Question

A particle has an initial velocity of $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. The magnitude of its velocity after $10s$ is

• A. $10units$
• B. $7\sqrt{2}units$
• C. $7units$
• D. $8.5units$

Answer 1

The correct option is B $7\sqrt{2}units$

The initial velocity is give as $V_i=3\hat{i}+4\hat{j}$

the acceleration is a $a=0.4\hat{i}+0.3\hat{j}$

and the time elapsed is $y=10s$

now final velocity after $10s$ is $V_f=\left(3\hat{i}+4\hat{j}\right)m/s+10s\left(0.4\hat{i}+0.3\hat{j}\right)m/s$

$V_f=7\hat{i}+7\hat{j}$

$V=\sqrt{{\left(7\hat{i}\right)}^2+{\left(7\hat{j}\right)}^2}=7\sqrt{2}$

Hence,

option $\left(B\right)$ is correct answer.