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Math Help - Parametric/velocity/distance Q

  1. #1
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    Parametric/velocity/distance Q

    A particle moves along a path given by:
    x(t) = 3cos(πt) and y(t) = 5sin(πt) and 0≤t≤6

    1) Velocity vector fot the particle at any time t?
    I just took the derivative of x(t) and y(t). Is that correct?

    2) Write an integral expression that gives the distance between t=1.25 and t=1.75
    Not sure what to do here.

    Help appreciated.
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  2. #2
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    Hello, Nerd!

    A particle moves along a path given by:
    . . x(t) .= .3Ěcos(πt)
    . . y(t) .= .5Ěsin(πt)
    where 0 ≤ t ≤ 6.

    1) Velocity vector fot the particle at any time t?
    I just took the derivative of x(t) and y(t). Is that correct?
    What did you do with the two expressions?
    The particle's position vector is: .s .= .[3Ěcos(πt)]i + [5Ěsin(πt)]j

    Its velocity vector is: .v .= .[-3πĚsin(πt)]i + [5πĚcos(πt)]j



    2) Write an integral expression that gives the distance
    between t = 1.25 and t = 1.75
    Do they mean "integral" or "integer"? .Either way, it doesn't make sense.

    . . . . . . . . . . . . . . . . . . . . . . . . . . . ._ . . . . ._
    When t = 5π/4, the particle is at: P(-3√2/2, -5√2/2)
    . . . . . . - . . - . . . . . . . . . . . . . . . . . _ . . . . ._
    When t = 7π/4, the particle is at: Q(3√2/2, -5√2/2)

    . . . - . . - . . . . . . . . . _
    The distance PQ is: .3√2


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    I think I get it . . . They want the Arc Length.
    . . . - . . - . . _______________
    . . L . = . ∫ √(dx/dt)▓ + (dy/dt)▓ dt

    . . . . . . . . . . . . . . . .________________________
    So we have: .L .= .∫ √9π▓Ěsin▓(πt) + 25π▓Ěcos▓(πt) dt

    . . evaluated from t = 5/4 to t = 7/4.

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  3. #3
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    Its velocity vector is: .v .= .[-3πĚsin(πt)]i + [5πĚcos(πt)]j
    My pre-cal teacher is going to be upset at me (I know I learned it)...but I forgot what the i and j stuff means. Please explain? I wrote it out as two separate function (vy(t) and vx(t) which I didn't think the people who made this problem were looking for)
    --------------------------------------
    Edit: Digging into the dark depths of my brain, I remember, actually. Thanks.
    --------------------------------------

    I think I get it . . . They want the Arc Length.
    Awesome. I completely forgot about that stuff.
    Last edited by Nerd; April 22nd 2007 at 06:35 PM.
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  4. #4
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    And help evaluating this integral would be really nice.
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