Question

An object of mass $3kg$ is at rest. Now a force of $\vec{F}=6t^2\hat{i}+4t\hat{j}$ is applied on the object then velocity of object at $t=3\sec$. is

• A. $18\hat{i}+3\hat{j}$
• B. $18\hat{i}+6\hat{j}$
• C. $3\hat{i}+18\hat{j}$
• D. $18\hat{i}+4\hat{j}$

Answer 1

Answer: (B)

Mass, $m=3kg$, force, $F=6t^2\hat{i}+4t\hat{j}$
$\therefore$ acceleration, $a=F/m$
$=\frac{6t^2\hat{i}+4t\hat{j}}{3}=2t^2\hat{i}+\frac{4}{3}t\hat{j}$
Now, $a=\frac{dv}{dt}=2t^2\hat{i}+\frac{4}{3}t\hat{j}$;
$\therefore dv=\left(2t^2\hat{i}+\frac{4}{3}t\hat{j}\right)dt$
$\therefore v=\underset{0}{\overset{3}{\int }}\left(2t^2\hat{i}+\frac{4}{3}t\hat{j}\right)dt$
$=\frac{2}{3}{t}^3\hat{i}+{\frac{4}{6}{t}^2\hat{j}|}_0^3=18\hat{i}+6\hat{j}$