This is not a homework question, but a derivation in my class which I can't get around.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Step1 [tex]F=ma[/tex]

Step2 [tex]\vec{F} = m\frac{d\vec{v}}{dt}[/tex]

Step3: Multiply both side by v [tex]\vec{F}.\vec{v} = m\vec{v}.\frac{d\vec{v}}{dt}[/tex]

Step4 [tex]Power = \frac{d}{dt}\frac{1}{2}m\vec{v}.\vec{v}[/tex]

Step5 [tex]Power = \frac{d}{dt}\frac{1}{2}mv^{2} = \frac{dK}{dt}

[/tex]

2. Relevant equations

3. The attempt at a solution

I just can't figure out where did the [tex]\frac{1}{2}[/tex] come from in step 4.

Please help & thanks in advance!

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# Homework Help: V dot (dv/dt) = (0.5)*(d/dt)*(v^2) ?

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