Question

An object of mass $3kg$ is at rest. If a force $\overrightarrow{F}=(6t^2\hat{i}+4t\hat{j})N$ is applied on the object, then the velocity of the object at $t=3s$ 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

The correct option is D $18\hat{i}+4\hat{j}$

Given

Mass = m = 3 kg

$F=(6t^2\hat{i}+4/3t\hat{j})$

$Force=mass\times acceleration-------\left(1\right)$

And

$Acceleration=a=\frac{dv}{dt}=\frac{F}{m}=F=(2t^2\hat{i}+4/3t\hat{j})$

$\Rightarrow dv=(2t^2\hat{i}+\frac{4}{3}t\hat{j})dt$

Integrating on both sides we get,

$\overrightarrow{v}=2\left[\frac{t^3}{3}\right]\hat{i}+\frac{4}{3}[\frac{t^2}{2}\hat{j}$

At t = 3 sec,

$\overrightarrow{v}=2\left[\frac{3^3}{3}\right]\hat{i}+\frac{4}{3}[\frac{3^2}{2}\hat{j}$

$\overrightarrow{v}=18\hat{i}+6\hat{j}$ m/s.