Distance,_Displacement,_Speed,_and_Velocity_notes.ppt

scalar vs vector

1. Distance, Displacement, Speed, and VelocityDistance, Displacement, Speed, and Velocity

2. DistanceDistance

Distance (d) – how far an object travels.Distance (d) – how far an object travels.

Does Does notnot depend on direction. depend on direction.

Imagine an ant crawling along a ruler.Imagine an ant crawling along a ruler.

What What distancedistance did the ant travel? did the ant travel?

d = 3 cmd = 3 cm
cm
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3. DistanceDistance
Distance does not depend on direction.Distance does not depend on direction.

Here’s our intrepid ant explorer again.Here’s our intrepid ant explorer again.
Now what distance did the ant travel?Now what distance did the ant travel?

d = 3 cmd = 3 cm
Does his direction change the answer?Does his direction change the answer?
cm
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4. DistanceDistance

Distance does not depend on direction.Distance does not depend on direction.

Let’s follow the ant again.Let’s follow the ant again.

What distance did the ant walk this time?What distance did the ant walk this time?

d = 7 cmd = 7 cm
cm
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5. DisplacementDisplacement

Displacement (Displacement (d) – difference between an object’s d) – difference between an object’s
final position and its starting position.final position and its starting position.

DoesDoes depend on direction. depend on direction.

Displacement = final position – initial positionDisplacement = final position – initial position
d = dd = d
finalfinal – d – d
initialinitial

In order to define displacement, we need directions.In order to define displacement, we need directions.

Examples of directions:Examples of directions:

+ and –+ and –

N, S, E, WN, S, E, W

AnglesAngles

6. Displacement vs. DistanceDisplacement vs. Distance

Example of distance:Example of distance:

The ant walked 3 cm.The ant walked 3 cm.

Example of displacement:Example of displacement:

The ant walked 3 cm EAST.The ant walked 3 cm EAST.

An object’s distance traveled and its An object’s distance traveled and its
displacement aren’t always the same!displacement aren’t always the same!

7. cm
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+-
DisplacementDisplacement

Let’s revisit our ant, and this time we’ll find Let’s revisit our ant, and this time we’ll find
his displacement.his displacement.

Distance: 3 cmDistance: 3 cm

Displacement: +3 cmDisplacement: +3 cm

The positive gives the ant a direction!The positive gives the ant a direction!

8. DisplacementDisplacement

Find the ant’s displacement again.Find the ant’s displacement again.

Remember, displacement has direction!Remember, displacement has direction!

Distance: 3 cmDistance: 3 cm

Displacement: -3 cmDisplacement: -3 cm
cm
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+-

9. DisplacementDisplacement

Find the distance and displacement of the Find the distance and displacement of the
ant.ant.

Distance: 7 cmDistance: 7 cm

Displacement: +3 cmDisplacement: +3 cm
cm
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+-

10. Displacement vs. DistanceDisplacement vs. Distance

An athlete runs around a track that is 100 meters An athlete runs around a track that is 100 meters
long three times, then stops.long three times, then stops.

What is the athlete’s distance and displacement?What is the athlete’s distance and displacement?

Distance = 300 mDistance = 300 m

Displacement = 0 mDisplacement = 0 m

Why?Why?

11. SpeedSpeed

Speed (s) – Rate at which an object is Speed (s) – Rate at which an object is
moving.moving.

speed = distance / timespeed = distance / time

s = d/ts = d/t

Like distance, speed Like distance, speed does notdoes not depend on depend on
direction.direction.

12. SpeedSpeed

A car drives 100 meters in 5 seconds.A car drives 100 meters in 5 seconds.

What is the car’s average speed?What is the car’s average speed?

s = d/ts = d/t
s = (100 m) / (5 s) = 20 m/ss = (100 m) / (5 s) = 20 m/s
100 m
1 s2 s3 s4 s5 s

13. SpeedSpeed

A rocket is traveling at 10 m/s. How long does it A rocket is traveling at 10 m/s. How long does it
take the rocket to travel 30 m?take the rocket to travel 30 m?

14. SpeedSpeed

A racecar is traveling at 85.0 m/s. How far A racecar is traveling at 85.0 m/s. How far
does the car travel in 30.0 s?does the car travel in 30.0 s?

15. VelocityVelocity

Velocity (v) – speed with direction.Velocity (v) – speed with direction.

velocity = displacement / timevelocity = displacement / time

v = v = d / td / t

Has magnitude and direction!Has magnitude and direction!

Magnitude – a measure that has a valueMagnitude – a measure that has a value

16. Pulling It All TogetherPulling It All Together

Back to our ant explorer!Back to our ant explorer!

Distance traveled: 7 cmDistance traveled: 7 cm

Displacement: +3 cmDisplacement: +3 cm

Average speed: (7 cm) / (5 s) = 1.4 cm/sAverage speed: (7 cm) / (5 s) = 1.4 cm/s

Average velocity: (+3 cm) / (5 s) = +0.6 cm/sAverage velocity: (+3 cm) / (5 s) = +0.6 cm/s
cm
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1 s2 s3 s4 s5 s