Speed, Velocity and Acceleration

GCSE Physics · Forces

Key definitions

Speed – how fast you travel (scalar, no direction).
Velocity – speed in a given direction (vector).
Acceleration – how quickly velocity changes.

Equations

speed = distance ÷ time            v = s / t
acceleration = change in velocity ÷ time      a = (v − u) / t
v² = u² + 2 a s        (uniform acceleration)

(u = start velocity, v = final velocity, a = acceleration, s = distance)

Worked example

A car speeds up from 5 m/s to 25 m/s in 4 s:

a = (25 − 5) / 4 = 20 / 4 = 5 m/s²

Distance–time graphs

Flat line = stationary.
Straight slope = constant speed (gradient = speed).
Curved = accelerating.

Velocity–time graphs

Gradient = acceleration.
Area under the graph = distance travelled.

Typical speeds

Walking ≈ 1.5 m/s, running ≈ 3 m/s, cycling ≈ 6 m/s.

Exam tip

Convert units first (km → m, minutes → s). On a v–t graph, gradient = acceleration and area = distance.