1. Distance & Displacement

2. 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.

3. 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 012345678910

4. Distance Distance does not depend on direction. Now what distance did the ant travel? d = 3 cm cm 012345678910

5. Distance Distance does not depend on direction. Follow the ant again: What distance did the ant walk this time? d = 7 cm cm 012345678910

6. 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.

7. Displacement

8. cm 012345678910 + - Displacement Displacement has direction. Distance: 3 cm Displacement: +3 cm  The positive gives the ant a direction

9. Displacement Find the ant’s displacement again. Distance: 3 cm Displacement: -3 cm cm 012345678910 + -

10. Displacement Find the distance and displacement of the ant. Distance: 7 cm Displacement: +3 cm = 5cm – 2cm = +3cm cm 012345678910 + -

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

12. Displacement E.g. the distance travelled here by a driver was 14.5 km even though the displacement was only 2.7 km [North].

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

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

15. Displacement 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] 2 m 1 m

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

17. 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.

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

19. 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

20. 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!

21. 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?

22. Complete worksheet