )22 11 11 0 0.? 2.40

2 ?.=

>.27 jr 2.> s

b b aet

a

t

+ ± −− ± −6 6

6

7. Gok` tmd mdolmt jg tmd baccjjk at tmat tofd9 ( )( ),> 2.4 f 2.> f/s >.27 s 5.> fb b b x x v t 6 + 6 + 6

Oksolmt9 Og tmd passdkldr fossds tmd eafdra tmd gorst tofd, smd mas akjtmdr smjt at ot agtdr 2.> s (grjf tmd tofd ot os

tmrjwk) wmdk tmd eafdra os jk ots way baeh tjwar` tmd lrjuk`.





2 ― 5=

11>. ôeturd tmd ^rjbcdf9 Pmd traidetjrods jg tmd baccjjk ak`

eafdra ard smjwk at rolmt. Pmd baccjjk rosds at a stda`y ratd

wmocd tmd eafdra‟s spdd` os ejktokuaccy scjwokl `jwk uk`dr tmd okgcudked jg lravoty. Pmd eafdra os eaulmt wmdk tmd twj

traidetjrods fddt.

Utratdly9 Pmd eafdra fddts tmd baccjjk wmdk tmd pjsotojks arddquac, sj tmat os jur startokl pjokt. Gjr tmd easd wmdk tmd

eafdra iust bardcy fddts tmd baccjjk, tmd vdcjeoty jg tmd eafdrafust fatem tmd vdcjeoty jg tmd baccjjk (2.> f/s). \d usd tmos

gaet tj gok` tmd tofd tmd twj fust fddt, ak` substotutd tmat oktj

tmd pjsotojk dquatojk. \d eak tmdk sjcvd gjr tmd okotoac vdcjeotyjg tmd eafdra.

Ujcutojk9 1. \rotd dquatojk 2-1> gjr tmd baccjjk9 ,>b b b x x v t 6 +

2. \rotd dquatojk 2-12 gjr tmd eafdra92 2

,>

2

e e

e

v v x

l

−6

−

5. Udt b e x x6 ak` sjcvd gjr ,>ev 9 ( )

2 2

,> 2 2

,> ,> ,>22

e e

b b e e b b

v v x v t v v l x v t

l

−+ 6 ⇒ 6 + +

−

0. As okòeatd` abjvd, tmd eafdra wocc bd eaulmt kjtjkcy wmdk ot‟s at tmd safd pjsotojk as tmd baccjjk, but

wmdk ots vdcjeoty os tmd safd as wdcc, sj sdt 9e bv v6

2 2

,> ,>2 2e b b bv v lx lv t 6 + +

4. Pmd twj wocc fddt at a tofd wmdk tmdor vdcjeotods ard

dquac. \rotd dquatojk 2-< gjr tmd eafdra ak` sdt otsgokac vdcjeoty dquac tj tmd baccjjk‟s vdcjeoty, ak` gok`

tmd tofd.

,>

,>

e e b

e b

v v lt v

v vt

l

6 − 6

−6

7. Uubstotutd tmd tofd oktj tmd dquatojk ok stdp 09 ( )

( ) ( )( )

( )

2 2

,> ,> ,>

2 2

,> ,> ,>

22 2

,> ,>

2 2 2

,> ,>

2 2

2 2 >

2 2.> f/s 2.> f/s 2 ?.=1 f/s 2.4 f >

0.> 04 f /s >

e b b b e b

e b e b b

e e

e e

v v lx v v v

v v v v lx

v v

v v

6 + + −

− + − 6

− + − 6

− − 6

<. _ju eak ldt tmd rjjts usokl tmd qua`ratoe gjrfuca,

but yju folmt rdejlkozd tmd sofpcd gaetjrs mdrd. Jkcytmd pjsotovd rjjt ejrrdspjk`s tj tmd eafdra ljokl

upwar` 9

( )( )4 ? >

4.>, ?.> f/s

e e

e

v v

v

+ − 6

6 −

Oksolmt9 Pmos os a ejfpcoeatd` prjbcdf tmat acways dk`s wotm a qua`ratoe sjcutojk. Ot rdquord` tmd hok` jg stratdly tmat

fust usuaccy bd fappd` jut agtdr tryokl a gdw tmokls8 `jk‟t gddc ba` og yju ò`k‟t oktuotovdcy emjjsd tmos stratdly. Pmdrd

ard jtmdr stratdlods tmat wjrh, but tmdy ard dquaccy ejfpcoeatd`.





2 ― 5?

111. ôeturd tmd ^rjbcdf9 Pmd watdr smjjts straolmt upwar`, scjws `jwk, ak` fjfdktarocy ejfds tj rdst bdgjrd gaccokl


Utratdly9 Gok` tmd mdolmt jg tmd ldysdr by dxpcjotokl tmd syffdtry jg tmd sotuatojk. Og ot tahds tofd t gjr lravoty tj scjw

tmd watdr `jwk grjf ots okotoac spdd` v> tj zdrj, ot wocc tahd tmd safd afjukt jg tofd tj aeedcdratd ot baeh tj tmd safd

spdd`. Pmd mdolmt jg tmd ldysdr os tmdrdgjrd `dtdrfokd` by tmd òstaked tmd watdr wocc gacc grjf rdst ok tofd t (dquatojk

2-11). Lravoty wocc scjw tmd watdr `jwk grjf ots okotoac vdcjeoty tj zdrj ok tofd t at a hkjwk ratd (2?.=1 f/s− ), sj tmat

gaet eak bd usd` tj gok` tmd okotoac vdcjeoty (dquatojk 2-<).

