Question

Proof of work energy theorum

Answer 1

Work energy theorem states that the change in kinetic energy of an object is equal to the net work done on it by the net force. Hence, work done on a body by a force is equal to the change in its kinetic energy.

From Newton’s Second Law of motion, we know that F = ma, and because of the definition of acceleration we can say that

F= ma = m dv/dt

If we multiply both sides by the same thing, we haven’t changed anything, so we multiply by v:

Fv=mv dv/dt

But remember that v = dx/dt:

F dx/dt=mv dv/dt

We rearrange and integrate:

F dx = mv dv

integration

Fx = m(½v2) = ½mv2 = Ek

But Fx = Work; therefore Work = ΔEk.

Hope It Helps !!!