Distance & Displacement. Distance Distance (d) – how far an object travels Does not depend on direction Imagine an ant crawling along a ruler What distance.

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Presentation transcript:

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

Distance Imagine our ant crawling again, now what distance did the ant crawl? d = 3 cm Did the direction change the answer? No cm

Distance Let’s follow the ant again What distance did the ant travel this time? d = 7 cm cm

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

Displacement Find the ant’s distance and displacement Distance? 3 cm Displacement? -3 cm (the negative means backward direction) cm

Displacement Find the ant’s distance and displacement Distance? 7 cm Displacement? +3 cm cm

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

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 con’t Use Pythagorean Theorem to find the displacement (Δx) at an angle. 2 m 1 m ΔxΔx ΔxΔx 8 m 8m + 2m 6m – 1m

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 Example Distance = Displacement = ? 10 m

Speed & Velocity

Speed (s) – rate at which an object is moving Does not depend on direction speed = distance ÷ time (s = d/t) Constant Speed – speed that does not change Speed

A car drives 100 meters in 5 seconds What is the car’s speed? s = (100 m) / (5 s) = 20 m/s 100 m Speed

A racecar is traveling at 85.0 m/s. How far does the car travel in 30.0 s? What is the distance the car travels? s = d/t → d = s × t d = (85 m/s) × (30 s) = 2550 m Speed

A rocket is traveling at 10 km/s. How long does it take the rocket to travel 30 km? What is the time it takes the rocket to travel? s = d/t → t = d/s t = (30 km) / (10 km/s) = 3 s Speed

Velocity (v) – speed with direction velocity = displacement ÷ time V = Δx /t Velocity

Distance traveled? Displacement? Speed? Velocity? cm s2 s3 s4 s5 s Example 7 cm +3 cm (7 cm) / (5 s) = 1.4 cm/s (+3 cm) / (5 s) = +0.6 cm/s