Question 6
Consider the same graph again: the object travels 10 m between t = 0 and t = 4 s, stays at rest from t = 4 s to t = 6 s, and returns to its starting point between t = 6 s and t = 8 s.
| t (s) | 0 | 4 | 6 | 8 |
|---|---|---|---|---|
| s (m) | 0 | 10 | 10 | 0 |
What is the magnitude of the object's maximum velocity over the whole time?
The right answer is the one marked above.
5 m s-1. Velocity is the gradient, so the maximum velocity is found on the steepest part of the graph — the stretch from t = 6 s to t = 8 s.
gradient = (0 − 10) m ÷ (8 − 6) s = −5 m s-1
The negative sign says the motion is in the return direction; the magnitude is 5 m s-1, the largest of the three sections.
For comparison: the gradient of the first section is 10 m ÷ 4 s = 2.5 m s-1, and the gradient of the flat section is 0. The object came back in half the time it took to go out, so on the way back its velocity was twice as big.