# The force applied against an object moving horizontally on a linear path is described by F(x)=8-x. By how much does the object's kinetic energy change as the object moves from  x in [ 2, 4]?

Mar 7, 2018

The change in kinetic energy is $= 10 J$

#### Explanation:

The change in kinetic energy is equal to the work done,

$\Delta K E = W$

The work done is

$\mathrm{dW} = F \left(x\right) \cdot \mathrm{dx}$

$W = {\int}_{2}^{4} \left(8 - x\right) \mathrm{dx}$

$= {\left[8 x - {x}^{2} / 2\right]}_{2}^{4}$

$= \left(32 - 8\right) - \left(16 - 2\right)$

$= 24 - 14$

$= 10 J$