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Unit 1 Day 1 – Displacement v. Distance Mr. Rana 9/6/12 Bell Ringer (3 min) Intro (3 min) If you were driving from one house to the other, what would be the shortest path? If you were walking from one house to the other, what would be the shortest path? Which one is the shorter path? Distance • Distance (d) – how far an object travels. – Does not depend on direction. • Imagine an ant crawling along a ruler. 0 cm 1 2 3 4 5 6 7 • What distance did the ant travel? – d = 3 cm 8 9 10 Distance • Distance does not depend on direction. • Here’s our intrepid ant explorer again. 0 cm 1 2 3 4 5 6 7 8 • Now what distance did the ant travel? – d = 3 cm • Does his direction change the answer? 9 10 Distance • Distance does not depend on direction. • Let’s follow the ant again. 0 cm 1 2 3 4 5 6 7 8 • What distance did the ant walk this time? • d = 7 cm 9 10 Displacement • Displacement (x) – shortest difference between an object’s final position and its starting position. – Does depend on direction. • Displacement = final position – initial position • In order to define displacement, we need directions. • Examples of directions: – + and – – N, S, E, W – Angles Displacement • Let’s revisit our ant, and this time we’ll find his displacement. - + 0 cm 1 2 3 4 5 6 7 8 • Distance: 3 cm • Displacement: +3 cm – The positive gives the ant a direction! 9 10 Displacement • Find the ant’s displacement again. – Remember, displacement has direction! - + 0 cm 1 2 3 4 • Distance: 3 cm • Displacement: -3 cm 5 6 7 8 9 10 Displacement • Find the distance and displacement of the ant. - + 0 cm 1 2 3 4 5 • Distance: 7 cm • Displacement: +3 cm 6 7 8 9 10 Example 1 (5 min) You walk 20 meters to the bus stop, but you notice you forgot your homework you run 20 meters back home. With homework in hand you walk 20 meters to the bus. Picture: Displacement: Distance: Example 2 (5 min) • 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? Guided Practice (10 min) Example 3 (5 min) • Dezmond ran 30 meters north, 30 meters east, 30 meters, south and 30 meters west. • Picture: Displacement: Distance: Guided Practice (10 min) A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. What is the distance traveled? What is the displacement? Independent Practice (10 min) Independent Practice (10 min) A car is driven from Buffalo to Albany and on to New York City, as shown in the diagram to the right. Compared to the size of the car's total displacement, is distance driven shorter, longer, or the same? Why? Independent Practice (10 min) If you were to pay for gas by the mile, but you got to choose whether you paid for your mileage measured by distance or displacement, which would you choose? Why? Independent Practice (10 min) Describe a situation where your distance and displacement would be the same. Independent Practice (10 min) Describe a situation where your distance and displacement would be different. Extra Marshall walks 3 meters north and 4 meters east. What is his displacement? Distance traveled? Fantasia walks 6 blocks south and 8 blocks west. What is her displacement? Distance traveled?