# The derivative of position with respect to time VS the derivative of time with res

1. Oct 5, 2010

### Femme_physics

I know that the derivative of position with respect to time is instantaneous velocity. What is the derivative of time with respect to position then? Is it even meaningful?

2. Oct 6, 2010

### Staff: Mentor

Re: The derivative of position with respect to time VS the derivative of time with re

It would be the reciprocal of the velocity, in units of time over distance.

3. Oct 6, 2010

### Femme_physics

Re: The derivative of position with respect to time VS the derivative of time with re

Is there any use to that? I never saw it in exercises.

4. Oct 6, 2010

### Staff: Mentor

Re: The derivative of position with respect to time VS the derivative of time with re

I can't say that I recall any, but if you know time t as a function of displacement x, then it would be natural to talk about the rate of change of t with respect to x; that is, dt/dx.

5. Oct 6, 2010

### Tac-Tics

Re: The derivative of position with respect to time VS the derivative of time with re

There's a lot more math in the world than there are uses for things.

6. Oct 7, 2010

### Femme_physics

Re: The derivative of position with respect to time VS the derivative of time with re