Question

Find the work done by a force $\overrightarrow{F}=x\hat{i}+y\hat{j}N$ acting on a particle to displace it from point A(0,0) to B(2,3):

• A. $\frac{13}{2}$
• B. $13$
• C. $6$
• D. $\frac{15}{2}$

Answer 1

The correct option is A $\frac{13}{2}$

We know that $W=\overrightarrow{F}.\overrightarrow{s}$

$dW=\overrightarrow{F}.ds=(x\hat{i}+y\hat{j}).(dx\hat{i}+dy\hat{j})$

$W={\int }_0^{2}xdx+{\int }_0^{3}ydy={\left[\frac{x^2}{2}\right]}_0^2+{\left[\frac{y^2}{2}\right]}_0^3=\frac{13}{2}$