A particle moves along the x–axis with velocity v(t)=1+t26t(t≥0), where t is measured in seconds and velocity in meters per second.
(1) Part 1: Determine the particle’s acceleration a(t).
(2) Part 2: Find all values of t for which a(t)=0 and classify each as a local maximum or minimum of v(t).
(3) Part 3: Identify the intervals of time on which the particle’s velocity is increasing and the intervals on which it is decreasing. Support your conclusions analytically.
(4) Part 4: Compute t→∞lima(t) and interpret the result in terms of the particle’s motion.