Distance Displacement Distance is a Scalar A measure

Distance & Displacement

Distance is a Scalar • A measure of the length of a path an object takes in moving from one position to another is called distance. • Distance is how far an object has moved • Distance is a scalar quantity.

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. 0 cm 1 2 3 4 5 6 7 8 • Now what distance did the ant travel? d = 3 cm 9 10

Distance • Distance does not depend on direction. • 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 is a Vector • Displacement is the change in position of an object and includes a description of the direction of motion. • Determined by drawing a straight line from starting position to ending position • Is not always equal to distance traveled.

Displacement

Displacement • Displacement has direction. - + 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. - + 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 • = 5 cm – 2 cm = +3 cm 6 7 8 9 10

QUESTION: How far (in km) will a car travel in 15 min at 20 m/s ? d=sxt = (20 m) x (60 s) (15 min) s min = 18 000 m (divide 1000 for km) = 18 km

Displacement E. g. the distance travelled here by a driver was 14. 5 km even though the displacement was only 2. 7 km [North].

• E. g If a person travels 40 m east, turns and travels 30 m west, the displacement of the person is 10 m east. • If a person travels 40 m east and then travels another 50 m east, the displacement is 90 m east.

Displacement Example: Mandisa walks 2 m [East] and then 1 m [West]. What was her distance travelled? What was her displacement? Distance travelled: Dd = 2 m + 1 m = 3 m Displacement: 1 m 1 m She is 1 m [East] of her original starting position.

Displacement 2 m 1 m 1 m We can represent [East] as the positive direction and [West] as the negative direction: = 2 m [East] + 1 m [West] =+2 m– 1 m =+1 m = 1 m [East]

What is the difference between distance and displacement? Distance: How far something travels Displacement: How far something travels in a given direction in a straight line from start to finish.

• A soccer player changes position back and forth on the field. In the diagram below each position is marked where the player reverses direction. The player moves from position A to B to C to D. • Find the distance and displacement of travel.

Solution: Distance = 85 m Displacement = 55 m left of A

Displacement • Therefore, displacement = difference between an object’s final position and its starting position. – Does depend on direction. • Displacement = final position – initial position • Examples of directions: – + and – – N, S, E, W – Angles

Displacement vs. Distance • Example of distance: – The car drove 30 km. • Example of displacement: – The car drove 30 km. EAST. • An object’s distance traveled and its displacement aren’t always the same!

Displacement vs. Distance • 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?

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