## Transformation Vs. Physical Law

 Quote by DaleSpam That isn't the only correct way to work the problem.
True, it is the most direct way of solving the problem. In fact, it is the standard way of solving this problem, there is no need to introduce any notion of "number of laps" (the variable $a$ in your derivation).

Mentor
 Quote by GAsahi True, it is the most direct way of solving the problem. In fact, it is the standard way of solving this problem, there is no need to introduce any notion of "number of laps" (the variable $a$ in your derivation).
Agreed.

But again, there is no reason not to introduce a either. Reparameterizations are common and well accepted, no matter if they are needed or not.

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