Question

An object of mass $3 \,kg$ is at rest. Now a force of $\vec{F}=6 t^{2} \hat{i}+4 t \hat{j}$ 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, $m=3 \,kg$, force, $F=6 t^{2} \hat{i}+4 t \hat{j}$
$\therefore $ acceleration, $a=F / m$
$=\frac{6 t^{2} \hat{i}+4 t \hat{j}}{3}=2 t^{2} \hat{i}+\frac{4}{3} t \hat{j}$
Now, $a=\frac{d v}{d t}=2 t^{2} \hat{i}+\frac{4}{3} t \hat{j}$;
$\therefore d v=\left(2 t^{2} \hat{i}+\frac{4}{3} t \hat{j}\right) d t$
$ \therefore v=\int\limits_{0}^{3}\left(2 t^{2} \hat{i}+\frac{4}{3} t \hat{j}\right) d t$
$=\frac{2}{3} t^{3} \hat{i}+\left.\frac{4}{6} t^{2} \hat{j}\right|_{0} ^{3}=18 \hat{i}+6 \hat{j}$