A remote-controlled drone travels along a straight vertical path. For 0≤t≤9 seconds, its velocity (in ms−1) is modeled by v(t)=4cos(3πt)−1. Answer the following questions about the motion.
a. Part 1: (a) Solve v(t)=0 for t in the interval 0≤t≤9. Express exact values of t.
b. Part 2: (b) Construct a sign chart for v(t) on [0,9] and use it to state the open sub-intervals on which the drone ascends and the sub-intervals on which it descends.
c. Part 3: (c) At each rest time identified in part (a), determine whether the drone changes direction. Justify your conclusion.