If `K_(1)` and `K_(f)` are the initial and final value of kinetic energy of a body respectively, then the work done by the net force on the body is equal to

Options

A. `(K_(f)K_(i))/(K_(f)-K_(i))`
B. `K_(f)+K_(i)`
C. `(K_(f)+K_(i))/2`
D. `K_(f)-K_(i)`

Explanation

To solve the question, we will use the work-energy theorem, which states that the work done by the net force on an object is equal to the change in its kinetic energy.

### Step-by-Step Solution:

1. **Understand the Work-Energy Theorem**: The work-energy theorem states that the work done (W) on an object is equal to the change in its kinetic energy (ΔK). Mathematically, this can be expressed as:
\[ W = K_f - K_i \]
where \(K_f\) is the final kinetic energy and \(K_i\) is the initial kinetic energy.

2. **Define Kinetic Energy**: Kinetic energy (K) of an object is given by the formula:
\[ K = \frac{1}{2}mv^2 \]
where \(m\) is the mass of the object and \(v\) is its velocity.

3. **Express Change in Kinetic Energy**: The change in kinetic energy can be expressed as:
\[ \Delta K = K_f - K_i \]
This means that the work done by the net force is equal to the difference between the final and initial kinetic energies.

4. **Substitute Values**: If we let \(K_i\) be the initial kinetic energy and \(K_f\) be the final kinetic energy, we can write:
\[ W = K_f - K_i \]

5. **Conclusion**: Therefore, the work done by the net force on the body is equal to the change in kinetic energy, which is:
\[ W = K_f - K_i \]

### Final Answer:
The work done by the net force on the body is equal to \(K_f - K_i\).

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