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

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

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

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 $y$-axis, therefore its velocity along $x$-axis will be zero.

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