Velocity / Time Graphs

Here is a velocity time graph for an object travelling with a uniform acceleration.

If the graph is a straight line then the acceleration is just the change in speed divided by the time. But what if the acceleration isn't constant so the graph isn't a straight line?

To find the acceleration at any point in time we find the gradient of the tangent at that point. This tells us the "rate of change" of velocity at an instant, i.e. the acceleration.   a = dv / dt

We can see that on this graph the gradient, and hence the acceleration is decreasing and approaches 0. The object is approaching a maximum velocity, like a car accelerating from rest.

The area under the curve is equal to the displacement of the object. There are various ways to find the area from the graph. Some are more accurate than others but the method of approximating the area below will do for us.