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

The correct option is B

10 s

Step 1: Given data

1. Mass of the body is $m=5kg.$
2. Force on the body, $\overrightarrow{F}=\left(-3i+4j\right)$$N$.
3. The initial velocity of the body, $\overrightarrow{v}=\left(6i-12j\right)m/s$.

Step 2: Concepts

1. The velocity will be along the y-axis when the x component($v_x$) of velocity will be zero.
2. We know the kinematics equation $v=u+at$, where v and u are the final and initial velocities respectively, a is the acceleration of the body.

Step 3: Find the time

The velocity will be directed along the y-axis, when, $v_x=0$, i.e, the final velocity will zero along the x-axis.

Now, force along x-axis,

$$\begin{gathered} F_x=-3 \\ ora=\frac{-3}{m}=\frac{-3}{5} \\ ora=\frac{-3}{5} \end{gathered}$$ (Since, $Force=Mass\times acceleration$)

So, from, $v=u+at$ we get,

$$\begin{gathered} 0=6+\left(\frac{-3}{5}\times t\right) \\ ort=6\times \frac{5}{3}=10 \\ ort=10sec. \end{gathered}$$

The time when the velocity will be directed only along the y axis is $10sec.$

So, option (B) is correct.