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Need HELP! equation of motion with variable acceleration

  1. Jan 29, 2007 #1
    1. The problem statement, all variables and given/known data
    A particle is dropped from rest, at the surface, into a tank containing oil
    The acceleration of the particle in the oil is a = g – kv
    where g is the gravitational acceleration and –kv being denoted by
    the resistance put on the particle by the oil.
    Solve for x as a function of time!

    3. The attempt at a solution
    I'm attaching an image file containing my calculations.
    As can be seen I get a differential equation of the second order
    but as I proceed to solve this equation and try to determine the
    constants the whole thing turns into ZERO?!!?! What am I doing wrong??

    Attached Files:

    • en.jpg
      File size:
      37.4 KB
  2. jcsd
  3. Jan 29, 2007 #2
    You don't need to consider this as a 2. order diff. equation. You can view the equation as

    [tex] \ddot{x} = g - k\dot{x} [/tex]
    [tex] \dot{v} = g - kv [/tex]

    The second equation is just a 1. order diff. equation with respect to the velocity v.
  4. Jan 29, 2007 #3
    Yeah, you're right.. but one SHOULD be able solve it by puting it up as a second order right? I just wanna know what I'm doing wrong, it really bugs me.
  5. Jan 29, 2007 #4
    what have you got? Kind of hard to know whats wrong when we just have a generic list of eqns....
    John S
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