Work Energy Theorem

Principle:

The work-energy theorem is a generalized description of motion that states that the work done by the sum of all forces acting on an object is equal to the change in that object's kinetic energy.

f = ma

f = m dv/dt

We know that

dw = fdx

w = ∫ f. dx

= ∫ m. a dx

= ∫ m. (dv/dt) dx

= m ∫dv dx/dt

= m ∫ v. dv

Applying limits

Initial Velocity = u;

Final Velocity = v;

= m ∫_u^v v dv

= m [v²/2]_u^v = ½ mv² - ½ mu²

= Δ KE

So, Work done = Change in KE

Hence proved.