Question

Show that dp/dt =_dv/dx

Answer 1

The momentum of an object is $p=mv$

$\frac{dp}{dt}=\frac{d(mv)}{dt}$

$=m\frac{d(v)}{dt}$

$=m\frac{dv}{dt}(\frac{dx)}{dx})$

$=m(\frac{dx}{dt})(\frac{dv}{dx}) =mv(\frac{dv}{dx})$ $since (\frac{dx}{dt})=v$

Therefore,

$\frac{dp}{dt}=mv(\frac{dv}{dx})$