Distance or displacement?
Displacement is the net change of position.
There and back
An athlete runs from the start O to a far point A, and then runs part of the way back to a point B. She stops at B.
Which do you think is smaller: the length of the path she ran, or the change from her starting position to her stopping position?
What this lesson covers
The idea
Displacement is the net change in an object's position between two instants: its magnitude is the distance between the two positions, and its direction is from the first position towards the second.
There and back
An athlete runs from the start O to a far point A, and then runs part of the way back to a point B. She stops at B.
Which do you think is smaller: the length of the path she ran, or the change from her starting position to her stopping position?
- The change from start to stop
- They are about the same
- The length of the path she ran
Run the clock
Slide the clock to 10 s and then to 16 s. Compare the two measures.
Net change in position
At 16 s the athlete had run OA + AB = 100 m + 60 m = 160 m in total. But her stopping position B is only 40 m from O, so her position changed by 40 m, towards the right.
Displacement is the net change in the position of an object between two instants. Its magnitude is the distance between the two positions, and its direction is from the first position towards the second.
Notes
Displacement = net change of position between two instants: magnitude is the distance between the two positions, direction is from the first towards the second.
Check yourself
An athlete runs from O to A (100 m) and back to B, 60 m from A. What is the total distance she travelled?
Answer: 160 m
Total distance = OA + AB = 100 m + 60 m = 160 m.
Her start O is 0 m and her stop B is 40 m to the right of O. What is the magnitude of her displacement?
Answer: 40 m
The distance between O and B is 40 m.
What is the direction of the displacement from O to B?
What is displacement?
- From B towards O. The direction of displacement goes from the first position towards the second. The first position is O.
- From O towards B, the positive direction — correct. Yes!
- It has no direction. Displacement needs a direction as well as a magnitude.
- The total length of the path travelled. That is the total distance travelled, which can be larger than the displacement.
- The time taken to move from one place to another. That is the time interval, not displacement.
- The net change in the position of an object between two instants — correct. Yes!