04-2 displacement (3)
TRANSCRIPT
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Distance and displacements
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Simon is in Causeway Bay. He needs to
1 take a book to Mary at the exit gate ofMongkok MTR, and
2 pass a gift to Jenny at the HKEAA in
Wan Chai.
Wan Chai Causeway Bay
Mongkok
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$3.8Wan ChaiCauseway Bay
$10.0Wan ChaiMongkok$10.0MongkokCauseway Bay
Adult FareToFrom
(a) What is the minimum fare for Simonswhole journey?
He doesnt go out of thegates at Mongkok station.
He doesnt go out of thegates at Mongkok station.
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$3.8Wan ChaiCauseway Bay
$10.0Wan ChaiMongkok$10.0MongkokCauseway Bay
Adult FareToFrom
Warm-up(a) What is the minimum fare for Simons
whole journey?
his position changes from Causeway Baystation to Wan Chai station.
his position changes from Causeway Baystation to Wan Chai station.
For his whole journey,
For his whole journey,
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More should be paid forlonger distance travelled.
Agree
(b) Do you agree with the followingstatements about travelling by MTR?
Disgree
Fare depends on wherehe passes the exit gateonly.
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SI unit: metre
Symbol: m North Pole X
Y
1 Unit of length
1 m was defined as 107 ofa quadrant of the Earth.
1 m was defined as 107 ofa quadrant of the Earth.
Old definition:
But no need to rememberthe exact value
But no need to rememberthe exact value
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Lengthof a straight line going from theold to the new positions
Direction of the movement
2 Displacement and distance
Displacement requires :
i.e. size/magnitude
Simulation
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yourhome
yourschool
A displacement has
Size = lengthof this arrow
displacement fromhome to school
displacement fromhome to school
2 Displacement and distance
To go to school from home...
size &direction.
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Distance = length ofpathyou travelled
( size ofdisplacement)
l1l2
l3
2 Displacement and distance
To go to school from home...yourhome
yourschool
= l1 + l2 + l3
http://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exe -
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Vectora quantity described by its
E.g.displacement,
3 Vectors and scalars
&magnitude (size)direction
velocity,force
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A vector can be represented by an arrow.
It tells us:
length = magnitude
direction
3 Vectors and scalars
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displacement written asAB
startpoint
endpoint
A B
3 Vectors and scalars
To go fromAto B...
path taken
displacement
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quantity described by its magnitude
(size) only
3 Vectors and scalars
Scalar
E.g. temperature,
mass, energydistance, speed,
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total distance = ?
total displacement = ?
= (3 + 4) km = 7 km
total distance
total displacement= (3 + 4) kmnorth
= 7 kmnorth
N
4 km
7 kmnorth
3 km
4 Adding displacementsa Graphical methodA car travels 4 km northA car travels 4 km north then 3 km north.
http://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exe -
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4 Adding displacements
A car travels 4 km northA car travels 4 km north then 3 km south.
4 km
1 kmnorth
3 km
total distance = ?
total displacement = ?
= (3 + 4) km = 7 km
total distance
total displacement= (3 + 4) kmnorth
= 1 kmnorth
N
a Graphical method
http://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exe -
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4 Adding displacements
A car travels 4 km northA car travels 4 km north then 3 km east.
4 km
3 km
5 km
total distance = ?
total displacement = ?
= (3 + 4) km = 7 km
total distance
total displacement= 5 km37 east of north(by measurement)
N
a Graphical method
http://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exe -
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tip ofp joined to tail ofq
p q
p + q
Tip-to-tail method:
4 Adding displacement
a Graphical method
http://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exe -
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d5 km
4 Adding displacementsb Algebraic methodIt is easy to add displacements if they areperpendicular to each other.
E.g.
N
4 km
3 km
d2 = 42 + 32
d= 5 km
= 37tan =
34
http://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exehttp://var/www/apps/conversion/current/sim/sim0401.exe -
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A girl cycles a circular track of diameter 70 m
(a)Distance travelled= ?Distance travelled
= perimeter of track= 70
= 220 m
Example 2
and stops at the starting point.
70 m
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it is becauseshe goes backtothe startingposition.
(b) Does she change her position?
No,
Example 2
70 m
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A car travels 5 km north and 4 km east.
(a) Total distance travelled = ?
Total distance
= 5 + 4 = 9 km
5 km
4 km
Example 3
N
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(c) What is her displacement?
Her overall
displacement
= 0 m
Example 2
70 m
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(b) What is the displacement?
22 45 +
6.4 km
size =
Example 3
= 6.40 km
A car travels 5 km north and 4 km east.
N
5 km
4 km
5
4 =
38.7tan =
Total displacement:
6.40 km 38.7 east of north
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60
o
1 m
Q1 A ball suspended...
A ball hung by a string swings from Xto Y.
1 mX Y
What is the size ofthe displacement of
the ball?
A /3 m
B 1 m
C 1 m towardsthe right
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8/2/2019 04-2 Displacement (3)
25/25
Q2 Is the speed limit...
Is the speed limit a vector or a scalar?
Scalar!Scalar!
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