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Math Help - Tangential Accel and Normal Accel.

  1. #1
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    Tangential Accel and Normal Accel.

    1. The position of a particle in motion in the plane at time is
    At time , determine the following:
    (a) The speed of the particle
    8.85663593
    (b) The unit tangent vector to
    .9936053 .112909688

    (c) The tangential acceleration
    ?
    (d) The normal acceleration
    ?
    I figured out the speed and T(t) but i have no idea how to find the aT and aN. Please help out.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    you're answer to b is correct but it is T(0) not T(t)

    This is not going to be very clean anyway you approach it--so have a cup of coffee and a cigarette

    if s is the speed = |v|


    It might be easiest to compute aN = k(ds/dt)^2

    then aT = sqrt( |a|^2 - aN^2)

    Where k = |T'|/|r'|



    Normally you can compute the components by :

    if s is the speed = |v|

    Then aT = d^2s/dt^2

    Without having to compute the curvature you can compute

    aN = sqrt( |a|^2 - aT^2)

    where a = (8.8)^2 e^(8.8t) i + e^t j

    However for this problem d^2s/dt^2 is very cumbersome
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