Force from a velocity graph
A velocity–time graph shows how a trolley moves. Can it also show the force?
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Step 1 of 4
- A 4 kg trolley. Its velocity is drawn against time.
- Speeding up: the line slopes up. a = 2 m/s², so F = 4 × 2 = 8 N.
- Steady speed: the line is flat. a = 0, so no net force.
- Slowing down: the line slopes down. a = −3 m/s², so F = −12 N.
The rule
The slope of a velocity–time graph is the acceleration. Then net force = mass × acceleration.
Slope means the change in velocity divided by the time taken. The trolley moves forward. A plus sign means the force is along the motion. A minus sign means the force is against the motion.
The velocity rises from 0 to 6 m/s in 3 s. It stays at 6 m/s until 7 s. Then it falls to 0 at 9 s.
| Part | Line | Slope | Acceleration | Net force |
|---|---|---|---|---|
| 0 to 3 s | up | 6 ÷ 3 | 2 m/s² | 8 N |
| 3 to 7 s | flat | 0 ÷ 4 | 0 | 0 N |
| 7 to 9 s | down | −6 ÷ 2 | −3 m/s² | −12 N |
Here net force = 4 × acceleration. That gives 8 N, 0 N and −12 N.
Watch out!
A flat line does not mean the trolley is still. It moves at 6 m/s, with no net force.