Kinetic Energy

It is a matter of common experience that a fast moving stone can break a windowpane, falling water can rotate turbines and moving air can rotate windmills and propel sailboats. In all these examples, the moving body possesses energy. Work is done by the body in motion. This type of energy possessed by moving objects, is known as kinetic energy.

 

Kinetic energy is defined as the energy possessed by an object by virtue of its motion. Kinetic energy is represented by the letter 'T'. All moving objects possess kinetic energy.

Expression for Kinetic Energy of a Moving Body

Consider a body of mass 'm' which is initially at rest. When a force 'F' is applied on the body, let it start moving with a velocity 'v' and cover a distance 'S'. The force produces acceleration 'a' in the body.

The force 'F' does work when it moves the body through a distance 'S' and this work done is stored in the body as its kinetic energy.

By definition, W = F x S ...(1)

F = ma [Newton's second law of motion]

W = mas ...(2 )

Also, v² - u² = 2aS [Newton's third law of motion]

v² - 0 = 2aS [Initial velocity u = 0 as the body is initially at rest]v² = 2aS

 

 

Substituting the value of 'a' in equation (2) we get,

But since work done is stored in the body as its kinetic energy equation (3) can be written as

 

 

From the above equation we can conclude that the kinetic energy of a body is directly proportional to (1) its mass and (2) the square of its velocity.

Note :

When a force 'F' changes the initial velocity 'u' to final velocity 'v' then the change in the kinetic energy is . In the expression , 'v' stands for velocity of a moving body.