Distance, Time & Distance, Time & SpeedSpeed

A long time ago in a A long time ago in a land far, far away…land far, far away…

What is “distance”?What is “distance”? Distance – the amount of space between two Distance – the amount of space between two

points.points. We measure distance using kilometres (km), We measure distance using kilometres (km),

metres (m), centimetres (cm) or millimetres metres (m), centimetres (cm) or millimetres (mm) – it depends on how big the space is to be (mm) – it depends on how big the space is to be measured.measured.

Now for the tough one…What is “time”?Now for the tough one…What is “time”? Time – The duration between events. (Easy stuff!)Time – The duration between events. (Easy stuff!) We measure time using days (d), hours (h), We measure time using days (d), hours (h),

minutes (min) or seconds (s) – depending on how minutes (min) or seconds (s) – depending on how long we have to wait.long we have to wait.

Converting UnitsConverting Units In order to solve problems we must be able to In order to solve problems we must be able to

convert units of both distance and time – it’s convert units of both distance and time – it’s easy stuff though…just watch.easy stuff though…just watch.

Let’s do distance first…Let’s do distance first…

DISTANCEDISTANCE x1000x1000 x100 x100 x10 x10

kmkm mm cmcm mmmm

÷1000÷1000 ÷100 ÷100 ÷10÷10

Converting TimeConverting Time

TIMETIME x24x24 x60 x60 x60 x60

dd hh minmin s s

÷24÷24 ÷60 ÷60 ÷60 ÷60

Think, Ricky…Think!Think, Ricky…Think! Our old friend Julian, from the Sunnyvale Trailer Park, Our old friend Julian, from the Sunnyvale Trailer Park,

says this to Ricky whenever he misses the obvious and says this to Ricky whenever he misses the obvious and comes up with something that is totally wrong.comes up with something that is totally wrong.

You might be a “Ricky” if you don’t watch it…you have You might be a “Ricky” if you don’t watch it…you have to remember when to divide and when to multiply…it to remember when to divide and when to multiply…it makes a huge difference.makes a huge difference.

Lets see what I mean…Lets see what I mean… How many metres are in 2.5km?How many metres are in 2.5km? Well…I know that one km has 1000m…So do I divide Well…I know that one km has 1000m…So do I divide

or multiply by 1000?or multiply by 1000? If I divide (2.5 ÷ 1000) I get 0.0025m. (Less than a If I divide (2.5 ÷ 1000) I get 0.0025m. (Less than a

single metre…is 2.5km less than a single metre?)single metre…is 2.5km less than a single metre?) If I multiply (2.5 x 1000) I get 2500m.If I multiply (2.5 x 1000) I get 2500m. Which one seems right?…Think, Ricky…Think!Which one seems right?…Think, Ricky…Think!

Boys, I know what I’m Boys, I know what I’m doin’!doin’!

• Make sure you have Make sure you have the number written the number written correctly.correctly.

• Make sure to use the Make sure to use the right conversion factor.right conversion factor.

• Multiply or Divide the Multiply or Divide the two numbers.two numbers.

• Make sure your answer Make sure your answer makes sense – think makes sense – think Ricky!Ricky!

• Pass Grade 10!!!Pass Grade 10!!!

Practice Problems in Practice Problems in ConvertingConverting

Try these practice problems. Convert the Try these practice problems. Convert the following units…following units…

a)a) 250m = 250m = kmkm k) 360s =k) 360s = minminb)b) 1475cm =1475cm = mm l) 45min =l) 45min = hhc)c) 3.45km =3.45km = mm m) 3.5h =m) 3.5h = minmind)d) 459mm =459mm = cmcm n) 75min =n) 75min = sse)e) 20cm =20cm = mm o) 3.75d =o) 3.75d = hhf)f) 506000cm =506000cm = kmkm p) 5d =p) 5d = minming)g) 7.56km =7.56km = mmmm q) 2400min =q) 2400min = ddh)h) 8340mm =8340mm = mm r) 3600s =r) 3600s = hhi)i) 96.45m =96.45m = mmmm s) 58000s =s) 58000s = ddj)j) 2470km =2470km = cmcm t) 0.68d =t) 0.68d = ss

Converting UnitsConverting Units These are the answers to the practice problems.These are the answers to the practice problems.

