JEE Main 2025 — Laws Of Motion Question with Solution

To determine the velocity of the body as it emerges from the force field, we can break this process down as follows:

Force and Acceleration Calculation:

The body is subjected to a constant force of 6 N, which acts along the positive z-axis. The mass of the body is 2 kg.

Using Newton's second law, $\vec{F}=m\vec{a}$, the acceleration $\vec{a}$ can be calculated as:

$\vec{a}=\frac{\vec{F}}{m}=\frac{6\hat{k}}{2}=3\hat{k}{\text{ ms}}^{-2}$

Initial Velocity:

The initial velocity of the body is given by:

$\vec{u}=3\hat{i}+4\hat{j}{\text{ ms}}^{-1}$

Time of Motion:

The time the body spends in the force field is:

$t=\frac{5}{3}\text{ seconds}$

Final Velocity Calculation:

The final velocity $\vec{v}$ is given by the equation of motion:

$\vec{v}=\vec{u}+\vec{a}t$

Substituting the known values:

$\vec{v}=(3\hat{i}+4\hat{j})+3\hat{k}\left(\frac{5}{3}\right)$

Simplifying the expression gives:

$\vec{v}=3\hat{i}+4\hat{j}+5\hat{k}$

Therefore, the velocity of the body as it exits the force field is $3\hat{i}+4\hat{j}+5\hat{k}{\text{ ms}}^{-1}$.