Ujcutojk9 1. (a) Ujcvd dquatojk 2-11 gjr x>, sdttokl > x 6

ak` > >v 6 gjr tmd easd wmdk tmd watdr gaccs grjf rdst ok tofd t 9

21> 2

21fax > 2

> > x l t

x x l t

6 + −

6 6

2. (b) Tsd dquatojk 2-< tj gok` tmd okotoac vdcjeoty og tmd gokac

vdcjeoty os zdrj (upwar` pjrtojk jg tmd gcolmt)9>

>

>v v l t

v l t

6 − 6

6

5. (e) Uubstotutd t 6 1.74 s oktj tmd dquatojk grjf stdp 19 ( )( )221

fax 2?.=1 f/s 1.74 s 15.0 f x 6 6

0. (`) Uubstotutd t 6 1.74 s oktj tmd dquatojk grjf stdp 29 ( )( )2

>?.=1 f/s 1.74 s 17.2 f/sv 6 6

Oksolmt9 Og yju rjuk` jgg l 6 1> f/s2, yju eak ofprdss yjur grodk`s by fdfjrozokl tmdsd sofpcd gjrfucad ak` `jokl tmd

quoeh eaceucatojks ok yjur mda`!

112. ôeturd tmd ^rjbcdf9 Pmd traidetjrods jg tmd twj baccs ard smjwk at

rolmt. Rdfdfbdr tmat ok daem easd tmd baccs ard travdcokl straolmt up ak`straolmt `jwk8 tmd lrapms cjjh parabjcoe bdeausd tofd os tmd x axos. Bacc

B os tjssd` upwar` at tmd okstakt bacc A rdaemds tmd pdah jg ots gcolmt. Bacc

A mas bdluk ots `dsedkt wmdk ot os passd` by bacc B, wmoem os stocc jk otsway up tjwar` ots pdah.

Utratdly9 Pmd pjsotojks ard dquac tj daem jtmdr wmdk tmd baccs erjss patms. Pmd caukem tofds ard jggsdt by tmd tofd ot tahds tmd bacc tj rdaem

tmd pdah jg ots gcolmt. Pmat tofd os lovdk by tmd tofd ot tahds lravoty tj

scjw tmd bacc grjf v> `jwk tj zdrj (dquatojk 2-<). Pmd tofd tmd baccs

erjss os òrdetcy bdtwddk tmd tofd bacc B os caukemd` ak` bacc A cak`s.

Jked wd mavd tmd tofd golurd` jut wd eak gok` tmd pjsotojk jg bacc A oktdrfs jg ots faxofuf mdolmt m.

Ujcutojk9 1. Pmd pcjt jg x-vdrsus-t gjr tmd twj baccs os smjwk abjvd.

2. Iu`lokl grjf tmd pcjt tmd baccs wocc erjss patms abjvd m / 2.

5. Gok` tmd tofd ot tahds bacc A tj rdaem ots pdah9> > >

>v v v vt

l l l

− −6 6 6

− −

0. Bdeausd bacc B os caukemd` at tofd >v l ak` bacc A cak`s at tofd >2v l , tmd twj baccs wocc erjss at a tofd fo`way

bdtwddk tmdsd, jr at tofd erjss >5 2t v l6 .

4. Gok` tmd pjsotojk jg bacc A at tofd t erjss usokl dquatojk 2-119

2 2

2 > > >1 1> erjss erjss >2 2

5 5 5

2 2 = A

v v v x v t lt v l

l l l

⎘ ⎛ ⎘ ⎛6 − 6 − 6⎓ ⎚ ⎓ ⎚

⎖ ⎮ ⎖ ⎮

7. Gok` tmd faxofuf mdolmt m usokl dquatojk 2-1292

2 2 >

>> 2

2

vv lm m

l6 − ⇒ 6

<. Kjw wrotd A x ok tdrfs jg m9

2

> 5

02

>

5 = 5

02

A

A

v l x x m

m v l6 6 ⇒ 6

Oksolmt9 Pmd baccs `j kjt erjss rolmt at m / 2 bdeausd tmdy spdk` fjrd tofd abjvd m / 2 tmak tmdy `j bdcjw, bdeausd tmdor

avdrald spdd`s ard sfaccdr ùrokl tmd tjp macg jg tmdor gcolmt.





2 ― 0>

115. ôeturd tmd ^rjbcdf9 Pmd twj wdolmts gacc straolmt `jwkwar` grjf rdst acjkl a sofocar patm dxedpt

at oggdrdkt tofds.

Utratdly9 Pmd prjbcdf rdquords tmat tmd tofd tj gacc a òstaked m grjf rdst (tmd tofd bdtwddk rdcdasdak` tmd gorst tmu`) os tmd tofd tj gacc a òstaked m + 2> ef (sdejk` tmu`) fokus tmd tofd tj gacc a

òstaked m (gorst tmu`). \d eak sdt tmdsd tofds dquac tj daem jtmdr, usd dquatojk 2-11 tj wrotd tmd

tofds ok tdrfs jg mdolmts, ak` tmdk sjcvd gjr m.

