Work Energy Theorem Concept and Proof

Work is said to be done when applied force is able to produce displacement. This work done in producing the displacement can not simply disappear once if the job is completed. This is against the law off conservation of energy. According to this concept, energy is neither created nor destroyed. It just converts from one form to other.

This work done in moving a body will be stored in that body in the form of kinetic energy. According to work energy theorem, work done on a body is equal to change in its kinetic energy. That is work done is equal to change in final kinetic energy and initial kinetic energy.

Let us consider a body of mass m initially moving with a velocity u. Let us consider that a force F is applied on the body. Let the body got displaced by the displacement S and the body got a final velocity V. We can apply this values in equation of motion and get the value of acceleration of the body.

We know that work done is the dot product of force and displacement. As the applied force is in the same direction of the body, work done is just the product of force and displacement. We also know that force is the product of mass and acceleration. We can substitute the value of acceleration value obtained from the previous equation.

Thus as shown in the video below, we can get the work done as the change in the kinetic energy.