When distance and displacement agree
Motion in a straight line without turning back.
Straight on, or turn back
An athlete runs along a straight track. In one run she goes straight on. In another she goes on, then turns round and comes back a little.
In which run do you think the distance she travels equals the size of her displacement?
What this lesson covers
The idea
For motion in a straight line without turning back, the total distance travelled equals the magnitude of displacement, and the average speed equals the magnitude of the average velocity.
Straight on, or turn back
An athlete runs along a straight track. In one run she goes straight on. In another she goes on, then turns round and comes back a little.
In which run do you think the distance she travels equals the size of her displacement?
- The run in which she goes straight on
- The run in which she turns back
- Both runs
Two runs
Choose each run and compare the numbers.
When do they match?
Running straight on from O to A, the distance was 100 m and the displacement 100 m, and the average speed 10 m s⁻¹ equalled the average velocity 10 m s⁻¹ in size. After turning back to B the distance was 160 m but the displacement only 40 m, so the average speed 10 m s⁻¹ was larger than the size of the average velocity, 2.5 m s⁻¹.
For motion in a straight line without turning back, the total distance travelled equals the magnitude of displacement, and the average speed equals the magnitude of the average velocity.
Notes
Without turning back: distance = magnitude of displacement and average speed = magnitude of average velocity.
Check yourself
Which motion has a total distance equal to the magnitude of its displacement?
An athlete runs 100 m from O to A in 10 s without turning back. What is the magnitude of her average velocity?
Answer: 10 m s⁻¹
100 m ÷ 10 s = 10 m s⁻¹, the same as her average speed.
An athlete runs in one direction along a straight track without turning back. Her average speed is…
An athlete runs 160 m in total in 16 s but ends up only 40 m from where she began. What is the magnitude of her average velocity?
Answer: 2.5 m s⁻¹
40 m ÷ 16 s = 2.5 m s⁻¹.
- A car moves 50 m along a straight road without turning back — correct. Yes!
- A car moves 50 m forward and then 20 m back. After turning back, the distance is 70 m but the displacement is only 30 m, so they are not equal.
- A child goes once round a circular path and returns to the start. The displacement is zero because the child returns to the start, but the distance is not zero.
- greater than the magnitude of her average velocity. With no turning back the distance equals the magnitude of displacement, so the two are equal.
- equal to the magnitude of her average velocity — correct. Yes!
- smaller than the magnitude of her average velocity. With no turning back the distance and the magnitude of displacement are the same, so dividing both by the same time gives equal values.