Exercise 14

In Chapter, we showed that for an object moving along a straight line with position function $s(t)$, the object's “average velocity on the interval $[a,b]$ ” is given by $$\begin{gathered} AV_{[a,b]} = \frac{s(b)-s(a)}{b-a} \end{gathered}$$.

More recently in Chapter, we found that for an object moving along a straight line with velocity function $v(t)$, the object's “average value of its velocity function on $[a,b]$ ” is $$\begin{gathered} \displaystyle v_{\operatorname{AVG} [a,b]} = \frac{1}{b-a} \int_a^b v(t) \, dt \end{gathered}$$.

Are the “average velocity on the interval $[a,b]$ ” and the “average value of the velocity function on $[a,b]$ ” the same thing? Why or why not? Explain.