Question

State work energy theorem and prove.

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

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.

Answer 2

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.

HOPE U LIKED THE ANSWER :D