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Velocity dependent force question

  1. Sep 10, 2014 #1
    1. The problem statement, all variables and given/known data
    Initial speed = v, only for acting on it is retarding force F(v) = -Ae^(-cv). Find it's speed as a function of time.




    2. Relevant equations
    F=ma


    3. The attempt at a solution
    m(dv/dt) = -Ae^(-cv)
    dv / (-Ae^(-cv) = dt / m

    integrating gives
    [e^(-cv)/Ac] = t/m

    where the left side of that integral is evaluated from initial vi to final vf

    e^(-cvi)/Ac-e^(-cvf)/Ac = t / m

    multiplying by AC and taking the natural log of all of this...

    -cvf + cvi = ln(tAc/m)
    vf = vi - (1/c)*ln(tAc/m)

    Does this look correct? An online source says this is wrong. Thanks for the help, LaTex coming soon.
     
  2. jcsd
  3. Sep 10, 2014 #2

    vanhees71

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    Science Advisor
    2016 Award

    Well, check your signs. Principally, using "separation of variables" is the correct approach to solve this 1st order ODE.
     
  4. Sep 10, 2014 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You do know that [itex]1/e^{-cv}= e^{cv}[/itex], don't you? So simpler is
    [tex]me^{cv}dv= -Adt[/tex]
    and the integrating
    [tex]\frac{m}{c}e^{cv}= -At+ C[/tex]

     
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