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Representing dv independent of time?

  1. Mar 23, 2012 #1
    There are four basic equations for constant acceleration

    v = v_o +at
    v^2 = v_o^2 +2as
    and so on

    The first velocity is time dependent, while the second velocity relationship is time independent.

    In varying acceleration, we have

    v = ∫ a(t) dt

    Is there any other way we can define velocity so that it is independent of time, akin to the constant acceleration above?
     
  2. jcsd
  3. Mar 23, 2012 #2
    There are infinite such ways :-)

    But most of them aren't useful from practical point of view.

    Still I will state one or two for you.

    You can write v=ds/dt

    v=(ds/dt)*(dv/dv)

    [Multiplying by (dv/dv) makes no change]

    V=(ds/dv)*(dv/dt)
    V=(ds/dv)*a
    Since a=dv/dt

    On integration this yields your second equation when a is constant.


    Another would be

    v=(ds/dt)*(da/da)

    V=(ds/da)*j

    Where j is the jerk, the rate of change of acceleration.

    All these equations will give you formula's independent of t. But they will contain other variables which depend on time.


    Also
    Remember, in steady fluids we define the velocity as a function of space and not time.
    Even that picture may help you :-)
     
    Last edited: Mar 23, 2012
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