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

  1. Femme_physics

    Femme_physics 2,555
    Gold Member

    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. jcsd
  3. Mark44

    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.
     
  4. Femme_physics

    Femme_physics 2,555
    Gold Member

    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.
     
  5. Mark44

    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.
     
  6. 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.
     
  7. Femme_physics

    Femme_physics 2,555
    Gold Member

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

    Good answers
     
  8. arildno

    arildno 12,015
    Science Advisor
    Homework Helper
    Gold Member

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

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