State and prove work energy theorem for constant force

Asked by admin @ 12/08/2021 in Physics viewed by 298 People

State and prove work energy theorem by constant force

Answered by admin @ 12/08/2021

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

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

But remember that v = dx/dt:

We rearrange and integrate:

F dx = mv dv

Fx = m(½v2) = ½mv2 = Ek

But Fx = Work; therefore Work = ΔEk

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