Answer
$10\ m$
Work Step by Step
Step 1. Given $a=\frac{d^2s}{dt^2}=\pi^2\ cos(\pi t)\ m/s^2$, we have $v(t)=\int a dt=\int \pi^2\ cos(\pi t) dt $.
Step 2. Letting $u=\pi t$, we have $du=\pi dt$ and $v(t)=\int \pi\ cos(u) du=\pi\ sin(u)+C =\pi\ sin(\pi t)+C$,
where $C$ is a constant.
Step 3. As $v(0)=8$, we have $\pi\ sin(0)+C=8$ and $C=8$
Step 4. Use the know $v(t)$, we have $s(t)=\int v(t)dt=\int(\pi\ sin(\pi t)+8)dt=\int sin(\pi t)d(\pi t)+\int8dt=-cos(\pi t)+8t+D$,
where $D$ is a constant.
Step 5. With $s(0)=0$, we have $-cos(0)+8(0)+D=0$ and $D=1$
Step 6. At $t=1\ sec$, we have $s(1)=-cos(\pi)+8(1)+1=10\ m$
