Prove a = v(dv/ds)

[dagr8est]

a = acceleration
v = velocity
t = time
s = displacement

a = dv/dt = d(ds/dt)/dt

Then I'm stuck. I know it has something to do with the chain rule but I can't see it. Any help will be appreciated.

 

[skeeter]

$\displaystyle a = \frac{dv}{dt}$

$\displaystyle \frac{a}{v} = (\frac{dv}{dt}) (\frac{1}{v})$

$\displaystyle \frac{a}{v} = (\frac{dv}{dt}) (\frac{dt}{ds})$

$\displaystyle \frac{a}{v} = \frac{dv}{ds}$

$\displaystyle a = v (\frac{dv}{ds})$