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Velocity Dependent Forces

  1. Nov 6, 2012 #1
    1. The problem statement, all variables and given/known data
    A 1000kg boat is traveling at 25 m/s when its engine is shut off. The magnitude of the frictional force f between the boat and the water is proportional to the speed v of the boat: f=70v, where v is in meters per second and f is in newtons. Find the time required for the boat to slow to 12.5 m/s.


    2. Relevant equations
    F=ma
    a(t)=v'(t)

    3. The attempt at a solution
    70v = (1000 kg) * a
    a(t) = 70v(t) / (1000 kg)

    However, after this point I don't know what to do. I can't use the formula v2 = vo2 + 2a(Δx), because I don't know Δx. I don't know how I would find the anti-derivative of a(t), since a(t) is defined in terms of v(t). What am I missing?
     
  2. jcsd
  3. Nov 7, 2012 #2
    Does this look right?
     

    Attached Files:

  4. Nov 7, 2012 #3
    It probably is, but I don't understand it. We haven't gotten that far in ap calculus yet, so I'll ask my teacher about how that works tomorrow. Thanks for the help!
     
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