Answer
$a_{t=8}=\frac{dv}{dt}=0$ m/s$^2$
$s_{t=8}=30$ m
$a_{t=12}=-1$ m/s$^2$
$s_{t=12}=48$ m
Work Step by Step
At $t=8$ s
$a=\frac{dv}{dt}=0$ m/s$^2$
$\Delta s = \int v dt$
$s-0=\frac{1}{2}(4)(5)+(8-4)(5)=30$
$s=30$ m
At $t=12$ s
$a=\frac{dv}{dt}=\frac{-5}{5}=-1$ m/s$^2$
$\Delta s = \int v dt$
$s-0=\frac{1}{2}(4)(5)+(10-4)(5)+\frac{1}{2}(15-10)(5)-\frac{1}{2}(\frac{3}{5})(5)(\frac{3}{5})(5)$
$s=48$ m
