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Finding acceleration through given equation

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data

    The position of the front bumper of a test car under microprocessor control is given by:
    x(t) = 2.17 + (4.80m/s^2)t^2 - (0.100 m/s^6)t^6

    Find the acceleration at the first instant when the car has zero velocity.



    2. Relevant equations




    3. The attempt at a solution

    0m/s^2, 4.8m/s^2

    I know that the first instant that the car has zero velocity is at 2.17m at 0 seconds in time. I also know that the car is about to accelerate at this instant. I can't figure out how to determine what the acceleration is though.
     
    Last edited: Sep 15, 2011
  2. jcsd
  3. Sep 15, 2011 #2

    Doc Al

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    Staff: Mentor

    How did you determine this?
     
  4. Sep 15, 2011 #3
    delta x/delta t as t -> 0 is 2.17 (edit: this is wrong). It's because 2.17 is the starting point.

    I don't know how to solve 2nd derivatives, I barely know anything about derivatives, our physics course is moving faster then our calc course right now.
     
    Last edited: Sep 15, 2011
  5. Sep 15, 2011 #4

    Doc Al

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    In order to find the velocity as a function of time, you take the first derivative of the position. What does that give you?

    Once you have the velocity as a function of time, how would you find the acceleration?
     
  6. Sep 15, 2011 #5
    I thought that the derivative function would be 9.6t - .6t^5. But I haven't actually learned derivatives yet.
     
  7. Sep 15, 2011 #6

    Doc Al

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    Good! That's v(t). And you can solve for the first value of t to make that zero.

    Now find a(t).
    Seems like you know enough to get through this problem.
     
  8. Sep 15, 2011 #7
    so a(t) = 9.6 - 3.0t^4?

    so a(t) = 9.6 m/s^2?
     
  9. Sep 15, 2011 #8

    Doc Al

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    Right!
    Yes, that's the acceleration at t = 0. Call it a(t = 0), not a(t).
     
  10. Sep 15, 2011 #9
    Thanks for the help! My lectures go so fast and I have a hard time following all the formulas.
     
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