Derivative of Position w/r/t Time vs Derivative of Time w/r/t Position

[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?

 

[Mark44]

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

 

[Femme_physics]

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

 

[Mark44]

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.

 

[Tac-Tics]

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

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

 

[Femme_physics]

Good answers

 

[arildno]

Well, the reciprocal of the velocity tells you the the time required to traverse the unit distance.