Speed-Time Graphs

1. The gradient of a speed-time graph is the rate of change of speed. For straight-line motion in a fixed positive direction, it also gives signed acceleration.

\[\text{rate of change of speed}=\frac{\text{change in speed}}{\text{change in time}}.\] For a curved graph, use the tangent gradient at the stated time.

2. Types of Speed-Time Graphs

3. A positive speed-time gradient means speeding up; a negative speed-time gradient means slowing down.

In general, negative signed acceleration need not mean slowing down: compare its direction with velocity. A speed-time graph alone does not encode changes of direction.

For motion in the fixed positive direction, acceleration \(-30\text{ m/s}^2\) means a deceleration of magnitude \(30\text{ m/s}^2\).

4. Area under the speed-time graph = Distance travelled by the object.

5. \(\text{Average \ Speed =}\hspace{0.5em}\frac{\text{Total \ Distance \ Travelled}}{\text{Total \ Time \ Taken}}=\frac{\text{Area \ under \ the \ speed-time \ graph}}{\text{Total \ Time \ Taken}}\).