A= dv/dt

  1. I see in many text that a = dv/dt implies that

    dv = a dt

    How is that possible, can anybody please explain me. As far as i know dv/dt is a symbol for derivative of v w.r.t t and not ratio between dv and dt.
  2. jcsd
  3. What you wrote is in differential form.
  4. jgens

    jgens 1,621
    Gold Member

  5. dv/dt is not a symbol. It is the mathematical formula for the derivative of v with respect to t. This is how one would show any derivative of a dependent variable with respect to an independent variable.
  6. And what did I say :-)
  7. arildno

    arildno 11,265
    Science Advisor
    Homework Helper
    Gold Member

    Now, WHY can we utilize at times the dv=adt formula, in particular, WHERE is it usable?


    When doing integration with the technique called substitution of variables (i.e the "inverse" of the chain rule):

    Given a=dv/dt, we have, trivially:
    But the right-hand side can, by the theorem of substitution of variables, be reformulated, giving the identity:

    Now, by IGNORING that the limits of integration actually refers to the limits of DIFFERENT variables, we "may say" that the "integrands" are equal, i.e, adt=dv!

    Thus, adt=dv should, at this stage of your education, be regarded as notational garnish (or garbage, if you like!)
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