Q94 / 200 · NEET 2002 · Physics

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

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

Solution

From question $\vec{a}=\frac{\vec{F}}{m}=2 t^2 \hat{i}+\frac{4}{3} t \hat{j}$ $\therefore d \vec{V}=\left(2 t^2 \hat{i}+\frac{4}{3} t \hat{j}\right) d t$ Integrated both sides, We have, $\vec{V}=2\left[\frac{t^3}{3}\right] \hat{i}+\frac{4}{3}\left[\frac{t^2}{2}\right] \hat{j}$ at $t=3 \mathrm{sec}, \vec{V}=\frac{2}{3}(3)^3 i+\frac{4}{6}(3)^2 j$ $=18 \hat{i}+6 \hat{j}$

Hence, the correct answer is option: 'B'.

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