Compare velocity-time and speed-time graphs. Downward is positive for velocity, but speed is always positive.
Velocity includes direction. Since downward is positive, upward motion has negative velocity.
Speed does not include direction. It is the size of the velocity only: speed = |velocity|.
| Time | Situation | Velocity | Speed |
|---|---|---|---|
| 0 s | Released from rest | 0 m/s | 0 m/s |
| 2 s | Just before hitting ground | +20 m/s | 20 m/s |
| 2 s | Just after rebound | -10 m/s | 10 m/s |
| 3 s | At new maximum height | 0 m/s | 0 m/s |
The speed-time graph goes from:
(0, 0) to (2, 20), then drops suddenly to (2, 10), then decreases to (3, 0).
The graph does not go below the time axis because speed is always positive.
v² = u² + 2as
v² = 0² + 2(10)(20)
v² = 400
v = 20 m/s
Answer: V = 20 m/s
The ball first falls 20 m.
After rebound, its upward speed is half of 20 m/s: 10 m/s.
Rebound height: 0² = 10² - 2(10)s
100 = 20s, so s = 5 m.
Total distance travelled: 20 + 5 = 25 m
Answer: 25 m
Just before rebound, velocity is: +20 m/s
Just after rebound, velocity is: -10 m/s
Change in velocity: -10 - (+20) = -30 m/s
So the physically correct change in velocity during rebound is: -30 m/s.
If the question intended change in speed, then the speed changes from 20 m/s to 10 m/s, so:
10 - 20 = -10 m/s
This explains why the answer key may show -10 m/s: it is treating the quantity as change in speed, not change in velocity.