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 ∫uv v dv
= m [v²/2]uv = ½ mv² – ½ mu²
= Δ KE
So, Work done = Change in KE
Hence proved.