Question

state and prove work energy theorm ananlytically

Answer 1

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

F=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.