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Non-constant acceleration not sure how to solve

  1. Jan 29, 2006 #1
    I'm not certain how to solve this, as the acceleration is not constant and dependant on the velocity. Here's the problem:

    I take it I need to integrate the acceleration function, but I don't know how when I have dv/dt = -3.10 (dx/dt)^2. As this is just an introductory physics class and we are barely two weeks in, I'm wondering if there's not a simpler way to look at this. Any help pushing me in the right direction would be extremely appreciated!
  2. jcsd
  3. Jan 29, 2006 #2
    You have complecated the problem by writing v = dx/dt.

    You need a differential equation, witch connects v and t.

    Leave v as it is and write a = dv/dt. You have a simple integral to do.

    Hope this helps,

  4. Jan 29, 2006 #3
    I haven't learned differential equations yet. Is there no other way to solve it? I tried moving the v and dv to one side and the constant and dt to the other and solving it like that, but that didn't work..
  5. Jan 29, 2006 #4
    Nevermind, I got it using the method I said didn't work above.
  6. Jan 30, 2006 #5
    Is the answer about 0.239 seconds? (sorry, heh, but I'm trying to immerse myself in physics and I want to check my work)
  7. Jan 30, 2006 #6
    Your differential equation comes in the form of a simple harmonic motion.

    d^2x/dx^2-bdv/dt=0 is the equation you need to solve i think

    you will get something like x=bAsin{wt} I think but don't quote me on this where b is the -3.10

    you should be then able to change it around to get your answer
    Last edited: Jan 30, 2006
  8. Jan 30, 2006 #7
    a = -3.10v^2

    dv/dt = -kv^2 (k=3.10)

    separation of variables,

    dv/v^2 = -kdt

    -1/v = -kt +C

    No sinusidal solution.
  9. Jan 30, 2006 #8
    ahhhh yes you are right

    i apologise i thought there was something wrong
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