The area under a velocity-time graph gives the displacement. The velocity-time and acceleration-time graphs for common motions are shown below.

Key fact The gradient of speed-time and velocity-time graphs represent acceleration. The area under a speed-time graph represents the distance travelled.

Acceleration (a)- the rate of change of an object’s velocity over time. Displacement (s)- the total distance and the direction the object travels.

But if you calculate the acceleration without the graph, you are explicitly stating that the y-intercept is zero---which it might not be. So there are some actual reasons for making a graph.

With a fairly large time interval of 0.1 seconds, I still get a displacement fairly close to the analytical solution of 12 meters. Making a smaller time interval will clearly give a better solution.

Fuel-economy penalty of acceleration. Graph by Emissions Analytics. This is not something that's apparent in the gentle and controlled conditions of fuel-economy testing, researchers say.