The work-energy theorem is a fundamental principle in physics that relates the work done on an object to its change in kinetic energy. Simply put, it states that the net work done on an object is equal to the change in its kinetic energy. This theorem is derived from Newton's second law and can be expressed mathematically as:

W = ΔKE

where W is the net work done on the object and ΔKE is the change in its kinetic energy.

The work-energy theorem is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed.

Now, let's understand this theorem with the help of an example. Suppose we have a car of mass m moving with an initial velocity v_i. If a net force F_net acts on the car in the direction of motion for a distance d, the work done on the car can be calculated as:

W = F_net × d

If the car comes to rest after the force is applied, its final velocity v_f will be zero. Using the work-energy theorem, we can relate the work done to the change in kinetic energy as:

W = KE_f - KE_i = 1/2 m v_f^2 - 1/2 m v_i^2

Simplifying the equation, we get:

F_net × d = 1/2 m v_f^2 - 1/2 m v_i^2

This equation shows the connection between work, force, displacement, and the change in kinetic energy. By understanding and applying the work-energy theorem, we can analyze and predict the behavior of objects in motion.