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Dynamics velocity problem

  1. Feb 14, 2006 #1
    dynamics problem!!

    this is a problem about a resistive force that is a function of v, not x.
    a block with an initial velocity goes through a medium that resists motion with force proportional to the block's velocity, with proportionality constant K. so basically the resistive force = -Kx (i choose the pos x dir to be in the dir of initial velocity)
    i am supposed to find the stopping distance by finding v as a function of x and then i am supposed to find it again by finding v as a function of t.
    i cruised wikipedia because it helped me on an escape velocity problem, and it gave me some help, but i dont know how they got what they did and im not entirely sure if its what i want.

    they said:
    -Kx = ma = m dv/dt which i have and understand
    they say it integrates to
    v = v(initial) * e^(-Kt/m)
    can anyone explain how they got that? i am missing some math skillz here.
    any other insights to the problem would be greatly appreciated. :smile:
     
  2. jcsd
  3. Feb 16, 2006 #2

    Astronuc

    User Avatar

    Staff: Mentor

    The problem statement indicates that a resistive force a function of velocity, i.e. is proportional to velocity, then

    force = -Kv, or -K[itex]\dot{x}[/itex], and not force = -Kx.

    So the force balance becomes,

    m dv/dt = -Kv which is a first order linear differential equation,

    which gives the solution

    v = v(initial) * e^(-Kt/m) for v=v(initial) at t=0.
     
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