Answer
$$\frac{v_{0}}{2}$$
Work Step by Step
Free-fall model
$v(t)=v_{0}-g t=v_{0}-32 t$
$s(t)=v_{0} t+s_{0}-16 t^{2}$
The average speed
$s_{0}=v_{0} t+s_{0}-16 t^{2}$
$\Rightarrow v_{0} t-16 t^{2}=0$
$\Rightarrow \frac{v_{0}}{16}=t$
$s_{0}=s(t)$
$v_{a v e}=\frac{16}{v_{0}} \int_{0}^{v_{0} / 16}|v(t)| d t$
Determine zero of velocity
\[
\begin{array}{l}
0=v(t)=v_{0}-32 t \\
\Rightarrow \frac{v_{0}}{32}=t
\end{array}
\]
Evaluate the average speed
$v_{\text {ave}}=\frac{16}{v_{0}}\left(\int_{0}^{v_{0} / 32}\left(v_{0}-32 t\right) d t-\int_{v_{0} / 32}^{v_{0} / 16}\left(v_{0}-32 t\right)\right)$
$=\frac{v_{0}}{2}$
