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Explore distance, displacement, speed, and velocity in motion. Learn the differences and calculations between these concepts using examples and illustrations.
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Motion Speed
Motion • Motion: A change in position • Depends on reference point • Is the mom moving relative to the dad? • Is the mom moving if you were on the side of the road?
Distance vs. Displacement • What is distance? • How is displacement different from distance? • What is speed? • What is velocity?
1 2 3 4 5 6 7 8 9 10 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
1 2 3 4 5 6 7 8 9 10 Distance • Distance is scalar which means magnitude or quantity. • Now what distance did the ant travel? • d = 3 cm • Does his direction change the answer?
0 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
Displacement • Displacement (x) – difference between an object’s final position and its starting position. • Does depend on direction. • Displacement = final position – initial position • x = xfinal – xinitial • 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!
- + 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
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? Displacement vs. Distance
Speed • The distance an object moves in a certain amount of time • Formula:
Unit for Speed • Since the formula is • Then the unit for speed must be a unit of distance divided by a unit of time. • For example: • km/h • m/s
Speed • Look familiar? • Knowing any of the 2 variables, you can solve for the 3rd.
Calculating 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
Interpreting Graphs • The shape, or slope, of the line tells the story!
Interpreting a Graph • Now you try! • What does each graph tell you?
Tell the Story! • What story does the graph tell you as you ride your bike to your friend’s house?
Scalar vs. Vector • Scalar Quantity – has magnitude but not direction. • Distance and speed are scalar quantities. • Vector Quantity – has magnitude and direction. • Displacement and velocity are vector quantities.