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Particle's Equation, Velocity and Acceleration

  1. May 30, 2016 #1
    1. The problem statement, all variables and given/known data
    r(t) is the position of a particle in the xy-plane at time t. Find an equation in x and y whose graph is the path of the particle. Then find the particle’s velocity and acceleration vectors at the given value of t.
    Capture.PNG

    2. Relevant equations
    First derivative = velocity
    (velocity=distance/time)
    Second derivative = acceleration
    (acceleration=velocity/time)

    3. The attempt at a solution
    To find the Equation, I first organize it into a set:
    [ et, 2/9 e2t ]
    Then I just plug in the value of t (ln3)
    [ eln3, 2/9 e2(ln3) ]
    I then reconstruct the original problem with the new values:
    r(t) = eln3 i + 2/9 e2(ln3) j
    r(ln3) = e1.0986 i + 2/9 e2.1972 j
    then I change the i / j to x/y
    r(ln3) = e1.0986 x + 2/9 e2.1972 y
    -----------------------------

    As for velocity and acceleration, so far I have figured it like this:
    Velocity:
    [ et, 2/9 e2t ]
    [ te, 4/9 et ]
    Velocity = tei + 4/9etj

    Acceleration:
    [ e, 4/9 te]
    Acceleration = tei + 4/9 tej
    Am I taking the derivative correctly? As far as I know, e remains as e, even after the derivative, right?

    thanks in advance
     

    Attached Files:

  2. jcsd
  3. May 30, 2016 #2

    SteamKing

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    For the derivatives of et, you should review the rules of differentiation for such functions and not neglect application of the chain rule.

    http://www.themathpage.com/acalc/exponential.htm

    Remember, et is not differentiated like xn.
     
  4. May 31, 2016 #3

    SteamKing

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  5. May 31, 2016 #4

    Ray Vickson

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    You have not done the second part, which says "Find an equation in x and y whose graph is the path of the particle". This means that instead of representing the particle's orbit as ##(x(t),y(t))## you should represent the curve of the orbit (not including "time" information) as an equation of the form ##y = F(x)## or ##x = G(y)## or ##H(x,y) = 0##, and you are to figure out the functions ##F## or ##G## or ##H##, as needed.
     
  6. May 31, 2016 #5
    Got it! Thanks for your guys' help!!
     
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