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Integrating to determine speed as a function of time

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data

    2lk90kw.jpg

    2. Relevant equations

    The above formulas

    3. The attempt at a solution

    I'm lost on where to start with this. The object has an intial velocity in the X direction and has the resistive force of the plontons acting upon it when it lands. What exactly is the equation located in the problem?
     
  2. jcsd
  3. Oct 24, 2012 #2

    tiny-tim

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    Hi AryRezvani! :smile:
    That's good ol' Newton's second law, F = ma

    F = -bv, ma = mdv/dt, so mdv/dt = bv, so dv/v = -b/m dt :wink:

    (the "m =" appears to be a misprint)
     
  4. Oct 24, 2012 #3
    Thanks for the response Tiny-Tim :)

    Okay, so i follow you somewhat. F = -bv (general formula for resistive force).

    According to Newton's second law, F=ma which can be rewritten as F=m(dv/dt).

    You then equate those two, and you get m(dv/dt)=-bv.

    What happens after this? (dv/v) is the derivative of velocity with respect to velocity? :eek:
     
  5. Oct 24, 2012 #4

    tiny-tim

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    ah, no …

    ∫ dv/v is a short way of writing ∫ (1/v) dv …

    just integrate it! :smile:
     
  6. Oct 24, 2012 #5
    Ohh so when you integrate that you get ln(v)?
     
  7. Oct 24, 2012 #6

    tiny-tim

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    yes! :smile:

    (to be precise, ln(v) - ln(vo))
     
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