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} $.