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NEET Physics QUESTION #7331
Question 1

A force $\vec{F} = 6t^2\,\hat{i} + 4t\,\hat{j}$ acts on a particle of mass $3\text{ kg}$, initially at rest. Find its velocity at $t = 3\text{ s}$.

  • $18\hat{i}+6\hat{j}$✔️
  • $18\hat{i}+12\hat{j}$
  • $12\hat{i}+6\hat{j}$
  • None of these
Correct Answer Explanation

Acceleration: $\vec{a} = \dfrac{\vec{F}}{m} = 2t^2\,\hat{i} + \dfrac{4t}{3}\,\hat{j}$

Velocity: $\vec{v} = \displaystyle\int_0^3 \vec{a}\,dt = \left[\dfrac{2t^3}{3}\,\hat{i} + \dfrac{2t^2}{3}\,\hat{j}\right]_0^3 = \dfrac{2(27)}{3}\,\hat{i} + \dfrac{2(9)}{3}\,\hat{j} = \mathbf{18\hat{i} + 6\hat{j}}$