Problem 2. (a) Suppose the position vector r'(t) of a particle is smooth (that is, r'(t) / 0 and ""(t) exists ). Show that if the speed of the particle is constant, the velocity and acceleration vectors are orthogonal. (Hint: read the example on p898 (the 8th edition) or theorem 4 in sec 13.2 (the 9th edition)) (b) Let T(t) = FO1. 70.Then show that r'(t) and 7"(t) are perpendicular. (c) Let s(t) = ["'r'(o)|do. Notice that s = s(t) is one-to-one and differentiable so that the inverse function t = t(s) exists and is differentiable. Show that the re-parametriza function r(t(s)) has a constant speed with respect to the parameter s, therefore the velocity and acceleration vectors are always perpendicular. (Hint: (#4 ) (4 ) = 1)