Chapter 4 - Integration - 4.8 Average Value Of A Function And It's Applications - Exercises Set 4.8 - Page 335: 14

See explanation.

We know that $v_{0}+a t=v(t)$ since the acceleration is constant and therefore the velocity function is a linear function. Thus, we know that the average velocity at $[a, b]$ is equal to the velocity of the midpoint of the interval.