Speed-time graphs

Last time

Before we start: last time, in Direct and inverse proportion, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Your journey on a graph

A car pulls away from the lights, cruises, then slows to a stop. A speed-time graph draws the whole journey as one line. Two facts unlock every question: the slope is the acceleration, and the area underneath is the distance travelled.

Reading the graph

Here is a journey. In the first six seconds, the speed rises from zero to fifteen metres a second. Then it stays at fifteen for ten seconds. Then it falls to zero over the last five seconds. The total time is twenty-one seconds.

What each part means

A line sloping up means the speed is increasing: the object is accelerating. A flat line means the speed is constant. The object is still moving, but not speeding up or slowing down. A line sloping down means the speed is decreasing: deceleration, which is a negative acceleration. A line along the axis at zero means the object has stopped.

Acceleration is the gradient

Acceleration is the change in speed divided by the time taken. It is the gradient of the line. In the first part, the speed rises by fifteen in six seconds. That is fifteen over six: two point five metres a second squared. In the last part, the speed falls by fifteen in five seconds. The gradient is minus three, so the deceleration is three.