Displacement from a velocity-time graph – how to find out?

We can find the displacement of a moving object from its velocity-time graph.
This is given by the area under this graph:
displacement = area under velocity-time graph

Finding displacement from a velocity-time graph when the object is moving at a steady velocity

It is easy to see why this is the case for an object moving at a steady velocity.

The displacement is simply velocity x time, which is the area of the shaded rectangle (figure 1).

In this graph (a), the area of the shaded rectangle = 20 m/s x 15 s = 300m
So, displacement s = 300 m

Deducing displacement from a velocity-time graph for changing velocity

For changing velocity, again the area under the velocity-time graph gives displacement (Figure b).

The area of each square of the graph represents a distance traveled: in this case, 1 m/s x 1 s, or 1 m.

So, for this simple case in which the area is a triangle, we have displacement = (1/2) x base x height = (1/2) x 5 s x 10 m/s = 25 m