9. We return to the circle of radius 5 in 2-dimensional space centered at the origin, with our original parameterization of this circle as r(t)= (5 cos (t), 5 sin(t)), where t runs from 0 to 2. (a) If this parametrization represents the motion of a particle around a circle, how far has the particle traveled from time 0 to time t? We'll call this distance s. Write s as a function of t. (b) Solve for t in terms of s and plug this into your parameterization to get a new parameterization r(s). (This is called a parameterization by arc length or an arc length parametrization.) What do you notice about it?

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