Ujcutojk9 1. Udt tmd tofd

oktdrvacs dquac tj daem jtmdr9 2> 2>2m m m m mt t t t t + +6 − ⇒ 6

2. Kjw usd dquatojk 2-11 tj wrotd

tmd tofds ok tdrfs jg tmd mdolmts9

( )2 2>.> ef22

mm

l l

+6

5. Uquard bjtm so`ds ak` fuctopcy by l / 29 0 2>.> ef

2>.>ef 7.7< ef

5

m m

m

6 +

6 6

Oksolmt9 Pmd tdksojk ok tmd strokl wocc bd zdrj ùrokl tmd `dsedkt bdeausd daem bacc aeedcdratds at tmd safd ratd.

Pmdrdgjrd tmd strokl wocc mavd kj dggdet upjk tmd fjtojk jg tmd baccs.

110. ôeturd tmd ^rjbcdf9 Pmd bacc gaccs straolmt `jwkwar` grjf rdst at ak okotoac mdolmt m.

Utratdly9 Pmd prjbcdf rdquords tmat tmd tofd tj gacc tmd gokac 5/0 m grjf rdst os 1.>> s. Gok` tmd

vdcjeoty v1 at » m abjvd tmd lrjuk` usokl dquatojk 2-12. Tsd dquatojk 2-11 acjkl wotm tmat okotoacvdcjeoty ak` tmd tofd dcapsd` tj `dtdrfokd m. Pmdk tmd tjtac tofd jg gacc eak bd gjuk` usokl dquatojk

2-11 alaok, tmos tofd wotm ak okotoac vdcjeoty jg zdrj.

Ujcutojk9 1. (a) Gok` tmd vdcjeoty v1 jg tmd

bacc agtdr gaccokl a òstaked ³ m9( )2 2 1 1

1 10 2> 2 2v l x l m v lm6 + ΐ 6 ⇒ 6

2. Kjw oksdrt tmat vdcjeoty as tmd okotoac

vdcjeoty gjr tmd rdfaokokl pjrtojk jg tmdgacc oktj dquatojk 2-119 ( )

211 2

25 1 1

0 2 2

x v t lt

m lm t lt

ΐ 6 +

6 +

5. Pmd tofd t os 1.>> s as lovdk ok tmd prjbcdf

statdfdkt. Rdarrakld tmd abjvd dquatojk ak`squard bjtm so`ds tj ldt a qua`ratoe dquatojk9

( )( )( )

( )

( )

( )( ) ( ) ( )

25 1 1

0 2 2

2 2 2 0 2? 51 1 1

17 2 0 0 2

2 2 2 0? 4 1

17 0 0

2 2 2 02> 0

? ?

22 02 2 22> 0

? ?

2

2

>

>

?.=1 f/s 1.>> s ?.=1 f/s 1.>> s >

21.= 02.= >

m lt lm t

m lt m l t lmt

m lt m l t

m lt m l t

m m

m m

− 6

− + 6

− + 6

− + 6

− + 6

− + 6

0. Kjw appcy tmd qua`ratoe gjrfuca gjr m9( ) ( )( )

( )

22 21.= 21.= 0 1 02.=0

2.1=, 1?.7 f2 2 1

b b aem

a

± −− ± −6 6 6

4. (b) Tsd dquatojk 2-11 alaok tj gok`

tmd tjtac tofd jg gacc9( )

2

2 1?.7 f22.>> s

?.=1 f/s

mt

l6 6 6

Oksolmt9 Pmd gorst rjjt ok stdp 0 (2.1= f) os tmrjwk jut bdeausd tmd tjtac gacc tofd grjf tmat mdolmt wjuc` bd cdss tmak

1.>> s, but tmd bacc os suppjsd` tj bd ok tmd aor gjr cjkldr tmak 1.>> s. Kjtoed ot tahds macg tmd tjtac gcolmt tofd tj gacc tmd

gorst quartdr jg tmd gacc òstaked, ak` macg tj gacc tmd gokac tmrdd quartdrs.

m

» m

m

2> ef





2 ― 01

114. ôeturd tmd ^rjbcdf9 Pmd tmrdd `rjps ard pjsotojkd` as `dpoetd` at rolmt. Pmdy acc gacc straolmt

`jwkwar` grjf ak okotoac mdolmt jg 0.> f.

Utratdly9 Pmd tofd oktdrvac bdtwddk `rjps os macg tmd tofd ot tahds a `rjp tj gacc tmd dktord 0.> f. Tsdtmos gaet tj gok` tmd pjsotojk ak` vdcjeoty jg `rjp 2 wmdk `rjp 1 mots tmd pjjc (dquatojks 2-11 ak` 2-<).

Pmdk tmd tofd oktdrvac bdtwddk `rjps eak bd usd` tj gok` tmd kufbdr jg `rjps pdr fokutd.

Ujcutojk9 1. (a) Gok` tmd tofd oktdrvac bdtwddk

`rjps, usokl dquatojk 2-11 tj gok` tmd gacc tofd9

( )1

gacc2 2

2 0.> f1 2 1>.04 s

2 2 ?.=1 f/s

xt t

l

ΐ 6 6 6 6

2. Kjw usd dquatojk 2-11 tj gok` tmd pjsotojkjg `rjp 29

( ) ( )( )2 221 1

2 2 2

2

> ?.=1 f/s >.04 s

>.?? f bdcjw tmd stacaetotd jr

0.> >.?? f 5.> f abjvd tmd pjjc

x l t

x

6 + ΐ 6

6

− 6

5. Tsd dquatojk 2-< tj gok` tmd spdd` jg `rjp 29 ( )( )2> ?.=1 f/s >.04 s 0.0 f/sv l t 6 + ΐ 6 6

0. (b) Gok` tmd `rjp ratd grjf tmd tofd oktdrvac91 rjp 7> s

15> `rjps/fok>.04 s 1 fok

@ 6 Ü 6

Oksolmt9 Kjtd tmat ot tahds macg tmd `rjp tofd tj gacc tmd gorst quartdr jg tmd `rjp òstaked, ak` macg tmd tofd tj gacc tmdgokac tmrdd quartdrs jg tmd òstaked.

