Question

A force $F=x^2+2x+1$ acts on a particle in the x direction, where $F$ is in newton and $x$ in metre. Find the work done by this force during a displacement from $x=-1m$ to $x=2.0m$

Answer 1

Work done = ${\int }_{x_1}^{x_2}F.dx$

Here $F$ = $x^2+2x+1$

Therefore ,

Work done = ${\int }_{-1}^2(x^2+2x+1)dx$

= $\frac{x^3}{3}+x^2+x$

= $(\frac{8}{3}+4+2)-(\frac{-1}{3}+1-1)$

= $9$ $J$