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Homework Help: Deriving a kinematic equation.

  1. Sep 11, 2007 #1
    1. The problem statement, all variables and given/known data

    Derive (v_f)^2 = (v_i)^2 +2ad

    2. Relevant equations

    (v_f)^2 = (v_i)^2 + 2ad
    (v_f) = (v_i) + at
    d = (v_i)t + \frac{1}{2}at^2

    3. The attempt at a solution

    I have attempted to replace the variables with others from other kinematic equations such as v_f = v_i + at. However, I am getting no where. I have also taken the derivative of the equation (or so I think) but if I have not done it correctly, then I am just going no where.

    When taking the derivative of the equation (v_f^2 = v_i^2 + 2ad) I remembered dv/dt = a , a in this equation is constant, and dd/dt = v, thus I got 2a=2a+2v and once simplified brings me to 0=v? I feel I am deriving the equation incorrectly.

    Now, after having exhausted my thoughts, I've come asking for help.
  2. jcsd
  3. Sep 11, 2007 #2


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    Are you supposed to derive the equation from first principles? What i mean is are you allowed to use:

    [tex]d = (v_i)t + \frac{1}{2}at^2[/tex]
  4. Sep 11, 2007 #3
    Yes. I can use any type of equation. And any principles. I'm just at a loss as to how to get started. I should be fine with a little nudge in the right direction.
  5. Sep 11, 2007 #4


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    You can solve for t, in the equation vf = v0 + at... then substitute t into the d equation posted, that will give you the result.
  6. Sep 11, 2007 #5
    Thank you. I've got it now. I had returned to using the other equations, but the word "derive" kept making my brain do derivatives. I guess that's what I get for being a math minor and taking as few physics classes as possible.

    Thank you, again.
  7. Sep 11, 2007 #6


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    no prob.
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