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.

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.

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

Velocity-Time graph If we find the area under velocity-time graphs, then we actually find the distance travelled for the section of graph we are using.