A rock falling under its on weight and resistance r=0.001mv^2

show newtons second law gives vdv/dx=g-0.001v^2

Am I missing something?? when did vdv/dx = a having cancelled through by m

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- May 5th 2008, 02:44 PMi_zz_y_illcan't prove acceleration,slight worry
A rock falling under its on weight and resistance r=0.001mv^2

show newtons second law gives vdv/dx=g-0.001v^2

Am I missing something?? when did vdv/dx = a having cancelled through by m - May 5th 2008, 04:04 PMmr fantastic
You should know $\displaystyle a = \frac{dv}{dt} = \frac{d^2 x}{dt^2}$ and $\displaystyle v = \frac{dx}{dt}$.

Use the chain rule:

$\displaystyle {\color{red}a = \frac{dv}{dt} = \frac{dv}{dx} \cdot \frac{dx}{dt} = \frac{dv}{dx} \cdot v}$.

Using the chain rule again it follows that $\displaystyle a = \frac{d}{dx} \left[\frac{v^2}{2} \right]$.