The kinetic energy of a body is the energy that it has due to its movement and is defined as the work needed to accelerate a body of mass m from rest to a speed v.
The expression to calculate the kinetic energy of a body is as follows:
Ek = 1/2(mv^2)
Where m is the mass of the body, and v is its speed. This expression is obtained from the following analysis:
The work done by a force applied to a body, while moving a distance d is:
W = F d
We put the value of the force according to Newton's law:
W = ma d
The distance traveled under the action of a constant force is expressed as:
d = (vf^2 - vi^2)/2a
Then, substituting in the equation of work, we have:
W = ma (vf^2 - vi^2)/2a
W = m (vf^2 - vi^2)/2 = 1/2(mvf^2) - 1/2(mvi^2)
The expression 1/2 mv^2, is called kinetic energy of the body. So, the work is equal to the difference between the final and initial kinetic energy of the body.