scienceGrade 9-102 min read

Speed, velocity and acceleration: reading motion graphs

Three words students use interchangeably and shouldn't. Here's what each one means, the equations, and how to read a distance–time and velocity–time graph at a glance.

Speed, velocity, and acceleration describe motion, and they are not the same thing. Keeping them straight is the whole foundation of mechanics — and a lot of it is hiding in two kinds of graph.

The three definitions

Speed — how fast you're going, no direction. $\text{speed} = \dfrac{\text{distance}}{\text{time}}$ . Unit: m/s.
Velocity — speed with a direction. $30\,\text{m/s}$ north is different from $30\,\text{m/s}$ south, even though the speed is identical.
Acceleration — how fast the velocity is changing. Speeding up, slowing down, or turning all count. Unit: m/s².

a = \frac{\text{change in velocity}}{\text{time}} = \frac{v - u}{t}

A negative acceleration means slowing down (deceleration).

Distance–time graphs

Here the gradient is the speed.

Flat line → not moving (distance isn't changing).
Straight slope → steady speed.
Steeper slope → faster.
Curve getting steeper → speeding up.

Velocity–time graphs

These carry two pieces of information, which is why examiners love them:

The gradient is the acceleration (how fast velocity changes).
The area under the line is the distance travelled.

A horizontal line here means constant velocity (zero acceleration) — not "stationary". That mix-up, reading a velocity–time graph as if it were distance–time, is the most common error in the topic.

Worked example

A car speeds up from $u = 5\,\text{m/s}$ to $v = 20\,\text{m/s}$ in $t = 3\,\text{s}$ :

a = \frac{v - u}{t} = \frac{20 - 5}{3} = 5\ \text{m/s}^2

Read the axis labels before you read the line. The same straight, flat line means "stopped" on a distance–time graph but "cruising at steady speed" on a velocity–time graph. Always check which graph you're looking at first.

Last revised 30 August 2025.