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Strange physics question involving no constants and all variables.

  1. Sep 26, 2007 #1
    1. The problem statement, all variables and given/known data
    "K" is the time derivative of acceleration. Assume initial conditions of Ao, Vo, and Do.("o"=initial).

    Find:
    a(t):
    v(t):
    d(t):

    Show that:
    af^2=ao^2+2J(Vf-Vo)


    2. Relevant equations

    I'm honestly lost on this one..I don't know where to start. I could probably do it with numbers but clueless with variables!



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 26, 2007 #2
    Hey,

    Remember that what is common between the: displacement, velocity, and acceleration functions; are that they're all functions of time, indicating that [itex]t[/itex] is your only variable.

    Therefore, consider the following,

    [tex]
    {\frac{d}{dt}}{\left[a(t)\right]} = K
    [/tex]

    So, if the derivative with respect to [itex]t[/itex] was taken to get K, how do you get back [itex]a(t)[/itex]?

    Once you figure that out repeat for [itex]v(t)[/itex] and [itex]d(t)[/itex].

    Thanks,

    -PFStudent
     
    Last edited: Sep 26, 2007
  4. Sep 26, 2007 #3

    stewartcs

    User Avatar
    Science Advisor

    Hint: Use the Fundamental Theorem of Calculus.
     
  5. Sep 26, 2007 #4
    Integral maybe?
     
  6. Sep 26, 2007 #5
    Hey,

    Yes. To get you started here is how it looks,

    [tex]
    {a(t)} = {\int_{}^{}}{K}{dt}
    [/tex]

    Thanks,

    -PFStudent
     
  7. Sep 26, 2007 #6
    Well we haven't gotten there in calc yet but I'm sure I can find out how to do that online somewhere.
     
  8. Sep 27, 2007 #7

    stewartcs

    User Avatar
    Science Advisor

    Hint 1: K is the same as K^1
    Hint 2: a(t) = K^2/2 + C
     
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