Distance, displacement, speed and velocity
A close cousin of P5.1 (scalars vs vectors), but with key motion equations.
📖Definition— Definitions
- Distance — total path length (scalar, m).
- Displacement — straight-line distance from start to finish, with direction (vector, m).
- Speed — distance/time (scalar, m/s).
- Velocity — displacement/time (vector, m/s).
- Acceleration — rate of change of velocity (vector, m/s²).
Typical values
- Walking: ~1.5 m/s.
- Running: ~3 m/s.
- Cycling: ~6 m/s.
- Cars in town: ~13 m/s (30 mph).
- Cars on motorway: ~30 m/s (70 mph).
- Sound in air: ~340 m/s.
- Light/EM waves: 3 × 10⁸ m/s.
Acceleration
If velocity changes from $u$ to $v$ in time $t$:
$a = \dfrac{v - u}{t}$
- Positive $a$: speeding up (in chosen direction).
- Negative $a$: slowing down (or accelerating in the opposite direction).
- $a = 0$: constant velocity.
Uniform acceleration — SUVAT
For constant acceleration, you can use:
$v^2 - u^2 = 2as$
- $v$ — final velocity.
- $u$ — initial velocity.
- $a$ — acceleration.
- $s$ — displacement.
This is the only SUVAT equation explicitly required at AQA GCSE; it's often used to find $v$ given $u$, $a$, $s$ without needing time.
✦Worked example
A car accelerates from rest at 2.0 m/s² over 50 m. Find its final velocity.
- $v^2 = u^2 + 2as = 0 + 2 \times 2.0 \times 50 = 200$.
- $v = \sqrt{200} \approx 14.1$ m/s.
Free fall
In the absence of air resistance, all objects fall with acceleration $g \approx 9.8$ m/s².
After 1 second: 9.8 m/s. After 2 seconds: 19.6 m/s.
⚠Common mistakes
- Confusing distance and displacement.
- Mixing up units — speed in mph vs m/s requires conversion (×0.447).
- Forgetting that decelerating (slowing down) is just negative acceleration in the direction of motion.
- Using SUVAT without checking acceleration is constant.
AI-generated · claude-opus-4-7 · v3-deep-physics