Calculus/Work
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Work |
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${\begin{aligned}W=\int F\,dr&=\int ma\,dr\\&=\int m\,{\frac {dv}{dt}}\,dr\\&=m\int {\frac {dr}{dt}}\,dv\\&=m\int v\,dv\\&={\frac {mv^{2}}{2}}=\Delta E_{k}\end{aligned}}$