Chapter 11.9, Problem 62E

Same paths, different velocity The position functions of objects A and B describe different motion along the same path, for t ≥ 0.

1. a. Sketch the path followed by both A and B.
2. b. Find the velocity and acceleration of A and B and discuss the differences.
3. c. Express the acceleration of A and B in terms of the tangential and normal components and discuss the differences.

62. A: r(t) = 〈cos t, sin t〉, B: r(t) = 〈cos 3t, sin 3t〉