Question

A force F=a+bx acts on a particle in the x-direction where a and b are constants. Find the work done by this force during a displacement from x=0 to x=d.

Answer 1

Given that, F = a+bx

Where a and b are constants,

So, work done by this force during the

displacement x=0 to x=d is given by,

$W={\int }_0^{d}Fdx$

$={\int }_0^d(a+bx)dx$

$={\left[\begin{array}{c}ax+\frac{b{x}^2}{2}\end{array}\right]}_0^d$

$=ad+\frac{b{d}^2}{2}$