A particle moves along a straight line with velocity v(t)=3t2−12t+9 meters per second for 0≤t≤4, where t is measured in seconds.
(a) Calculate the displacement of the particle over the time interval 0≤t≤4 seconds.
(b) Determine the total distance traveled by the particle during the same interval.
(c) Compute the average velocity of the particle on 0≤t≤4 seconds.
(d) At what time in the interval does the particle momentarily come to rest? Justify your answer.