# The force applied against an object moving horizontally on a linear path is described by F(x)= cospix+1 . By how much does the object's kinetic energy change as the object moves from  x in [ 0, 3 ]?

Mar 31, 2018

The change in kinetic energy will be $3$ joules.

#### Explanation:

Recall that $\text{Work} = F \cdot d = \Delta K E$

Therefore, if we find $F \cdot d$ one $\left[0 , 3\right]$, we'll have our change in kinetic energy. Therefore, we will have to integrate the force function on $\left[0 , 3\right]$.

$I = {\int}_{0}^{3} \cos \left(\pi x\right) + 1$

$I = {\left[\frac{1}{\pi} \sin \left(\pi x\right) + x\right]}_{0}^{3}$

$I = \frac{1}{\pi} \sin \left(3 \pi\right) + 3 - \frac{1}{\pi} \sin \left(0\right) - 0$

$I = 3$

Therefore the change in kinetic energy will be $3$ Joules.

Hopefully this helps!