JEE Physics 2025 Question with Solution

Given: Initial velocity is $\vec{v}_{in} = 3 \hat{i} + 4 \hat{j} \, \text{ms}^{-1}$, mass is $m = 2 \, \text{kg}$, force is $\vec{F} = 6 \hat{k} \, \text{N}$, and time in the field is $t = \frac{5}{3} \, \text{s}$.

Find: The velocity of the body when it emerges from the force field.

Use Newton's second law to find the acceleration:

$$\vec{F} = m\vec{a}$$

So,

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

Now apply the equation of motion under constant acceleration:

$$\vec{v}_{final} = \vec{v}_{in} + \vec{a} \, t$$

Substituting the given values:

$$\vec{v}_{final} = (3 \hat{i} + 4 \hat{j}) + (3 \hat{k}) \cdot \frac{5}{3}$$

Therefore,

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

Thus, the velocity of the body when it emerges from the force field is $3 \hat{i} + 4 \hat{j} + 5 \hat{k}$. The correct option is B.

Given: The force acts only along the positive z-axis, with $\vec{F} = 6 \hat{k} \, \text{N}$, and the body has mass $2 \, \text{kg}$.

Find: The final velocity vector after $\frac{5}{3} \, \text{s}$.

Since the force is only along $\hat{k}$, the x- and y-components of velocity remain unchanged. Therefore, only the z-component changes.

Acceleration along z-axis is:

$$a_z = \frac{F_z}{m} = \frac{6}{2} = 3 \, \text{ms}^{-2}$$

Initial z-component of velocity is $0$. Hence,

$$v_z = 0 + a_z t = 3 \times \frac{5}{3} = 5$$

So the final velocity vector becomes:

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

Therefore, the correct option is B.