W = ∫ F d r = ∫ m a d r = ∫ m ⋅ d v d t d r = m ∫ d r d t d v = m ∫ v d v = m v 2 2 = Δ E k {\displaystyle W=\int F\,dr=\int ma\,dr=\int m\cdot {\frac {dv}{dt}}dr=m\int {\frac {dr}{dt}}dv=m\int vdv={\frac {mv^{2}}{2}}=\Delta E_{k}}
