2002 AIPMT Laws of MotionNewton's Second Law with Variable Force Medium Question 63 of 72 in Laws of Motion

An object of mass 3 kg 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 second is : -

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

The answer is B.

Solution

Acceleration: $\vec{a} = \dfrac{\vec{F}}{m} = \dfrac{6t^2\hat{i} + 4t\hat{j}}{3} = 2t^2\hat{i} + \dfrac{4}{3}t\hat{j}$
$d\vec{v} = \left(2t^2\hat{i} + \dfrac{4}{3}t\hat{j}\right)dt$
Integrating on both sides from rest (v = 0 at t = 0):
$\vec{v} = 2\left(\dfrac{t^3}{3}\right)\hat{i} + \dfrac{4}{3}\left(\dfrac{t^2}{2}\right)\hat{j} = \dfrac{2}{3}t^3\hat{i} + \dfrac{2}{3}t^2\hat{j}$
At t = 3 s: $\vec{v} = \dfrac{2}{3}(27)\hat{i} + \dfrac{2}{3}(9)\hat{j}$
$\vec{v} = 18\hat{i} + 6\hat{j}$

Concept Integrating acceleration to get velocity

Laws of Motion in past papers

72 questions from this chapter have appeared across 27 exam years.