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Help with Work-Energy theorem

  1. Jul 21, 2014 #1
    Hello,

    Someone could explain me why in the derivation below the mass m is divided by 2 in the last step?:

    ##\int\vec{F}\cdot d\vec{s}=m\int\frac{d\vec{v}}{dt}\cdot\vec{v}dt=\frac{m}{2}\int \frac{d}{dt}(v^{2})dt##
     
  2. jcsd
  3. Jul 21, 2014 #2

    jbriggs444

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    Science Advisor

    The derivitive ##\frac{d}{dt}(v^{2})## is equal to ##2\vec{v}\cdot\frac{d\vec{v}}{dt}##
     
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