Motion Graphs

In short: Motion graphs show how distance, speed or acceleration change with time. On a distance-time graph the gradient is the speed. On a speed-time graph the gradient is the acceleration and the area under the line is the distance travelled.

Distance-time graphs

Time goes on the x-axis. Distance goes on the y-axis.

Speed-time (velocity-time) graphs

Now speed goes on the y-axis. This changes everything, so always check the y-axis label first.

Acceleration-time graphs

Acceleration goes on the y-axis.

• A flat line above zero means constant acceleration.
• A flat line on zero means constant velocity (no acceleration).
• A flat line below zero means constant deceleration.
• Area under an acceleration-time graph = change in velocity.

Quick summary

• Distance-time: gradient = speed. Flat = stopped. Steeper = faster.
• Speed-time: gradient = acceleration. Area under = distance. Flat = steady speed.
• Acceleration-time: area under = change in velocity.
• Always read the y-axis label before you read the shape.
• Area of a triangle = $\frac{1}{2}\times \text{base}\times \text{height}$. Area of a rectangle = base × height.

Quiz