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Dynamics help - Motion

  1. Jan 27, 2009 #1
    1. The problem statement, all variables and given/known data
    An engineer designing a system to control router for a machining process models the system so that the router's acceleration (in in/s2) during an interval of time is given by a= -0.4v, where v is the velocity of the router in in/s2. When t=0, the position is s=0 and the velocity is v= 2 in/s. What is the position at t=3 seconds?

    2. Relevant equations

    a= dv/dt

    3. The attempt at a solution

    This section has to do with straight line motion when the acceleration depends on velocity or position.

    This is what I tried to do:

    a= -0.4v
    a= dv/dt

    dv/dt = -0.4v

    dv/v= -0.4 dt

    I integrated both sides and I got:

    ln v = -.4t + C ( C = constant)

    From my differential equations math class, we did problems like these and we got rid of the ln by making it all a power of e.

    eln v = e -.4t + C

    you get v= e-.4t+C or v= e-.4tC

    Now I know this is wrong because we know that when t=0 v=2. Am I on the right track or did i do this completely wrong? Thanks for any help.
  2. jcsd
  3. Jan 28, 2009 #2


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    Science Advisor
    Homework Helper

    vdfortd: Nice work. You are doing well, so far. You said, "Now I know this is wrong." That is not true. Go ahead and substitute t = 0 and v = 2 into your last equation, and see what you get. Solve for C. Now continue solving the problem.
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