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AP Physics differential equation

  1. Oct 1, 2015 #1
    1. The problem statement, all variables and given/known data
    A block of mass m, which has an initial velocity v0 at time t = 0, slides on a horizontal surface. If the sliding friction force f exerted on the block by the surface is directly proportional to its velocity (that is, f = -kv),
    A) Write a differential equation for the velocity v in terms of the given variables and fundamental constants.
    B) Find the acceleration a of the block in terms of m, k, and v.
    C) The speed v of the block as a function of time t.
    D) The total distance the block slides.

    2. Relevant equations
    F = m*a

    3. The attempt at a solution
    I understand why B is a = (-kv)/m, and I know the answer to a is dv/dt = -kv/m but I don't know why, and I have no idea how to solve for velocity. Assuming I get a function for the velocity, what general equation would I use to solve for the total distance? I originally thought x-x0 = v0*t + (1/2)*a*t^2, but the acceleration isn't uniform.
     
  2. jcsd
  3. Oct 1, 2015 #2
    You have two options:
    1. You can use separation of variables if you're familiar with it.
    2. The solution to linear ODEs with constant coefficients is found by assuming [itex]v=e^{s t}[/itex] and finding out what [itex]s[/itex] is.
     
  4. Oct 1, 2015 #3

    haruspex

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    What equation connects a with v?
    Rearrange the equation to have all the references to v on one side and all references to t on the other. This is the "separation of variables" method axmls refers to.
    You did well to realise you cannot use the SUVAT equations here.
    Suppose you have velocity as a function of time, v=f(t). What differential equation relates velocity to distance? (This is very like the first question I asked you in this post.)
     
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