# The force applied on a moving object with a mass of 1 kg  on a linear path is given by F(x)=x . How much work would it take to move the object over x in [1,3] ?

Mar 29, 2017

The work done is $= 4 J$

#### Explanation:

The force is $F \left(x\right) = x$

The work done is

$W = {\int}_{1}^{3} F \left(x\right) \mathrm{dx}$

$= {\int}_{1}^{3} x \mathrm{dx}$

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

$= \left(\frac{9}{2}\right) - \left(\frac{1}{2}\right)$

$= \frac{8}{2} = 4 J$