# Thread: can't prove acceleration,slight worry

1. ## can'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

2. Originally Posted by i_zz_y_ill
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
You should know $a = \frac{dv}{dt} = \frac{d^2 x}{dt^2}$ and $v = \frac{dx}{dt}$.

Use the chain rule:

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

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