Answer
$$
\begin{aligned}
& v_{\max }=100 \mathrm{~m} / \mathrm{s} \\
& t^{\prime}=40 \mathrm{~s}
\end{aligned}
$$
Work Step by Step
$v-t$ Function. The $v-t$ function can be determined by integrating $d v=a d t$. For $0 \leq t<15 \mathrm{~s}, a=6 \mathrm{~m} / \mathrm{s}^2$. Using the initial condition $v=10 \mathrm{~m} / \mathrm{s}$ at $t=0$,
$$
\begin{aligned}
& \int_{10 \mathrm{~m} / \mathrm{s}}^v d v=\int_0^t 6 d t \\
& v-10=6 t \\
& v=\{6 t+10\} \mathrm{m} / \mathrm{s}
\end{aligned}
$$
The maximum velocity occurs when $t=15 \mathrm{~s}$. Then
$$
v_{\max }=6(15)+10=100 \mathrm{~m} / \mathrm{s}
$$
For $15 \mathrm{~s}
