workdone by the force

is equal to change kinetic energy

When you accelerate an object, you are doing work against inertia. That work equals the change in kinetic energy of the object.

Proof that the relationship is true can be determined by starting with the standard equation for work against inertia. You then define the constant acceleration in terms of velocity and time, as well as the distance traveled.

By some simple algebraic substitution, you can derive the equation for work in terms of change in kinetic energy.

You want to prove that the equation for work in terms of the change in kinetic energy of an object is:

W = ΔKE

or

W = KE_f− KE_i

where

• W is the work done against the resistance of inertia
• ΔKE is the change in kinetic energy (Δ is Greek letter capital delta)
• KE_f is the final kinetic energy of the object (KE_f = mv_f²/2)
• KE_i is the initial kinetic energy of the object (KE_i = mv_i²/2)