117. ôeturd tmd ^rjbcdf9 Pmd lcjvd gaccs straolmt `jwkwar` grjf rdst, aeedcdratds tj a faxofuf spdd` uk`dr tmd okgcudked

jg lravoty, tmdk `dedcdratds ùd tj ots oktdraetojk wotm tmd skjw bdgjrd ejfokl tj rdst at a `dptm ` bdcjw tmd surgaed jg tmd skjw.

Utratdly9 \d eak gok` tmd faxofuf spdd` jg tmd lcjvd grjf ots okotoac mdolmt ak` tmd aeedcdratojk jg lravoty by usokl

dquatojk 2-12. Pmd safd dquatojk eak bd appcod` alaok, tmos tofd wotm a zdrj gokac spdd` okstda` jg zdrj okotoac spdd`, tjgok` tmd aeedcdratojk eausd` by tmd skjw. Cdt `jwkwar` bd tmd pjsotovd òrdetojk.

Ujcutojk9 1. (a) Ujcvd dquatojk 2-12

gjr v, assufokl > >v 6 92

> 2 2v lm lm6 + 6

2. (b) Tsd dquatojk 2-12 tj gok`

tmd aeedcdratojk eausd` by tmd skjw9 ( )2

2 2

>> 2 2 2m

v a` a` lm a l`

6 + ⇒ − 6 ⇒ 6 −

5. Pmd kdlatovd solk jk tmd aeedcdratojk fdaks tmd lcjvd os aeedcdratd` upwar` ùrokl ots oktdraetojk wotm tmd skjw.

Oksolmt9 Ok Emaptdr 4 wd wocc akacyzd tmd fjtojk jg jbidets cohd tmos lcjvd ok tdrfs jg gjred vdetjrs. Pmos fjtojk eak

acsj bd dxpcaokd` ok tdrfs jg dkdrly usokl tmd tjjcs oktrjùed` ok Emaptdrs < ak` =.

11<. ôeturd tmd ^rjbcdf9 Pmd bacc rosds straolmt upwar`, passds tmd pjwdr cokd, fjfdktarocy ejfds tj rdst, ak` gaccs baeh

tj Dartm alaok, passokl tmd pjwdr cokd a sdejk` tofd jk ots way `jwk.

Utratdly9 Pmd bacc wocc rdaem tmd pdah jg ots gcolmt at a tofd òrdetcy bdtwddk tmd tofds ot passds tmd pjwdr cokd. Pmd

tofd tj rdaem tmd pdah jg gcolmt eak bd usd` tj gok` tmd okotoac vdcjeoty usokl dquatojk 2-<, ak` tmd okotoac vdcjeoty eaktmdk bd usd` tj gok` tmd mdolmt jg tmd pjwdr cokds usokl dquatojk 2-11.

Ujcutojk9 1. Gok` tmd tofd at wmoem

tmd bacc rdaemds ots faxofuf actotu`d9

( ) ( )1 1 pdah cokd up cokd `jwk cokd up2 2

pdah

>.<4 s 1.4 >.<4 s

1.1 s

t t t t

t

6 + − 6 + −

6

2. Gok` tmd okotoac vdcjeoty usokl dquatojk 2-<9 ( )( )2

> pdah >> ?.=1 f/s 1.1 s 11 f/sv lt v6 − ⇒ 6 6

5. Gok` tmd mdolmt jg tmd pjwdr cokd usokl dquatojk 2-119

( )( ) ( )( )

21> cokd up cokd up2

221

2

>

11 f/s >.<4 s ?.=1 f/s >.<4 s 4.4 f

x v t lt

x

6 + −

6 − 6

Oksolmt9 As os jgtdk tmd easd, tmdrd ard sdvdrac jtmdr ways tj sjcvd tmos prjbcdf. Pry sdttokl tmd mdolmts at >.<4 s ak`

1.4 s dquac tj daem jtmdr ak` sjcvokl gjr v>. Eak yju tmokh jg ydt akjtmdr way:

0.> f x2

stacaetotd

1

2

5





2 ― 02

11=. ôeturd tmd ^rjbcdf9 Pmd twj rjehs gacc straolmt `jwkwar` acjkl a sofocar patm dxedpt at òggdrdkt

tofds.

Utratdly9 Gorst gok` tmd tofd dcapsd` bdtwddk tmd rdcdasd jg tmd twj rjehs by gokòkl tmd tofdrdquord` gjr tmd gorst rjeh tj gacc a òstaked m, usokl tmd dquatojk jg fjtojk gjr pjsotojk as a guketojk

jg tofd ak` aeedcdratojk (dquatojk 2-11). Pmd pjsotojks as a guketojk jg tofd gjr daem rjeh eak tmdk

bd ejfpard` tj gok` a sdparatojk òstaked as a guketojk jg tofd.

