Speed, velocity and acceleration: reading motion graphs

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 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 $t = 3\,\text{s}$:

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.