We have discussed how to calculate the velocity of an object using the position-time graph. We can do the reverse: given the velocity-time graph, we can calculate the change in position.

Recall that \(v = \frac{dr}{dt} \implies r = \int v(t) dt\). So, the displacement of an object is the integral of velocity. Whenever you see an integral, think of area under the curve. If the curve is below the y-axis, the area is negative.

For example, the area in the first rectangle in the animation equals the displacement from \(t=0\) to \(t=1\). The area of the second rectangle equals the displacement from \(t=1\) to \(t=3\).