This is an exercise from the textbook Apostol Vol 1 (page 525, second edition), and I do not know how to prove it:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose a curve C is described by two equivalent functions X and Y, where Y(t) = X[u(t)].

Prove that at each point of C the velocity vectors associated with X and Y are parallel, but

that the corresponding acceleration vectors need not be parallel.

I would really appreaciate some enlightenment.

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# I The two equivalent parallel velocity vectors

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