Distance, Displacement, Speed, and VelocityDistance, Displacement, Speed, and Velocity

Questions for ConsiderationQuestions for Consideration

What is frame of reference?What is frame of reference?What is distance?What is distance?How is displacement different from How is displacement different from

distance?distance?What is speed?What is speed?What is velocity?What is velocity?What are scalar and vector quantities?What are scalar and vector quantities?

Frame of ReferenceFrame of Reference

Coordinate frame within which to measure Coordinate frame within which to measure position, motion, or other properties of an position, motion, or other properties of an object.object.

OR...OR...Observational frame tied to the motion of Observational frame tied to the motion of

an observer.an observer. In Newtonian physics, all motion must be In Newtonian physics, all motion must be

defined in terms of a reference frame.defined in terms of a reference frame.Relative MotionRelative Motion

Reference FrameReference Frame Is the speed of the ball different relative to the Is the speed of the ball different relative to the

pitcher, the truck driver, and the jet pilot? Why pitcher, the truck driver, and the jet pilot? Why or why not?or why not?

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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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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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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DisplacementDisplacement

Displacement (Displacement (x) – difference between an object’s x) – 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 x = xx = xfinalfinal – x – xinitialinitial

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

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!

cm

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+-

DisplacementDisplacementLet’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 cmDisplacement: +3 cmDisplacement: +3 cm

The positive gives the ant a direction!The positive gives the ant a direction!

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 cmDisplacement: -3 cmDisplacement: -3 cm

cm

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+-

DisplacementDisplacement

Find the distance and displacement of the Find the distance and displacement of the ant.ant.

Distance: 7 cmDistance: 7 cmDisplacement: +3 cmDisplacement: +3 cm

cm

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+-

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?

SpeedSpeed

Speed (s) – Rate at which an object is Speed (s) – Rate at which an object is moving.moving.

speed = distance / timespeed = distance / times = d/ts = d/tLike distance, speed Like distance, speed does notdoes not depend on depend on

direction.direction.

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/ts = (100 m) / (5 s) = 20 m/ss = (100 m) / (5 s) = 20 m/s

100 m

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SpeedSpeed

A rocket is traveling at 10 km/s. How long does it A rocket is traveling at 10 km/s. How long does it take the rocket to travel 30 km?take the rocket to travel 30 km?

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?

VelocityVelocity

Velocity (v) – speed with direction.Velocity (v) – speed with direction.velocity = displacement / timevelocity = displacement / timev = v = x / tx / t

Pulling It All TogetherPulling It All Together

Back to our ant explorer!Back to our ant explorer!

Distance traveled: 7 cmDistance traveled: 7 cmDisplacement: +3 cmDisplacement: +3 cmAverage speed: (7 cm) / (5 s) = 1.4 cm/sAverage speed: (7 cm) / (5 s) = 1.4 cm/sAverage 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

Scalar and Vector QuantitiesScalar and Vector Quantities

Scalar Quantity – has magnitude but not Scalar Quantity – has magnitude but not direction.direction.Distance and speed are scalar quantities.Distance and speed are scalar quantities.

Vector Quantity – has magnitude Vector Quantity – has magnitude andand direction.direction.Displacement and velocity are vector Displacement and velocity are vector

quantities.quantities.