Question

A force $\overrightarrow{F}=6t^2\hat{i}+4t\hat{j}$, is acting on a particle of mass $3kg$ then what will be velocity of particle at $t=3$ sec. if at $t=0$, particle is at rest?

• A. $18\hat{i}+6\hat{j}$
• B. $18\hat{i}+12\hat{j}$
• C. $12\hat{i}+6\hat{j}$
• D. none

Answer 1

The correct option is A $18\hat{i}+6\hat{j}$

$\overrightarrow{F}=6t^2\hat{i}+4t\hat{j}$
$\overrightarrow{F}=\frac{d\overrightarrow{P}}{dt}\Rightarrow dP=Fdt$
$m({\overrightarrow{v}}_2-{\overrightarrow{v}}_1)=\int (6t^2\hat{i}+4t\hat{j})dt$
$m({\overrightarrow{v}}_2-{\overrightarrow{v}}_1)=\frac{6t^3}{3}\hat{i}+\frac{4t^2}{2}\hat{j}$
$\Rightarrow {\overrightarrow{v}}_2=\frac{1}{3}(\frac{6t^3}{3}\hat{i}+\frac{4t^2}{2}\hat{j}$ since
$\Rightarrow \overrightarrow{v_2}=18\hat{i}+6\hat{j}$