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.Work Energy Theoremf = 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 ∫uv v dv

= m [v²/2]uv = ½ mv² – ½ mu²

= Δ KE

So, Work done = Change in KE

Hence proved.