This is a speed-time graph for a car moving between two sets of traffic lights. The rate of change of speed is the slope or gradient of the speed-time graph Rate of change of speed = gradient of ...

the slope of a velocity-time graph will be the acceleration of the car. Notice that I have fit four linear functions to the data (I included the fitting equation for one of these linear fits).

Save guides, add subjects and pick up where you left off with your BBC account. The gradient of a velocity-time graph at a particular time gives the acceleration of the object at that time.