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Motion in 1D under a resistive force

  1. Oct 19, 2010 #1
    1. The problem statement, all variables and given/known data

    A particle moving on a straight line is subject to a resistive force of the magnitude kv^n, where v is the velocity at time t and k is a positive real constant.

    Find the times and distances at which the particle comes to rest i.e. v=0, for the following cases (this assumes at t=0, x=0, v=v0.)

    n<1 ?
    1<n<2 ?
    n=2 ?

    2. Relevant equations


    3. The attempt at a solution

    I've tried by getting two equations, one for time and one for distance.

    So I set F=ma= m(dv/dt) = -kv^n for time
    and F = ma = mv(dv/dx) = -kv^n for distance

    I then plodded along, and took v=0 to get two similar equations for time and distance...

    (m*v0^(1-n)) / (k (1-n)) = t and
    (m*v0^(2-n)) / (k (2-n)) = x

    but I'm not sure if that's at all right! They'd be fine for n<1, but the time one screws up for 1<n<2 and the distance is special for n=2.

    Basically I'm not sure I've gone the right way at all... I think I need an e^f(t) so I can take limits but I've just got my head in a muddle.
  2. jcsd
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