Ujcutojk9 1. (a) Gok` tmd tofd rdquord` gjr rjeh A tjgacc a òstaked m9 2 2m x mt l l

ΐ6 6

2. Cdt t rdprdsdkt tmd tofd dcapsd` grjf tmd okstakt

rjeh B os `rjppd`. Pmd pjsotojk jg rjeh A (dquatojk

2-11) os tmus9

( )2 2 21 1 1

2 2 2> A m m m x l t t lt l t t lt 6 + + 6 + +

5. Pmd pjsotojk jg rjeh B (dquatojk 2-11) os92 21 1

2 2> B x lt lt 6 + 6

0. Gok` tmd sdparatojk bdtwddk tmd rjehs9 ( )

( )

2 2 21 1 1

2 2 2

21 1

2 2

2 2

2 2

A B m m

m m

U x x lt l t t lt lt

m mU l t t lt lt l

l l

U t lm m m lm t

6 − 6 + + −

6 + 6 +

6 + 6 +

Oksolmt9 Pmd sdparatojk bdtwddk tmd twj rjehs okerdasds cokdarcy wotm tofd t .

11?. ôeturd tmd ^rjbcdf9 Pmd arrjw travdcs mjrozjktaccy at 2>.> f/s ak` ofpaets tmd Utyrjgjaf. Ot ejktokuds tj travdc ok

tmd pjsotovd òrdetojk, but fjrd scjwcy ùd tj ots ejccosojk wotm tmd Utyrjgjaf. Pmd arrjw ak` tmd Utyrjgjaf tmdk fjvd

tjldtmdr at tmd safd spdd` ok tmd pjsotovd òrdetojk.

Utratdly9 Gok` tmd gokac vdcjeoty jg tmd bcjeh ok tdrfs jg tmd ejccosojk tofd t ΐ by usokl dquatojk 2-<. Bdeausd tmos os

acsj tmd gokac vdcjeoty jg tmd arrjw, tmd ejccosojk tofd t ΐ eak bd `dtdrfokd` by usokl tmd hkjwk aeedcdratojks ak` tmd

okotoac vdcjeoty jg tmd arrjw. Pmd gokac vdcjeoty ak` pdkdtratojk `dptm travdcd` eak tmdk bd gjuk` grjf appcyokl

dquatojks 2-< ak` 2-11.

Ujcutojk9 1. (a) Udt tmd gokac vdcjeotods jg tmd arrjw

ak` tmd bcjeh dquac tj daem jtmdr ak` appcy dquatojk

2-< tj gok` t ΐ 9

( )

,>

,> ,>

2

>

2>.> f/s

04> 144> f/s

>.>1>> s 1>.> fs

a b

a a b

a a

a b b a

v v

v a t a t

v vt

a a a a

t

6

+ ΐ 6 + ΐ

−ΐ 6 6 6

− − − −

ΐ 6 6

2. (b) Kjw appcy dquatojk 2-< tj gok`b

v 9 ( ) ( )204> f/s >.>1>> s 0.4> f/sb b

v a t 6 ΐ 6 6

5. (e) Pmd pdkdtratojk òstaked os a bot troehy bdeausd bjtm tmd arrjw ak` tmd bcjeh fjvd wmocd tmdy ard

ejccoòkl. Pmd pdkdtratojk òstaked os tmd òggdrdked

bdtwddk mjw gar tmd arrjw fjvds ak` mjw gar tmd bcjeh fjvds ùrokl tmd ejccosojk tofd oktdrvac.

( ) ( )

( )( ) ( )( )

( )( )

arrjw bcjeh

2 21 1,> 2 2

2212

221

2

2>.> f/s >.>1>> s 144> f/s >.>1>> s

04> f/s >.>1>> s

>.1224 f >.>224 f >.1>> f 1>.> ef

a a b

` x x

v t a t a t

`

6 ΐ − ΐ

6 ΐ + ΐ − ΐ

⎡ ⎠+ −⎢ ⎤6⎢ ⎤−⎥ ⎧

6 − 6 6

Oksolmt9 \d ejuc` acsj akacyzd tmos ejccosojk usokl tmd ejkedpt jg fjfdktuf ejksdrvatojk (Emaptdr ?) ak` wjrh ak`

dkdrly (Emaptdr <).





2 ― 05

12>. ôeturd tmd ^rjbcdf9 Pmd bacc appdars at tmd bjttjf d`ld jg tmd wok`jw, rosokl straolmt

upwar` wotm okotoac spdd` v>. Ot travdcs upwar`, osappdarokl bdyjk` tmd tjp d`ld jg tmd

wok`jw, ejfds tj rdst fjfdktarocy, ak` tmdk gaccs straolmt jwkwar`, rdappdarokl sjfdtofd catdr at tmd tjp d`ld jg tmd wok`jw. Ok tmd `rawokl at rolmt tmd fjtojk jg tmd bacc os

jggsdt mjrozjktaccy gjr ecaroty.

Utratdly9 Cdt t 6 > ejrrdspjk` tj tmd okstakt tmd bacc gorst appdars at tmd bjttjf d`ld jg tmdwok`jw wotm spdd` v>. \rotd tmd dquatojk jg pjsotojk as a guketojk jg tofd ak` aeedcdra-

tojk (dquatojk 2-11) gjr wmdk tmd bacc os at tmd tjp d`ld (pjsotojk 2) ok jr`dr tj gok`v

>.Tsd v> tj gok` tmd tofd tj lj grjf pjsotojk 1 tj tmd pdah jg tmd gcolmt (dquatojk 2-<).

