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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