# Help on derivation of work

1. Feb 21, 2013

### sloane729

1. The problem statement, all variables and given/known data
I'm working through a derivation for work in Thornton's Classical Dynamics but I'm stuck at one step.
\begin{align} \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.

2. Relevant equations

3. The attempt at a solution
I don't know what the mathematical reasoning is.

2. Feb 21, 2013

### MrWarlock616

I don't get it too. Might be a mistake.

3. Feb 21, 2013

### sloane729

Last edited: Feb 21, 2013
4. Feb 21, 2013

### HallsofIvy

Staff Emeritus
You can't say that because you haven't defined "v^2". Since v is a vector, what you really mean is $\vec{v}\cdot\vec{v}= ||\vec{v}||^2$.
But, the basic idea is correct:
$$\frac{d(\vec{v}\cdot\vec{v})}{dt}= 2\vec{v}\cdot\frac{d\vec{v}}{dt}$$