## Sunday, December 27, 2015

### Kinetic Energy Mathematical Equation Derivation

Kinetic energy is the energy possessed by a body by virtue of its motion. We need to do some work in moving a body and this work done is stored in the form of kinetic energy. It depends on the mass of the body as well as velocity.

Let us consider a body of mass m is in the state of rest. Let a constant force F is applied on the body and it starts moving with a acceleration. Let the body is allowed to move for a time interval and let  it has acquired a final velocity after the journey.

Using the equation of motion,we can find the acceleration of the body in terms of initial velocity, final velocity and displacement.

Further substituting this acceleration value in the very definition of work done as force and displacement dot product, we can get the work done. Here in this case the angle between force and displacement is zero and hence the work done is maximum.

After the work is done, the energy used for doing this work done can not be disappeared. It is against the law of conservation of energy. As per this rule, energy is neither created or destroyed and it just converts from one format of the energy to other format of energy. Thus this work done is stored in the form of kinetic energy.

As shown in the below video, we can derive equation for the kinetic energy mathematical expression.