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Distance &
Displacement
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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
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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
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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
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DisplacementDisplacement (Δx) – shortest
path between point A (initial) and point B (final)Does depend on direction (need + and -, or N, S, W, E)
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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
+-
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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
+-
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DisplacementFind the ant’s distance and displacement
Distance?7 cm
Displacement?+3 cm
cm0 1 2 3 4 5 6 7 8 9 10
+-
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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?
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ExampleWhat is the distance traveled?
d = 17 m
8 m
6 m
2 m
1 m
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ExampleWhat is the displacement?
8 m
6 m
2 m1 m
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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
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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
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Speed &
Velocity
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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
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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
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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
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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
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Velocity (v) – speed with direction
velocity = displacement ÷ time
V = Δx /t
Velocity
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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