Question

A force $\overrightarrow{F}=(3t\hat{i}+5\hat{j})$ acts on body due to which its displacement varies as $\overrightarrow{s}=(2t^2\hat{i}-5\hat{j})$. Work done by this force in $t=0$ to $2sec$ is

• A. $23J$
• B. $32J$
• C. zero
• D. $35J$

Answer 1

The correct option is B $32J$

Given,
$\overrightarrow{F}=3t\hat{i}+5\hat{j}$
$\overrightarrow{s}=2t^2\hat{i}-5\hat{j}$

$\frac{d\overrightarrow{s}}{dt}=4t\hat{i}$
$w=\int \overrightarrow{F}.d\overrightarrow{s}={\int }_0^2(3t\hat{i}+5\hat{j}).\left(4t\hat{i}\right)dt={\int }_0^{2}12t^{2}dt=4(2^3-0^2)=32J$