# The force applied on a moving object with a mass of 2 kg  on a linear path is given by F(x)=x+3. How much work would it take to move the object over x in [0,2 ] ?

Apr 5, 2017

The work done is $= 8 J$

#### Explanation:

The mass is $m = 2 k g$

The force applied is

$F \left(x\right) = x + 3$

The work done is

$W = F \cdot d$

$d$ is the distance

So,

$W = \int F \left(x\right) \mathrm{dx}$

$= {\int}_{0}^{2} \left(x + 3\right) \mathrm{dx}$

$= {\left[\frac{1}{2} {x}^{2} + 3 x\right]}_{0}^{2}$

$= \left(2 + 6\right) - \left(0\right)$

$= 8 J$