Answer
At $s=100 \mathrm{~s}, \quad a=11.1 \mathrm{~m} / \mathrm{s}^2$
At $s=175 \mathrm{~m}, \quad a=-25 \mathrm{~m} / \mathrm{s}^2$
Work Step by Step
$0 \leq s \leq 150 \mathrm{~m}:$
$$
\begin{aligned}
v & =\frac{1}{3} s \\
d v & =\frac{1}{3} d s \\
v d v & =a d s \\
\frac{1}{3} s\left(\frac{1}{3} d s\right) & =a d s \\
a & =\frac{1}{9} s
\end{aligned}
$$
At $s=100 \mathrm{~m}, \quad a=\frac{1}{9}(100)=11.1 \mathrm{~m} / \mathrm{s}^2$
$$
\begin{aligned}
150 \leq s \leq 200 \mathrm{~m} ; \quad & =200-s, \\
d y & =-d s \\
v d y & =a d s \\
(200-s)(-d s) & =a d s \\
a & =s-200
\end{aligned}
$$
At $s=175 \mathrm{~m}, \quad a=175-200=-25 \mathrm{~m} / \mathrm{s}^2$
