Motion
In one line
An object is in motion when its position changes with time, and we describe that with distance, speed, velocity and acceleration.
Key points
- Distance
- The total length of the path travelled. It has size only (scalar). Unit: metre (m).
- Displacement
- The shortest straight-line distance from start to finish, with a direction (vector). It can be zero: walk round a track and come back, and your displacement is 0.
- Speed
- Distance ÷ time. Unit: m/s.
- Velocity
- Displacement ÷ time: speed in a given direction.
- Acceleration
- Change in velocity ÷ time: a = (v − u)/t. Unit: m/s². Negative acceleration (slowing down) is called retardation.
- Uniform motion: equal distances in equal time intervals.
- Average speed = total distance ÷ total time.
- Uniform circular motion: constant speed on a circle, but the direction keeps changing, so the velocity changes. It is accelerated motion. Speed = 2πr/t.
Equations of motion
For uniform acceleration, where u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement:
v = u + at
s = ut + ½at²
v² − u² = 2as
ExampleA car starts from rest and accelerates at 2 m/s² for 10 s.
v = 0 + 2 × 10 = 20 m/s. s = 0 + ½ × 2 × 10² = 100 m.
v = 0 + 2 × 10 = 20 m/s. s = 0 + ½ × 2 × 10² = 100 m.
BrakingA bus at 20 m/s brakes and stops in 5 s. a = (0 − 20)/5 = −4 m/s².
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Reading graphs
| Graph | Slope gives | Area under it gives | Straight line means |
|---|---|---|---|
| Distance–time | Speed | – | Uniform speed |
| Velocity–time | Acceleration | Displacement | Uniform acceleration |
A flat (horizontal) distance–time line means the object is at rest. A flat velocity–time line means it moves at constant velocity.
Common mistakes
- Treating distance and displacement as the same. Displacement is never more than distance.
- Forgetting units. Convert km/h to m/s by multiplying by 5/18. 72 km/h = 20 m/s.
- Averaging two speeds directly. Average speed is total distance ÷ total time, not (speed 1 + speed 2) ÷ 2.
Quick check
Revise in 30 seconds
| Speed | distance / time |
|---|---|
| Velocity | displacement / time |
| Acceleration | a = (v − u) / t, unit m/s² |
| Equations | v = u + at · s = ut + ½at² · v² − u² = 2as |
| Graphs | d–t slope = speed · v–t slope = acceleration · v–t area = displacement |
| km/h → m/s | × 5/18 |