An object moves along a straight track with acceleration a(t), measured in meters per second squared, described by the following piecewise-constant function for 0≤t≤9 seconds:
• a(t)=3 for 0≤t<2;
• a(t)=0 for 2≤t<5;
• a(t)=−4 for 5≤t<7;
• a(t)=2 for 7≤t≤9.
At time t=0, the velocity is v(0)=1m/s and the position is s(0)=0m.
(a) Determine the velocity of the object at t=2, t=5, t=7, and t=9 seconds. Show all work.
(b) Find the object’s maximum velocity on 0≤t≤9 seconds and the time at which it occurs. Justify your answer.
(c) Calculate the total distance traveled by the object during 0≤t≤9 seconds.