What is the work energy theorem?

The work energy theorem is a principle that states that the work done on an object is equal to the change in its kinetic energy.

This theorem can easily be derived using Newton's 2nd law of motion, some equations of kinematics, and the definition of work.

Work is defined as the product between force and displacement. In other words,

`W = Fd` .

For a moving object, the final velocity can be calculated if acceleration, distance travelled, and initial velocity are known. It is calculated as follows:

`v_f^2 = v_i^2 + 2ad` . Solving for d yields:

`d = (v_f^2 - v_i^2)/(2a)` , where a is the non-zero acceleration.

Substituting this to the equation for work,

`W = F((v_f^2 - v_i^2)/(2a)) = (Fv_f^2)/(2a) - (Fv_i^2)/(2a)` .

Using Newton's 2nd Law of motion, which states that F = ma,

`W = 1/2 mv_f^2 - 1/2 mv_i^2 = KE_f - KE_i` .