# The force applied against an object moving horizontally on a linear path is described by F(x)=x^2-3x +5. By how much does the object's kinetic energy change as the object moves from  x in [ 0 , 2 ]?

Aug 21, 2017

The change in kinetic energy is $= 6.67 J$

#### Explanation:

The change in kinetic energy is equal to the work

$\Delta K E = W$

$F \left(x\right) = {x}^{2} - 3 x + 5$

$\Delta W = F \cdot \Delta x$

$W = {\int}_{0}^{2} \left({x}^{2} - 3 x + 5\right) \mathrm{dx} = {\left[{x}^{3} / 3 - \frac{3}{2} {x}^{2} + 5 x\right]}_{0}^{2}$

$= \left(\frac{8}{3} - 6 + 10\right) - \left(0\right)$

$= \left(4 + \frac{8}{3}\right)$

$= \frac{20}{3} = 6.67 J$