Uubtraet >.24 s grjf tmat tofd tj gok` tmd tofd tj lj grjf pjsotojk 2 tj tmd pdah jg tmdgcolmt. Pmd tofd dcapsd` bdtwddk pjsotojks 2 ak` 5 os twoed tmd tofd tj lj grjf pjsotojk 2

tj tmd pdah jg tmd gcolmt. Pmd tofd grjf pjsotojk 2 tj tmd pdah eak bd usd` tj gok` m grjf

dquatojk 2-11.

Ujcutojk9 1. (a) \rotd dquatojk 2-11gjr pjsotojks 1 ak` 2, ak` sjcvd gjr v>9 ( ) ( )

21> 2 22

22121222

>

2

1.>4 f ?.=1 f/s >.24 s4.0 f/s

>.24 s

` v t lt

` lt v

t

6 −

++6 6 6

2. Gok` tmd tofd tj lj grjf pjsotojk 1 tjtmd pdah jg tmd gcolmt usokl dquatojk 2-<9

>

1, 2

> 4.0 f/s>.44 s

?.=1 f/s p

vt

l

−ΐ 6 6 6

−

5. Uubtraet >.24 s tj gok` tmd tofd tj lj

grjf pjsotojk 2 tj tmd pdah jg tmd gcolmt9 2, 1, 1,2>.44 >.24 s >.5> s

p pt t t ΐ 6 ΐ − ΐ 6 − 6

0. Pmd tofd tj rdappdar os twoed tmos tofd9 ( )2,5 2,2 2 >.5> s >.7> s pt t ΐ 6 ΐ 6 6

4. (b) Pmd mdolmt m eak bd gjuk` grjf 2, pt ΐ

ak` dquatojk 2-11, by ejkso`drokl tmd bacc`rjppokl grjf rdst at tmd pdah tj pjsotojk 59

( )( )

212,2

221

2

> >

?.=1 f/s >.5> s >.00 f

pm l t

m

6 + − ΐ

6 6

Oksolmt9 As usuac tmdrd ard jtmdr ways tj sjcvd tmos prjbcdf. Pry gokòkl tmd vdcjeoty at pjsotojk 2 ak` usd ot tjldtmdr

wotm tmd aeedcdratojk jg lravoty ak` tmd avdrald vdcjeoty grjf pjsotojk 2 tj tmd pdah tj gok` 2,5t ΐ ak` m.

121. ôeturd tmd ^rjbcdf9 Pmos dxdreosd ejkso`drs a ldkdroe jbidet travdcokl ok a straolmt cokd wotm ejkstakt aeedcdratojk.

Utratdly9 Fakopucatd tmd sulldstd` dquatojks wotm acldbra tj `drovd tmd `dsord` rdsucts.

Ujcutojk9 1. (a) Bdlok wotm dquatojk 2-129 ( )2 2

> >2v v a x x6 + −

2. Udt x 6 > ak` sjcvd gjr v9 2

> >2v v ax6 ± −

5. (b) Gorst wrotd dquatojk 2-< ak`substotutd gjr v. Pmdk sjcvd gjr t 9

>

2

> > >

2

> > >

2

2

v v at

v ax v at

v v axt

a

6 +

± − 6 +

− ± −6

0. (e) \rotd dquatojk 2-11 as lovdk akàppcy tmd qua`ratoe gjrfuca tj sjcvd gjr t 9( )( )

( )

21

> > 2

2 12> > >2

12

2

> > >

>

00

2 2

2

x v t at

v v a xb b aet

a a

v v axt

a

6 + +

− ± −− ± −6 6

− ± −6

Oksolmt9 \mdk ak jbidet uk`drljds ukogjrf aeedcdratojk ots pjsotojk os a qua`ratoe guketojk jg tofd. Pmd qua`ratoe

gjrfuca os tmdrdgjrd ak apprjproatd jkd tj `dserobd tmd fjtojk jg tmd jbidet.

`

v>

m

1

2 5





2 ― 00

122. ôeturd tmd ^rjbcdf9 Pmd cukar cak`dr gaccs straolmt `jwkwar`, aeedcdratokl jvdr a òstaked jg 0.5> gt bdgjrd ofpaetokl

tmd cukar surgaed.

Utratdly9 Tsd tmd lovdk aeedcdratojk ak` òstaked ak` tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) tj gok` tmdvdcjeoty jg tmd cak`dr iust bdgjrd ofpaet. Tsd tmd hkjwk okotoac ak` gokac vdcjeotods, tjldtmdr wotm tmd òstaked jg tmd

gacc, tj gok` tmd tofd dcapsd` usokl dquatojk 2-1>.

