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

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

Quote by Dory

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.

Similar Threads for: The derivative of position with respect to time VS the derivative of time with res...
Thread	Forum	Replies
Time derivative	General Physics	4
Time derivative with three variables	Calculus & Beyond Homework	2
derivative of a derivative with respect to something else	Calculus & Beyond Homework	6
having a hard time with a derivative	Calculus	6
derivative with respect to time ??	Introductory Physics Homework	3

Femme_physics Recognitions: Gold Member	The derivative of position with respect to time VS the derivative of time with res... Tweet 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 Mentor	It would be the reciprocal of the velocity, in units of time over distance.

arildno Recognitions: Gold Member Homework Help Science Advisor	Well, the reciprocal of the velocity tells you the the time required to traverse the unit distance.