The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 less than or equal to t less than or equal to 8.
(a) When is the position function decreasing? (Round your answers to one decimal place. Enter your answer using interval notation.)
(b) During how many time intervals is the particle's acceleration positive?
_______ time intervals
(c) At what time is the particle at the farthest distance away from its starting position in the negative direction? (Round your answer to one decimal place.)
t = __________
How far away is it from its original position? (Round your answer to the nearest integer.)
(d) At what time is the particle moving the fastest? (Round your answer to one decimal place.)
t =
At what speed is the particle moving the fastest? (Round your answer to the nearest integer.)