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10-172.

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 $v ( t ) = 5 \operatorname { cos } ( \frac { \pi } { 2 } t ) + 4 t$. 10-172 HW eTool (Desmos)Homework Help ✎

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

This is $v^\prime(4)$.

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

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

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

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