# The force applied against an object moving horizontally on a linear path is described by F(x)= x+3 N . By how much does the object's kinetic energy change as the object moves from  x in [ 1 , 2 ]?

Dec 29, 2015

It increases by $4 \text{J}$

#### Explanation:

Work done = force x distance moved in direction of force.

Because force varies with displacement we can say:

$W = {\int}_{1}^{2} F . \mathrm{dx}$

$\therefore W = {\int}_{1}^{2} \left(x + 3\right) . \mathrm{dx}$

$W = {\left[{x}^{2} / 2 + 3 x\right]}_{1}^{2}$

$W = \left[\frac{4}{2} + 6\right] - \left[1 + 3\right]$

$W = 8 - 4 = 4 \text{J}$

This work will appear as kinetic energy.