Answer
$$t =\frac{5}{2} \text{s}$$
Work Step by Step
We are given $$s(t)=t^{2}-t+10,\quad 0 \leq t \leq 5$$
We calculate the average speed over the $t-$interval $[0, 5]$
\begin{align*}
\frac{s(5)-s(0)}{5-0}&=\frac{30-10}{5}\\
&=4 \mathrm{cm} / \mathrm{s}
\end{align*}
and the instataneous velocity is $$ v(t)=s^{\prime}(t)=2 t-1$$
We set the two equal to find the time:
$$ 2t-1=4\ \ \ \to \ t =\frac{5}{2} \text{s}$$
