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10-154.

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?

2. What is the total distance the object covers during the interval 0 ≤ t ≤ 4?

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

This is v′(4).

This is x(4) where:

$x(t)=\int v(t)dt$

This is x(4) – x(0).