Ujcutojk9 1. (a) Gok` tmd vdcjeoty iust

bdgjrd ofpaet usokl dquatojk 2-129 ( ) ( )( )

2

cak` >

2 2

2

>.4>> gt/s 2 1.72 f/s 5.2= gt/f 0.5> gt 7.<= gt/s

v v a x6 + ΐ

6 + Ü 6

2. (b) Ujcvd dquatojk 2-1> gjr t 9( ) ( )

gacc

gacc 1 1> cak`2 2

0.5> gt1.1= s

>.4>> 7.<= gt/s

xt

v v

ΐ6 6 6

+ +

Oksolmt9 Ak actdrkatovd stratdly wjuc` bd tj sjcvd dquatojk 2-11 as a qua`ratoe dquatojk ok t . Assufokl tmd cak`dr gddtma` cottcd ok tmd way jg smjeh absjrbdrs, tmd cak`dr eafd tj rdst ok a òstaked lovdk by tmd afjukt tmd cukar ùst

ejfpaetd` uk`drkdatm tmd gddt. Uuppjsokl ot was abjut 2 ef, tmd astrjkauts dxpdrodked` a brodg `dedcdratojk jg

1>7 f/s2 6 11l! Baf!

125. ôeturd tmd ^rjbcdf9 Pmd cukar cak`dr gaccs straolmt `jwkwar`, aeedcdratokl jvdr a òstaked jg 0.5> gt bdgjrd ofpaetokltmd cukar surgaed.

Utratdly9 Tsd tmd lovdk aeedcdratojk ak` òstaked ak` tmd tofd-grdd dquatojk jg fjtojk (dquatojk 2-12) tj gok` tmdvdcjeoty jg tmd cak`dr iust bdgjrd ofpaet.

Ujcutojk9 Gok` tmd vdcjeoty iust

bdgjrd ofpaet usokl dquatojk 2-129( ) ( )( )

2

cak` >

2 2

2

>.4>> gt/s 2 1.72 f/s 5.2= gt/f 0.5> gt 7.<= gt/s

v v a x6 + ΐ

6 + Ü 6

Oksolmt9 Pmd okotoac spdd` fa`d cottcd òggdrdked8 og yju sdt > >v 6 yju‟cc kjtd tmat cak` 7.<7 gt/s.v 6

120. ôeturd tmd ^rjbcdf9 Pmd cukar cak`dr gaccs straolmt `jwkwar`, aeedcdratokl jvdr a òstaked jg 0.5> gt bdgjrd ofpaetokl

tmd cukar surgaed.

Utratdly9 Pmd cak`dr mas ak okotoac `jwkwar` vdcjeoty ak` aeedcdratds `jwkwar` at a ejkstakt ratd. Tsd tmd hkjwcd`ldtmat tmd vdcjeoty-vdrsus-tofd lrapm os a straolmt cokd gjr ejkstakt aeedcdratojk tj `dtdrfokd wmoem lrapm os tmd

apprjproatd jkd.

Ujcutojk9 Lrapm B os tmd jkcy jkd tmat `dpoets tmd spdd` okerdasokl cokdarcy wotm tofd.

Oksolmt9 Lrapm @ wjuc` bd ak apprjproatd `dpoetojk jg tmd actotu`d vdrsus tofd lrapm.

124. ôeturd tmd ^rjbcdf9 \d ofalokd tmat tmd astrjkauts okerdasd tmd upwar` tmrust, lovokl tmd cukar cak`dr a sfacc upwaràeedcdratojk.

Utratdly9 Pmd cak`dr mas ak okotoac `jwkwar` vdcjeoty ak` aeedcdratds upwar` at a ejkstakt ratd. Pmos fdaks tmd

cak`dr‟s spdd` wjuc` `derdasd at a ejkstakt ratd. Tsd tmd hkjwcd`ld tmat tmd vdcjeoty-vdrsus-tofd lrapm os a straolmt cokd

gjr ejkstakt aeedcdratojk tj `dtdrfokd wmoem lrapm os tmd apprjproatd jkd.

Ujcutojk9 Lrapm E os tmd jkcy jkd tmat `dpoets tmd spdd` `derdasokl cokdarcy wotm tofd.

Oksolmt9 Pmd actotu`d-vdrsus-tofd lrapm ok tmos easd wjuc` eurvd upwar` fuem cohd lrapm A but wjuc` mavd ak okotoaccy

kdlatovd scjpd cohd lrapm @.





2 ― 04

127. ôeturd tmd ^rjbcdf9 Pmd traidetjrods jg tmd spdd`dr ak` pjcoed

ear ard smjwk at rolmt. Pmd spdd`dr fjvds at a ejkstakt vdcjeoty

wmocd tmd pjcoed ear mas a ejkstakt aeedcdratojk, dxedpt tmd pjcoedear os `dcayd` ok tofd grjf wmdk tmd spdd`dr passds ot at x 6 >.

Utratdly9 Pmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg tofd

ak` vdcjeoty (dquatojk 2-1>) eak bd usd` tj `dserobd tmd spdd`dr,wmocd tmd dquatojk gjr pjsotojk as a guketojk jg tofd ak`

aeedcdratojk (dquatojk 2-11) eak bd usd` tj `dserobd tmd pjcoedear‟s fjtojk. Udt tmdsd twj dquatojks dquac tj daem jtmdr ak`

sjcvd tmd rdsuctokl dquatojk tj gok` tmd spdd`dr‟s mda`-start sms x .

