Bob's cat, Alice, is still doing wind sprints up and down his hallway. This time suppose that Alice's acceleration after $t$ seconds is given by the formula $a ( t ) = - \pi \operatorname { sin } \frac { \pi t } { 5 }$. As Alice hits the hallway, her velocity is already $6$ feet per second, so $v(0) = 6$.

1. Find a formula for Alice's velocity at time $t$.

   Hint (a):

   To find the velocity formula, will need to use the given initial velocity.

2. Find Alice's displacement between $t = 5$ and $t = 10$.