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.