Distance, Displacement, Speed, and Velocity

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Presentation transcript:

Distance, Displacement, Speed, and Velocity

Distance Distance (d) – how far an object travels. Does not depend on direction. Imagine an ant crawling along a ruler. What distance did the ant travel? d = 3 cm cm 1 2 3 4 5 6 7 8 9 10

Distance Distance does not depend on direction. Here’s our intrepid ant explorer again. Now what distance did the ant travel? d = 3 cm Does his direction change the answer? cm 1 2 3 4 5 6 7 8 9 10

Distance Distance does not depend on direction. Let’s follow the ant again. What distance did the ant walk this time? d = 7 cm cm 1 2 3 4 5 6 7 8 9 10

Displacement Displacement (d) – difference between an object’s final position and its starting position. Does depend on direction. Displacement = final position – initial position d = dfinal – dinitial In order to define displacement, we need directions. Examples of directions: + and – N, S, E, W Angles

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

Displacement Let’s revisit our ant, and this time we’ll find his displacement. Distance: 3 cm Displacement: +3 cm The positive gives the ant a direction! cm 1 2 3 4 5 6 7 8 9 10 + -

Displacement Find the ant’s displacement again. - + Distance: 3 cm Remember, displacement has direction! Distance: 3 cm Displacement: -3 cm cm 1 2 3 4 5 6 7 8 9 10 + -

Displacement Find the distance and displacement of the ant. - + Distance: 7 cm Displacement: +3 cm cm 1 2 3 4 5 6 7 8 9 10 + -

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

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

Speed A car drives 100 meters in 5 seconds. What is the car’s average speed? s = d/t s = (100 m) / (5 s) = 20 m/s 100 m 5 s 4 s 1 s 2 s 3 s

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

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

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

Pulling It All Together Back to our ant explorer! Distance traveled: 7 cm Displacement: +3 cm Average speed: (7 cm) / (5 s) = 1.4 cm/s Average velocity: (+3 cm) / (5 s) = +0.6 cm/s cm 1 2 3 4 5 6 7 8 9 10 + - 5 s 4 s 1 s 2 s 3 s