Question

A position-dependent force $f=7-2x+3x^2$ newton acts on a small body of mass $2$kg and displaces from $x=0$ to $x=5$. Calculate the work done by the force.

Answer 1

Given force $f=7-2x+3x^2$

And we know,

Work done$W=force\times displacement=fx$

Now integrating the above equation with respect to x from limit$x=0$ to $x=5$, we get,

$\int dW={\int }_0^5\left(7-2x+3x^2\right)dx$

$=|7x-\frac{2x^2}{2}+\frac{{3x}^3}{3}{|}_0^5$

$=35-25+125=135$ J