Question

A force $\overrightarrow{F}=(3t\hat{i}+5\hat{j})$N acts on a body due to which its position varies as $\overrightarrow{S}=(2t^2\hat{i}-5\hat{j})$. Find the work done by this force in initial $2s$.

• A. $23J$
• B. $32J$
• C. $Zero$
• D. $48J$

Answer 1

The correct option is D $48J$

Given,

Force, $F=(3t\hat{i}+5\hat{j})N$

Displacement, $s=(2t^2\hat{i}-5\hat{j})m$

$ds=(4t\hat{i}+0\hat{J})dt$

$dw=F.ds$

${\int }_0^{w}dw={\int }_0^2(3t\hat{i}+5\hat{j})(4t\hat{i}+0\hat{j})dt$

$W={12t^2|}_0^2=48J$

Net work done is $48J$