Question

A body with mass 5 kg is acted upon by a force $\overrightarrow{F}=(-3\hat{i}+4\hat{j})N$. If its initial velocity at $t=0$ is $\overrightarrow{u}=(6\hat{i}-12\hat{j})m{s}^{-1}$, the time at which it will just have a velocity along the y-axis is

• A. $0$
• B. $10s$
• C. $2s$
• D. $15s$

Answer 1

Answer: (B)

$10s$

Here, m=5 kg. $\overrightarrow{F}=-3\hat{i}+4\hat{j}N$

$\overrightarrow{u}=6\hat{i}-12\hat{j}m{s}^{-1}$

The acceleration of the body is

$\overrightarrow{a}=\frac{\overline{F}}{m}=\frac{(-3\hat{i}+4\hat{j})N}{5kg}=-\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j}m{s}^{-2}$

Velocity of the body along x-axis at any time t is

$v_x=u_x+a_{x}t=6-\frac{3}{5}t$

As the body will have a velocity along the y-axis, therefore its velocity along x-axis will be zero.

i.e.$v_x=0$ or $6=\frac{3}{5}t\Rightarrow t=\frac{30}{3}=10s$