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Really quick differential question

  1. Feb 27, 2006 #1
    If I am rewriting v in terms of x and t, I write it as dx/dt, but how about v^2?
     
  2. jcsd
  3. Feb 27, 2006 #2
    urnt? Are you talking about Reduction of order?
    Like:

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  4. Feb 27, 2006 #3
    I don't know, my prof likes to ask questions on things he doesn't teach :\

    I mean, in an equation like: F=-mv, you can rewrite it like m [(d^2 x)/(dt^2)] = -m dx/dt

    But how would you rewrite F=-m(v^2) ?
     
  5. Feb 27, 2006 #4
    [tex] (v)^2 = v*v[/tex]
    [tex] (\frac{dx}{dt})^2 = \frac{dx}{dt} * \frac{dx}{dt} [/tex]

    Let's say [itex] x=t^2+t^4 [/itex] then [itex] v = \frac{dx}{dt}[/itex]. So we then have [itex] F = mv^2 = m \times \frac{dx}{dt} \frac{dx}{dt} = 2t+4t^3 \times 2t+4t^3[/itex]

    assuming F = mv
     
    Last edited: Feb 27, 2006
  6. Feb 27, 2006 #5
    Okay, thanks a lot!
     
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