Question

A force $\overrightarrow{F}=(3t\hat{i}+5\hat{j})$N acts on a body due to which its displacement varies as $\overrightarrow{S}=(2t^2\hat{i}-5\hat{j})m$. Work done by this force in $2$ second is

• A. 32 J
• B. 24 J
• C. 46 J
• D. 20 J

Answer 1

The correct option is A 32 J

$\overrightarrow{v}=\frac{d\overrightarrow{S}}{dt}=\left(4t\right)\hat{i}$

$P=\overrightarrow{F}\cdot \overrightarrow{v}=12t^2$

$\therefore W={\int }_0^{2}Pdt={\int }_0^2\left(12\right)t^{2}dt=32J$.