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Differential equation dv/dt = 9.8 - v/5, v(0) = 0

  1. Jan 26, 2013 #1
    A falling object satisfies the initial value problem:

    dv/dt = 9.8 - v/5, v(0) = 0

    1.Find the time that must elapse for the object to reach 98% of its limiting velocity.

    answer: t = 19.56, and for completeness, v = -49e-t/5 + 49

    2.How far does the object fall in the time found in part a?

    Integrating yields the wrong answer, which should = 718.34?

    p(t) = 245e-t/5 + 49t
     
  2. jcsd
  3. Jan 26, 2013 #2

    SammyS

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    What was it you integrated, and how did you do it?
     
  4. Jan 26, 2013 #3
    The p(t) at the bottom of the OP is suggests he/she integrated v(t) from part 1. Must be a problem with the limits of integration. I've gotten the right answer, and double-checked it.
     
  5. Jan 26, 2013 #4

    SammyS

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    Fair enough !

    To OP:

    What is p(19.56) - p(0) ?
     
  6. Jan 26, 2013 #5
    It was pointed out to me elsewhere that was how to do it. I did an indefinite integral and then evaluated p(19.56). I'm having a difficult time intuiting why that would yield a wrong answer though.
     
  7. Jan 26, 2013 #6

    SammyS

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    Because for, p(t), as you have it, p(0) ≠ 0 . You could have used a constant of integration to make p(0) = 0 .
     
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