If the velocity of a particle is $v(t) = t\operatorname{cos} (πt)$,

1. For what value(s) of $t$ is the particle at rest?

   Hint (a):

   When $t = 0$ or $\operatorname{cos}(πt) = 0$.

2. What is the acceleration of the particle at $t = 2$?

   Hint (b):

   $a(t) = \operatorname{cos}(πt)-t(π)\operatorname{sin}(πt)$

3. Find the position function $x(t)$ if $x(0) = 5$.

   Hint (c):

   $s(t)=\int v(t)dt$
   Use integration by parts. Let $f = f$ and $dg =\operatorname{cos}(πt)dt$.
   Solve for $C$ given $x(0) = 5$.