Distance & Displacement

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 Imagine our ant crawling again, now what distance did the ant crawl? d = 3 cm Did the direction change the answer? No cm 1 2 3 4 5 6 7 8 9 10

Distance Let’s follow the ant again What distance did the ant travel this time? d = 7 cm cm 1 2 3 4 5 6 7 8 9 10

Displacement Displacement (Δx) – shortest path between point A (initial) and point B (final) Does depend on direction (need + and -, or N, S, W, E)

Displacement Let’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) cm 1 2 3 4 5 6 7 8 9 10 + -

Displacement Distance? Displacement? Find the ant’s distance and displacement Distance? 3 cm Displacement? -3 cm (the negative means backward direction) cm 1 2 3 4 5 6 7 8 9 10 + -

Displacement Distance? Displacement? Find the ant’s distance and displacement Distance? 7 cm Displacement? +3 cm cm 1 2 3 4 5 6 7 8 9 10 + -

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

Example What is the distance traveled? d = 17 m 8 m 6 m 2 m 1 m

Example What is the displacement? 8 m 6 m 2 m 1 m

Example 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 m 2 m Distance = Displacement = ? 10 m