To address the question, we must determine which statement is correct about the work done on a particle moving under a force field.

Let's analyze each option:

1. The net work equals the change in kinetic energy.
2. The force is conservative.
3. The force is constant.
4. The velocity must always increase.

We begin by understanding the relationship between work and kinetic energy. According to the Work-Energy Theorem, the net work done by forces acting on a particle is equal to the change in kinetic energy of that particle. Mathematically, this is represented as:

\(W_{\text{net}} = \Delta K\ = \frac{1}{2} m (v_f^2 - v_i^2)\)

where \(W_{\text{net}}\) represents the net work done, \(\Delta K\) is the change in kinetic energy, \(v_f\) is the final velocity, \(v_i\) is the initial velocity, and \(m\) is the mass of the particle.

From the given information, the work done depends only on the initial and final speeds, implying that the net work equals the change in kinetic energy. Hence, option 1 is correct.

Now, let's rule out the other options:

• The force is conservative: While a conservative force is one where the work done is dependent only on initial and final positions, the problem specifies dependency on speeds, not positions. Hence, this doesn't necessarily imply that the force is conservative.
• The force is constant: A constant force would imply a uniform acceleration, which is not stated or required per the question.
• The velocity must always increase: This condition is unnecessary because the net work could result in a decrease in speed (deceleration), depending on the initial and final kinetic energy.

Therefore, the correct statement in the context of the problem and the given conditions is that the net work equals the change in kinetic energy.