Motion: scalars and vectors
Scalars vs vectors
A scalar has size only. A vector has size and direction.
| Scalar | Vector |
|---|---|
| Distance | Displacement |
| Speed | Velocity |
| Time | Acceleration |
| Mass | Force |
Distance is the total path travelled. Displacement is the straight-line distance from start to finish, with direction. A 400 m runner returning to the start has covered 400 m of distance but 0 m displacement.
Speed and velocity
Speed = distance ÷ time. Average speed (m/s) = total distance (m) / total time (s).
Velocity is speed in a stated direction. A car travelling at 30 m/s east has the same speed as one travelling 30 m/s west, but a different velocity.
Typical speeds (Edexcel Foundation may quote): walking 1.5 m/s, running 3 m/s, cycling 6 m/s, car 13–30 m/s, train 50 m/s, sound in air 330 m/s.
Acceleration
Acceleration is the rate of change of velocity:
a = (v − u) / t
- a = acceleration in m/s².
- u = initial velocity (m/s), v = final velocity (m/s).
- t = time (s).
A negative value (deceleration) shows the object is slowing down.
SUVAT (Higher only — Edexcel Combined)
For uniform acceleration:
v² = u² + 2 a s (where s = displacement)
Useful when time is unknown.
✦Worked example
A car accelerates from 5 m/s to 25 m/s in 8 s.
- a = (25 − 5) / 8 = 2.5 m/s².
A train brakes from 40 m/s to rest over 200 m.
- v² = u² + 2as → 0 = 40² + 2 × a × 200 → a = −1600 / 400 = −4 m/s² (decelerating at 4 m/s²).
Edexcel exam tip
Whenever a question gives you "decelerating", "slowing down" or "comes to rest", expect a negative acceleration and final velocity = 0. Many marks are lost by leaving the sign positive.
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