MediumCurves in space

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.1 The Position Vector, #26 · Multivariable Calculus · Curves in space

Why is … generally different from

Why is $∣ a ∣$ generally different from $d^{2} s / d t^{2}$ ? Give an example of the difference, and an example where they are equal.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.1 The Position Vector, #26

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