Reference no: EM131010844
(a) Consider the curve whose parameterization, for t ≥ 0, is r→ (t) = <x(t), y(t), z(t)>, where
x(t) = 0∫t sin (u2/2) du
y(t) = 0∫t cos (u2/2) du
z(t) = 0
Perform the decomposition a→ = aT T→ +aN N→ at any time t ≥ 0.
(b) What is the radius, ρ, of the osculating circle at any time t > 0, for the curve in part (a)? Given that the curve is defined for all t ≥ 0, why does this question not ask for the radius, at any time t ≥ 0?
(c) The magnitude of the vector Nm→ (t) is considered to be a useful estimator of the discomfort which a human will experience while riding in a train, which is rounding a track parameterized by r→ (t). What is the magnitude of this vector, at all times t ≥ 0, for the curve in part (a)?
(d) What is the arc length, s(t), at any time t > 0, for the curve in part (a)? Now give the arc length parameterization, r→ (t(s)) = r→ (s), for the curve.
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: What is the radius, ρ, of the osculating circle at any time t > 0, for the curve in part (a)? Given that the curve is defined for all t ≥ 0, why does this question not ask for the radius, at any time t ≥ 0?
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