Distance &

Displacement

DistanceDistance (d) – how far an object travels

Does not depend on directionImagine an ant crawling along a ruler

What distance did the ant travel?d = 3 cm

cm0 1 2 3 4 5 6 7 8 9 10

DistanceImagine our ant crawling again, now what

distance did the ant crawl?d = 3 cm

Did the direction change the answer?No

cm0 1 2 3 4 5 6 7 8 9 10

DistanceLet’s follow the ant again

What distance did the ant travel this time?d = 7 cm

cm0 1 2 3 4 5 6 7 8 9 10

DisplacementDisplacement (Δx) – shortest

path between point A (initial) and point B (final)Does depend on direction (need + and -, or N, S, W, E)

DisplacementLet’s visit the ant again

What is the ant’s distance?3 cm

What is the ant’s displacement?+3 cm (the positive means forward direction)

cm0 1 2 3 4 5 6 7 8 9 10

+-

DisplacementFind the ant’s distance and displacement

Distance?3 cm

Displacement?-3 cm (the negative means backward direction)

cm0 1 2 3 4 5 6 7 8 9 10

+-

DisplacementFind the ant’s distance and displacement

Distance?7 cm

Displacement?+3 cm

cm0 1 2 3 4 5 6 7 8 9 10

+-

Displacement vs. DistanceAn athlete runs around a track that is 100

meters long three times, then stops.What is the athlete’s distance?What is the athlete’s displacement?Distance = 300 m

Displacement = 0 m

Why?

ExampleWhat is the distance traveled?

d = 17 m

8 m

6 m

2 m

1 m

ExampleWhat is the displacement?

8 m

6 m

2 m1 m

Example con’tUse Pythagorean Theorem to find the displacement (Δx) at an angle.

2 m

1 m

Δx

Δx

222

222

)( bax

bac

][18.11][25][100

)5()10(

)5()10()(

1628)(

22

22

222

222

mxmmx

mmx

mmx

mmmmx

8 m

8m + 2m

6m – 1m

A turtle crawls 5 m North, then 3 m East, and then 2 m South. What is his distance traveled and displacement?

5 m

3 m2 m

Example

Distance =

Displacement = ?

10 m

Speed &

Velocity

Speed (s) – rate at which an object is movingDoes not depend on direction

speed = distance ÷ time (s = d/t)

Constant Speed – speed that does not change

Speed

A car drives 100 meters in 5 seconds

What is the car’s speed?s = (100 m) / (5 s) = 20 m/s

100 m

Speed

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

What is the distance the car travels?s = d/t → d = s × td = (85 m/s) × (30 s) = 2550 m

Speed

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

What is the time it takes the rocket to travel?s = d/t → t = d/st = (30 km) / (10 km/s) = 3 s

Speed

Velocity (v) – speed with direction

velocity = displacement ÷ time

V = Δx /t

Velocity

Distance traveled?

Displacement?

Speed?

Velocity?

cm0 1 2 3 4 5 6 7 8 9 10

+-1 s2 s3 s4 s5 s

Example

7 cm

+3 cm

(7 cm) / (5 s) = 1.4 cm/s

(+3 cm) / (5 s) = +0.6 cm/s