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Homework Help: Using F=kvx in order to describe x as a function of t

  1. Oct 2, 2011 #1
    1. The problem statement, all variables and given/known data
    The force acting on a particle of mass m is given by
    F=kvx
    in which k is a positive constant. The particle passes through the origin with the speed v naught at time t=0. Find x as a function of (t)


    2. Relevant equations
    F=ma
    a=(dx/dt)(dv/dx)



    3. The attempt at a solution
    F=kvx

    ma=kvx

    a=kvx/m

    (dx/dt)(dv/dx)=kvx/m

    v(dv/dx)=kvx/m

    dv/dx=kx/m

    dv=(kx/m)dx

    integral of both sides left in terms of dv and right in terms of dx

    V-Vnaught=kx^2/2m

    I'm not sure where to go from here. Help would be very much appreciated!
     
  2. jcsd
  3. Oct 2, 2011 #2
    Nevermind I figured it out. For anyone who's curious.

    V=(kx^2/2m)+Vnaught
    dx/dt=(kx^2/2m)+Vnaught
    dx/((kx^2/2m)+Vnaught)=dt
    then integrate both sides.
     
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