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 × 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
or a=v2/2s
Substituting the value of 'a' in equation (2) we get,
w=(mv2/2S) S
w=(mv2/2).....(3)
But since work done is stored in the body as its kinetic energy equation (3) can be written as
Kinetic energy(T) =1/2mv2
T=1/2mv2
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.