# Derivatives problem help

1. Nov 1, 2005

### Mathnewbie

Hello can someone point in the right direction on this one.

A particle moves along a strainght line with displacement s(t), velovity v(t), and acceleration a(t). Show that

a(t) = v(t) dv/ds

Explain the difference between the meanings of the derivatives dv/dt and dv/ds.

Does dv/dt mean differance of velocity over the differance time ?

Does dv/ds mean differance of velocity over the differance displacement ?

Any help would be great? Thanks

2. Nov 1, 2005

### HallsofIvy

Staff Emeritus
Basically yes: how fast the speed changes "per foot" rather than "per second", for example.
To do the first part, use the chain rule:
$$\frac{dv}{dt}= \frac{dv}{ds}\frac{ds}{dt}$$