Investigation A particle moves on an elliptical path given by the vector-valued function r(t) = 6 cos ti + 3 sin tj.

(a) Find

(b) Use a graphing utility to complete the table.

(c) Graph the elliptical path and the velocity and acceleration vectors at the values of given in the table in part (b).
(d) Use the results of parts (b) and (c) to describe the geometric relationship between the velocity and acceleration vectors when the speed of the particle is increasing, and when it is decreasing.

Transcribed Image Text:

v(t), ||v(t)||, and a(t).