For an object moving with constant acceleration starting from rest, the average velocity over the interval from 0 to t is which of the following relative to the final velocity v?

• A. v
• B. v/2
• C. 2v
• D. sqrt(v)

Answer: (B)

Constant acceleration from rest makes velocity grow linearly with time. If you start at 0 and reach a final velocity v after time t, the average velocity over that interval is simply the average of the endpoints on a straight-line velocity-vs-time graph: (0 + v) / 2 = v/2. You can also see this from distance: the distance traveled in time t is s = (1/2) a t^2, and with v = a t, that becomes s = (1/2) v t, so average velocity is s/t = (1/2) v. So the average velocity over 0 to t is half the final velocity.