a)a) 250m = 250m = 0.25 0.25 kmkm k) 360s =k) 360s = 66 minminb)b) 1475cm =1475cm = 14.75 14.75 mm l) 45min =l) 45min = 0.750.75 hhc)c) 3.45km =3.45km = 3450 3450 mm m) 3.5h =m) 3.5h = 210210 minmind)d) 459mm =459mm = 45.9 45.9 cmcm n) 75min =n) 75min =45004500 sse)e) 20cm =20cm = 0.2 0.2 mm o) 3.75d =o) 3.75d = 9090 hhf)f) 506000cm =506000cm = 5.06 5.06 kmkm p) 5d =p) 5d = 72007200 minming)g) 7.56km =7.56km = 7560000 7560000 mmmm q) 2400min =q) 2400min = 1.671.67 ddh)h) 8340mm =8340mm = 8.34 8.34 mm r) 3600s =r) 3600s = 11 hhi)i) 96.45m =96.45m = 96450 96450 mmmm s) 58000s =s) 58000s = 0.670.67 ddj)j) 2470km =2470km = 247000000 247000000 cmcm t) 0.68d =t) 0.68d = 5875258752 ss

SpeedSpeed Speed is a measure of the amount of Speed is a measure of the amount of

distance traveled per unit of time. We distance traveled per unit of time. We say the speed of a car is 100km/h – it say the speed of a car is 100km/h – it travels 100km in 1 hour.travels 100km in 1 hour.

The units we use to measure speed The units we use to measure speed also tell us how it is also tell us how it is measured/calculated. The 100km/h measured/calculated. The 100km/h shows us that distance (km) is divided shows us that distance (km) is divided by the time (h). The “/” in the unit is by the time (h). The “/” in the unit is the same as a division sign.the same as a division sign.

So to calculate speed, we simply take So to calculate speed, we simply take the distance and divide it by the time.the distance and divide it by the time.

The Speed FormulaThe Speed Formula The formula for speed is shown below…The formula for speed is shown below…

v = v = ΔΔdd

ΔΔtt In this formula:In this formula:

• ““v” is the symbol for speed.v” is the symbol for speed.• ““ΔΔ” is the Greek symbol Delta = change.” is the Greek symbol Delta = change.• ““ΔΔd” is the symbol for “change in distance”. d” is the symbol for “change in distance”.

It can be measured as It can be measured as ΔΔd = dd = d22 – d – d11. (Change . (Change = Final – Initial)= Final – Initial)

• ““ΔΔt” is the symbol for “change in time”. It t” is the symbol for “change in time”. It can be measured as can be measured as ΔΔt = tt = t22 – t – t11. (Change = . (Change = Final – Initial)Final – Initial)

The Speed TriangleThe Speed Triangle You may also use a formula triangle – see below:You may also use a formula triangle – see below:

This triangle gives you the formula This triangle gives you the formula for any one of the three parts of the for any one of the three parts of the speed equation. You can now solve speed equation. You can now solve for speed, distance or time. (Cover for speed, distance or time. (Cover it up and see what’s left)it up and see what’s left)

Types of SpeedTypes of Speed

Average SpeedAverage Speed – The total distance – The total distance traveled divided by the total time traveled divided by the total time elapsed.elapsed.

Instantaneous SpeedInstantaneous Speed – The speed an – The speed an object is traveling at a particular instant object is traveling at a particular instant in time.in time.

Constant SpeedConstant Speed – Traveling the same – Traveling the same distance for each successive unit of time. distance for each successive unit of time. Constant speed is also known as Constant speed is also known as uniform motionuniform motion..

How to Solve Motion How to Solve Motion ProblemsProblems

For every problem, you must show:For every problem, you must show:– The correct formula.The correct formula.– Proper substitution of values & units.Proper substitution of values & units.– The correct answer with proper units.The correct answer with proper units.

Every time one of these things is missing Every time one of these things is missing – you will lose a mark – I promise.– you will lose a mark – I promise.

Sample ProblemsSample Problems (We will do together.) (We will do together.) Page 355 – Sample Problem #1Page 355 – Sample Problem #1 Page 356 – Sample Problems #2 & #3.Page 356 – Sample Problems #2 & #3. Page 357 – Sample Problem #4Page 357 – Sample Problem #4

Just a Few Just a Few Reminders…Reminders…

Always check your Always check your measurements and measurements and conversions!!!conversions!!!

Always make sure your Always make sure your answers make sense…answers make sense…or else!!!or else!!!

Listen to your teachers, Listen to your teachers, stay out of trouble and stay out of trouble and it’ll be mission it’ll be mission accomplished!!!accomplished!!!

THE END!!!THE END!!!