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Deriving terminal velocity

  1. Hello PF,
    I have once simple (well, not so simple for me) question.

    I'm trying to derive an equation for the velocity of a falling body with accordance to terminal velocity.

    The equation incorporates drag proportional to the speed.



    mg/b=terminal velocity vt

    So the steps I took were:





    Integrating both sides would give

    But the textbook says that I'm supposed to get negative (b/m)t on the left side.

    Have I made a mistake on the integration part?

    Any help will be deeply appreciated.
  2. jcsd
  3. hmm. I seem to have gotten the answer if I just divided the entire equation by -b in the beginning without bringing the bv to the left side. Have I made a mistake on the integration part?
  4. You just missed the minus sign while integrating (chain rule)
  5. pshh. I can't believe I missed that. Thanks so much king vitamin!
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