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Finding the acceleration at any time

  1. Mar 5, 2009 #1
    1. The problem statement, all variables and given/known data

    The relationship between displacement s and velocity v is given by 1/3s^2 - 4v^2 = 12. Find the acceleration a at any time.

    2. Relevant equations

    3. The attempt at a solution

    I know that velocity is found with the derivative of the displacement function, and acceleration is the derivative of the velocity function. Im not sure how to go about it with this type of function.

    Up to now the type of functions Ive delt with have been something like s = 2t^2-5t+4 etc

    Thank you for your help!
    Last edited: Mar 5, 2009
  2. jcsd
  3. Mar 5, 2009 #2


    Staff: Mentor

    Is there more to this problem. It doesn't seem to be asking you to do anything.
    But velocity and acceleration are not just any old derivatives: they are time derivatives. In particular, v = ds/dt. This might be a hint.
    In anticipation of what the problem might be asking, I'm guessing that it asks you to find s(t) based on the equation you gave. If you use my hint, you'll get an equation that involves s and ds/dt, which maybe you can solve.
  4. Mar 5, 2009 #3
    Ive editted the question. Im sorry I did leave out what its asking for.

    I get that v = ds/dt, and a = dv/dt but as I said the functions ive dealt with are pretty straight forward. I dont know where to start when there is s and v in the same function. Where do I start for this question?
    Last edited: Mar 5, 2009
  5. Mar 5, 2009 #4
    Upon some investigation and further study, I got a = (1/12)s for this question.

    Am I in the ball park with that one?
  6. Mar 5, 2009 #5


    User Avatar
    Science Advisor

    You are given that 1/3s^2 - 4v^2 = 12. Unfortunately, without parentheses it is not clear whether that first term is (1/3)s^2 or 1/(3s^2)= (1/3)s^(-2). In either case, differentiate with respect to t. Since acceleration is dv/dt, solve for dv/dt, remembering that v= ds/dt.
  7. Mar 5, 2009 #6
    The first term is (1/3)s^2. I did what you suggested and I got (2/3)s / 8 which = (1/12)s. What do you think?
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