sloane729
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Homework Statement
I'm working through a derivation for work in Thornton's Classical Dynamics but I'm stuck at one step.
\begin{align}<br /> \vec{F} \cdot d\vec{r} &= m\frac{d\vec{v}}{dt} \cdot \frac{d\vec{r}}{dt}dt = m\frac{d\vec{v}}{dt} \cdot \vec{v}dt \\ &= \frac{m}{2}\frac{d}{dt}(\vec{v}\cdot \vec{v})dt \end{align}
I'm having trouble getting from the last equality on the first line to the second line.
Homework Equations
The Attempt at a Solution
I don't know what the mathematical reasoning is.