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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.

