The velocity of a body moving in a straight line is increased by applying a constant force F, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.

Explanation

To prove that the increase in kinetic energy of a body is equal to the work done by a constant force F applied over a distance, we can follow these steps:

### Step 1: Define Initial and Final Velocities
Let the initial velocity of the body be \( u \) and the final velocity after applying the force be \( v \).

### Step 2: Write the Expression for Kinetic Energy
The kinetic energy (KE) of an object is given by the formula:
\[
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