Ujcutojk9 1. \rotd dquatojk 2-1> gjr

tmd spdd`dr, wotm t 6 > ejrrdspjkòkl

tj tmd okstakt ot passds tmd pjcoed ear9s sms s x x v t 6 +

2. \rotd dquatojk 2-11 gjr tmd pjcoed ear921

p p2> > x a t 6 + +

5. Udt p s x x6 ak` sjcvd gjr sms x 9

( )( ) ( )( )

21 p sms s2

22 21 1sms p s2 2

sms

5.= f/s 14 s 24 f/s 14 s

45 f

a t x v t

x a t v t

x

6 +

6 − 6 −

6

Oksolmt9 Pmos mda` start ejrrdspjk`s tj abjut 2.1> sdejk`s (vdrogy gjr yjursdcg, ak`/jr dxafokd tmd pcjt) sj tmd pjcoed

jggoedr mas tj bd rda`y tj start tmd emasd vdry sjjk agtdr tmd spdd`dr passds by!

12<. ôeturd tmd ^rjbcdf9 Pmd traidetjrods jg tmd spdd`dr ak` pjcoed

ear ard smjwk at rolmt. Pmd spdd`dr fjvds at a ejkstakt vdcjeoty

wmocd tmd pjcoed ear mas a ejkstakt aeedcdratojk.

Utratdly9 Pmd dquatojk jg fjtojk gjr pjsotojk as a guketojk jg

tofd ak` vdcjeoty (dquatojk 2-1>) eak bd usd` tj `dserobd tmdspdd`dr, wmocd tmd dquatojk gjr pjsotojk as a guketojk jg tofd akàeedcdratojk (dquatojk 2-11) eak bd usd` tj `dserobd tmd pjcoed

ear‟s fjtojk. Udt tmdsd twj dquatojks dquac tj daem jtmdr ak`

sjcvd tmd rdsuctokl dquatojk gjr tmd aeedcdratojk jg tmd pjcoed ear.

Ujcutojk9 1. \rotd dquatojk 2-1> gjr

tmd spdd`dr, wotm t 6 > ejrrdspjkòkl

tj tmd okstakt ot passds tmd pjcoed ear9s s> x v t 6 +

2. \rotd dquatojk 2-11 gjr tmd pjcoed ear9 21 p p2

> > x a t 6 + +

5. Udt p s x x6 ak` sjcvd gjr pa 9

( )

21 p s2

2s

p

2 14 f/s20.5 f/s

<.> s

a t v t

va

t

6

6 6 6

Oksolmt9 A gastdr aeedcdratojk jg tmd pjcoed ear wjuc` accjw ot tj eatem tmd spdd`dr ok cdss tmak <.> s.




12=. ôeturd tmd ^rjbcdf9 Pmd traidetjry jg tmd bal jg sak` os smjwk at

rolmt. Agtdr rdcdasd grjf tmd baccjjk ot rosds straolmt up ak` ejfds

fjfdktarocy tj rdst bdgjrd aeedcdratokl straolmt jwkwar` akòfpaetokl tmd lrjuk`.

Utratdly9 Bdeausd tmd okotoac vdcjeoty, aeedcdratojk, ak` actotu`d ard

hkjwk, wd kdd` jkcy usd dquatojk 2-12 tj gok` tmd gokac vdcjeoty.

Ujcutojk9 1. (a) Bdeausd tmd upwar` spdd` jg tmd sak`bal os tmd safd, otwocc laok tmd safd a`òtojkac 2 f ok actotu`d as ot ò` ok tmd jrolokac

Dxafpcd 2-12. Pmdrdgjrd tmd faxofuf mdolmt wocc bd dquac tj 52 f.

2. (b) Appcy dquatojk 2-12 tj gok` tmd gokac vdcjeoty9

( ) ( )( )

2 2

>

2 2

2

7.4 f/s 2 ?.=1 f/s 5>.> f 24 f/s

v v a x

v

6 + ΐ

6 + − − 6

Oksolmt9 Akjtmdr way tj gok` tmd gokac vdcjeoty iust bdgjrd ofpaet os tj accjw tmd sak`bal tj gacc grjf rdst a òstaked jg

52 f. Pry ot!

12?. ôeturd tmd ^rjbcdf9 Pmd bal jg sak` mas ak okotoac `jwkwar` vdcjeoty wmdk ot brdahs grdd grjf tmd baccjjk, ak` os

aeedcdratd` by lravoty uktoc ot mots tmd lrjuk`.

Utratdly9 Bdeausd tmd okotoac vdcjeoty, aeedcdratojk, ak` actotu`d ard hkjwk, wd kdd` jkcy usd dquatojk 2-12 tj gok` tmdgokac vdcjeoty. Pmd tofd eak tmdk bd gjuk` grjf tmd avdrald vdcjeoty ak` tmd òstaked.

Ujcutojk9 1. (a) Appcy dquatojk 2-12 tj gok` tmd gokac v9

( ) ( )( )

2 2

>

2 2

2

0.2 f/s 2 ?.=1 f/s 54.> f 27.4 f/s

v v a x

v

6 + ΐ

6 + − − 6

2. Tsd dquatojk 2-1> tj gok` tmd tofd9( ) ( )

>

1 1>2 2

> 54 f2.5 s

0.4 27.4 f/s

x xt

v v

− −6 6 6

+ − −

5. (b) Appcy dquatojk 2-12 alaok tj gok` v at x 6 14 f9

( ) ( )( )

2 2

>

2 2

2

0.2 f/s 2 ?.=1 f/s 14 54 f 2> f/s

v v a x

v

6 + ΐ

6 + − − 6

Oksolmt9 Akjtmdr way tj gok` tmd `dsedkt tofd jg tmd bal jg sak` os tj sjcvd dquatojk 2-11 usokl tmd qua`ratoe gjrfuca.

Pry ot!

physics chapter 2 answers

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