The velocity (in mi/hr) of a hiker walking along a straight trail is given by v(t) = 3 sin² (πt/2), for 0 ≤ t ≤ 4. Assume that s(0) = 0 and t is measured in hours.

a. Determine and graph the position function, for 0 ≤ t ≤ 4. sin² t = 1/2 (1 - cos 2t).)

b. What is the distance traveled by the hiker in the first 15 min of the hike?

c. What is the hiker’s position at t = 3?