Distance-time and displacement-time graphs Distance-time graphs show distance on the vertical axis and time on the horizontal axis. The gradient of a distance-time graph represents speed because: ...

If the velocity-time graph is curved, the acceleration can be found by calculating the gradient of a tangent to the curve.

Let's start with the definition of velocity (in one dimension): But what if I represent this as a graph? Here is a velocity vs time graph for this same situation.

Here is what I get. Since the acceleration is defined as the change in velocity divided by the change in time, the slope of a velocity-time graph will be the acceleration of the car.