A snail is traveling along a straight path. The snail’s velocity can be modeled by v(t) = 1.4In (1+t^2) inches per minute for 0 ≤ t ≤ 15 minutes.
(a) Find the acceleration of the snail at time t = 5 minutes

(b) What is the displacement of the snail over the interval 0 ≤ t ≤ 15 minutes?

(c) At what time t, 0 ≤ t ≤ 15, is the snail’s instantaneous velocity equal to its average velocity over the interval 0 ≤ t ≤ 15?

(d) An ant arrives at the snail’s starting position at time t = 12 minutes and follows the snail’s path. During the interval 12 ≤ t ≤ 15 minutes, the ant travels in the same direction as the snail with a constant acceleration of 2 inches per minute per minute. The ant catches up to the snail at time t = 15 minutes. The ant’s velocity at time t = 12 is B inches per minute. Find the value of B.