Answer
See explanations.
Work Step by Step
Step 1. The Mean Value Theorem states that for a continuous function in a closed interval $[a,b]$ and differentiable in $(a,b)$, we can find at least one point $c$ in the interval such that $f'(c)=\frac{f(b)-f(a)}{b-a}$
Step 2. In the case of this problem, we simulate the trip as a continuous function $s(t)$, and the average speed can be found as $\bar v=\frac{s(2)-s(0)}{2-0}$
Step 3. The speed function is the derivative of the distance function $v(t)=s'(t)$. Using the above result, we can find at least a time $t_1$ such that $s'(t_1)=\frac{s(2)-s(0)}{2-0}$ (the Mean Value Theorem) which means that $v(t_1)=\bar v$.
