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

The correct option is A $10s$
Step 1: Find acceleration

Formula used: $\overrightarrow{a}=\frac{\overrightarrow{F}}{m}$

Given,

Mass$=5kg$

$\overrightarrow{F}=(-3\overrightarrow{i}+4\overrightarrow{j})N$

$\overrightarrow{u}=(6\overrightarrow{i}-12\overrightarrow{j})$

The acceleration of the body is

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

Step 2: Find velocity at time $t$.

Formula used:$v_x=u_x+a_{x}t$

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

$v_x=u_x+a_{x}t=6-\frac{3}{5}t$ $a_x$ from equation (i)

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

$v_x=0$

$0=6-\frac{3}{5}t\Rightarrow t=\frac{30}{3}=10s$

Final Answer: (b)