An object moves along the $x$-axis with an initial position of $x(0) = 2$. The velocity of the object when $t > 0$ is given by the equation $v ( t ) = 5 \operatorname { cos } ( \frac { \pi } { 2 } t ) + 4 t$. . 

1. What is the acceleration of the object when $t = 4$?

   Hint (a):

   This is $v^\prime(4)$.

2. What is the position of the object when $t = 4$?

   Hint (b):

   This is $x(4)$ where: $x ( t ) = \int v ( t ) d t$

3. What is the total distance the object travels over $0 ≤ t ≤ 4$?

   Hint (c):

   This is $x(4) - x(0)$.

   Check your answer using the Desmos Graphing Calculator