Question pattern: Directed position, distance & displacement
Original question 2 of 2 in this pattern
Same displacement, different paths
Two robots start at the origin of the same straight test track. Positive position is to the right. Robot A visits the listed waypoints in order. Robot B moves directly from the origin to x = −50 m.
a) Calculate the distance travelled by each robot.
b) Compare their displacements and explain why the displacements are equal even though the distances differ.
| Waypoint | Position / m |
|---|---|
| Start | 0 |
| 1 | +300 |
| 2 | +100 |
| Finish | −50 |
Worked answer
Solution
- Step 1
Robot A travels
|300 - 0| + |100 - 300| + |-50 - 100| = 300 + 200 + 150 = 650 m. - Step 2
Robot B travels directly from 0 m to −50 m, so its distance is 50 m.
- Step 3
Both start at 0 m and finish at −50 m, so both have displacement
-50 - 0 = -50 m, or 50 m to the left.
Final answer
Robot A distance = 650 m; Robot B distance = 50 m; both displacements are −50 m (50 m left).
Common mistake
Assuming that equal displacement means equal distance travelled.
Concepts tested
- path length
- displacement
- coordinate direction
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