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Math Help - Vector, Parametrics help

  1. #1
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    Exclamation Vector, Parametrics help

    A particle moves in the plane in such a manner that its coordinates at time t are:
    x=3cos((pi/4)t)
    y=5sin((pi/4)t)

    a)Find the length of the velocity vector at t=3
    b)find the x- and y- components of acceleration of the particle at t=3
    c)Find a single equation in x and y for the path of the particle

    Please explain to me how to do this or possible phrase these questions better, thank you.
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  2. #2
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    Quote Originally Posted by maximade View Post
    A particle moves in the plane in such a manner that its coordinates at time t are:
    x=3cos((pi/4)t)
    y=5sin((pi/4)t)

    a)Find the length of the velocity vector at t=3
    b)find the x- and y- components of acceleration of the particle at t=3
    c)Find a single equation in x and y for the path of the particle

    Please explain to me how to do this or possible phrase these questions better, thank you.
    a) |v| = \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2}

    ... evaluated at t = 3

    b) a_x = \frac{d^2x}{dt^2}

    a_y = \frac{d^2y}{dt^2}

    ... both evaluated at t = 3

    c) x^2 = 9\cos^2\left(\frac{\pi t}{4}\right)

    \frac{x^2}{9} = \cos^2\left(\frac{\pi t}{4}\right)

    y^2 = 25\sin^2\left(\frac{\pi t}{4}\right)

    \frac{y^2}{25} = \sin^2\left(\frac{\pi t}{4}\right)

    \frac{x^2}{9} + \frac{y^2}{25} = \cos^2\left(\frac{\pi t}{4}\right) + \sin^2\left(\frac{\pi t}{4}\right)<br />

    finish it ...
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