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Instantaneous acceleration from coordinates?

  1. Apr 21, 2015 #1
    1. The problem statement, all variables and given/known data
    The coordinate of an automobile in meters is x(t) = 5 + 3t + 2t2 and y(t) = 7 + 2t + t3, where t is in seconds. What is the instant acceleration of the car at time t = 2 s?

    ANSWERS:
    A. 10.2 m/s2
    B. 9.5 m/s2
    C. 7.9 m/s2
    D. 15.0 m/s2
    E. 12.6 m/s2

    2. Relevant equations
    ains = limt->0 dv / dt
    = limt->0 d2x / dt2

    3. The attempt at a solution
    My attempt went as follows:

    a for x-coordinate:
    ains = limt->2 d2(5 + 3t + 2t2) / dt2
    = limt->2 4 m/s2
    = 4 x 2 = 8 m/s2

    a for y-coordinate:
    ains = limt->2 d2(7 + 2t + t3) / dt2
    = limt->2 3 m/s2
    =3 x 2 = 6 m/s2

    For a:
    √82 + 62 = 10 m/s2

    Just wondering what I am doing incorrectly, any advice would be appreciated.
     
  2. jcsd
  3. Apr 21, 2015 #2
    Solved thanks! derived a for the y-coordinate incorrectly.
     
  4. Apr 21, 2015 #3
    Good job. Welcome to PF, by the way.
     
  5. Apr 21, 2015 #4
    Why did you multiply by two?
     
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