On this page we'll show you how to determine displacement from a velocity graph, both when velocity is constant and when there is acceleration. Then we'll derive the displacement formula, for use when there is acceleration.
To begin, let's look at constant velocity. In the first graph below you can see the result of an object moving at a constant velocity of 6 m/s for a time interval of 8 seconds.
Since there is no acceleration, this is equivalent to using the formula d = v · t
Now let's look at an example where there is acceleration. We'll begin with the case where an object starts from rest.
Since there is acceleration, and vi = 0, this is equivalent to using the formula d = 1/2 · t · (vf - vi)
Finally, let's examine the case where there is acceleration, but the initiial velocity is not zero.
This is equivalent to using the formula: d = vi · t + 1/2 · a · t2 We'll show you where this formula comes from below.
We're going to redo the calculation we did earlier, but this time we won't specify actual numbers. Instead, we'll use vi, vf and t. We'll calculate areas 1 and 2 again, using the area formulas for a rectangle and triangle.
Notice in line 4, above right, we replaced (vf - vi) for a · t, as we said we would.
The final step gives us the standard formula for displacement:
Now we'll redo the example from above, using this formula: