Describing motion: Distance and Displacement

Distance vs. Displacement Abigail leaves her house and travels 4 blocks north, 4 blocks west, 4 blocks south and then 4 blocks east. How far did she go? There are 2 correct answers. Can you name them both? Answer 1: 16 blocks. 4+4+4+4 = 16 Answer 2: Nowhere. She ended right where she started. One of these answers describes Abigail’s distance and the other describes Abigail’s displacement. What is the difference?

Distance vs. Displacement Distance = How far an object has moved Abigail’s distance was 16 blocks. Displacement = The distance AND direction an object has moved from its starting point to its ending point Abigail’s displacement was 0 blocks. From her beginning location to her ending location was a distance of 0 blocks. We won’t add a direction because the difference is 0.

Distance vs. Displacement In a football game, the ball is placed on the line of scrimmage. It’s hiked back and the quarterback drops back 7 yards from the line of scrimmage. He then throws the ball 29 yards where it is caught by the wide receiver. The ball is carried an additional 4 yards where the wide receiver is pushed back 6 yards and tackled. What distance did the ball travel from the line of scrimmage? How far was the ball displaced from the line of scrimmage?

Distance vs. Displacement The ball travels a distance of 7 + 29 + 4 + 6 = 46 yards. When we calculate distance, direction doesn’t matter! The ball is displaced -7 + 29 + 4 + – 6 = 20 yards. When we calculate displacement, direction matters! Part of displacement is labeling the direction in which something was displaced. In this case it would just be down the football field and direction wasn’t given in traditional terms. Let’s try another!