Question

A force $\overrightarrow{F}=2\hat{i}+3\hat{j}$ acting on a particle which displace it from a point ($1,2$) $m$ to a point ($3,2$) $m$. Find the work done by this force.

Answer 1

Let $ds=dx\hat{i}+dy\hat{j}$

Then

$dw=F.ds$

$dw=(2\hat{i}+3\hat{j}).(dx\hat{i}+dy\hat{j})$

$dw=2dx+3dy$

$w=2\underset{1}{\overset{3}{\int }}dx+3\underset{2}{\overset{2}{\int }}dy$

$=2{x^{}}_1^3+0$

$=4J$