# 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 [1,2] ?

May 13, 2017

The work is $= 4.5 J$

#### Explanation:

The work $W$ is

$W = F \cdot d$

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

$\mathrm{dW} = \left(x + 3\right) \mathrm{dx}$

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

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

$= \left(2 + 6\right) - \left(\frac{1}{2} + 3\right)$

$= 4.5 J$