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Math Help - nstantaneous radius of curvature

  1. #1
    Junior Member
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    nstantaneous radius of curvature

    An object is moving along an elliptical track and its x and y coordinates are recorded in meters by a stroboscope as follows:
    x = ct

    y = 1 - 2 c2 t2

    with c=0.707 and t measured in seconds. What is the instantaneous radius of curvature at t = T?


    T[s] = 0.96;

    Could someone please show me how to solve it
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  2. #2
    MHF Contributor Calculus26's Avatar
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    For r(t) = x(t) i + y(t) j


    k = |T '(t)|/ | r ' (t) |



    Where T(t) = r ' (t)/ |r ' (t)|

    The radius if curvature is then the reciprocal of the curvature p = 1/k
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