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Friction and nonconstant acceleration?

  1. May 24, 2004 #1
    A problem in my book reads as follows:

    A 1000 kg boat is traveling at 90 km/h when its engine is shut off. The magnitude of the frictional force [itex]\vec{f_k}[/itex] between boat and water is proportional to the speed v of the boat: [itex]f_k = 70v[/itex], where v is in meters per second and [itex]f_k[/itex] is in newtons. Find the time required for the boat to slow to 45 km/h.

    My question with this is: g'nhuh? If the magnitude of the frictional force is a function of velocity, that seems to imply that the acceleration is not constant. I was under the impression that the equations for motion and friction that I had been given so far applied only to constant acceleration. I tried to solve this by converting the measurements into meters per second (25 m/s when the engine is shut off, slows to 12.5 m/s) and then guessing that, since a=f/m, then a=70v/1000, and perhaps I could say v = 25 - 70 v / 1000 * t. I solved this for v, and graphically found that v = 12.5 when t is about 14.6. Unfortunately, that wasn't the right answer, which isn't particularly surprising since I'm unsure where to go with this from the very start.

    A little help?
  2. jcsd
  3. May 24, 2004 #2

    Doc Al

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    Staff: Mentor


    The force and the acceleration are not constant. You can't apply the simple kinematic equations for uniform acceleration to this problem. You have to apply F=ma to set up a simple differential equation. You'll need to integrate! I hope you've covered a little calculus.

    [tex] F = ma = m \frac{dv}{dt}[/tex]
    [tex] 70v = m \frac{dv}{dt}[/tex]

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