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To write x as a function of time doubt.

  1. Sep 17, 2011 #1
    Hello!

    1. The problem statement, all variables and given/known data

    It is more a conceptual problem. If all the variables are known, and I am asked to write x as a function of time, why the equations below are not equivalent when equation (b) is derived from (a) after substituting "v_f = v_i + at" ?

    (a) x_f = x_i + 1/2(v_f + v_ i)(t)

    (b) x_f = x_i + v_i(t) + 1/2(a)(t^2)

    If I suppose: x_i = 0, v_f = 50, v_i = 0, t = 5, and a= 3.33. Am I supposed to get same answers? It seems not, and I don't understand why.

    I could say that x = 0 + 1/2(a)(t^2) = 1/2(3.33)(t^2) or x_f = 1.67(t^2). [using (b)]

    But for (a) x_f = 0 + 1/2(50)(t) or x_f = 25(t)
     
  2. jcsd
  3. Sep 17, 2011 #2

    Doc Al

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    Staff: Mentor

    These numbers don't make sense. (You can't just pick arbitrary values and expect it to work.)
     
  4. Sep 17, 2011 #3
    Ok. But may I ask two more questions?

    (a) Why these numbers do not make sense? physicaly impossible? What sort of numbers would make sense?

    (b) And if looked from a mathematical point of view, why both equations must have particular values in order to be equivalent? Or are they not equivalent?
     
    Last edited: Sep 17, 2011
  5. Sep 17, 2011 #4

    Doc Al

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    Staff: Mentor

    Yes, those numbers are physically impossible. For example: If vi = 0, vf = 50, t = 5, then a is determined by the physics to be 50/5 = 10 m/s2.
    They are equivalent.
     
  6. Sep 17, 2011 #5
    ...

    Well, now I see clearly the mistake. I am only going to say that this is depressing. Perhaps I need some rest.

    Thank you!
     
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