A silver dollar is dropped from the top of a building that is 1399 feet tall. Use the position function below for free-falling objects.

s(t) = 16t² + v₀t + s₀

(a) Determine the position and velocity functions for the coin.

s(t) =

v(t) =

(b) Determine the average velocity on the interval [3, 4]. ft/s (c) Find the instantaneous velocities when t = 3 seconds and t = 4 seconds.

v(3) =........ ft/s

v(4) = ........ ft/s

(d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.) t = s (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) ft/s

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Q2)

Find the particular solution of the differential equation that satisfies the initial condition(s).

f'(s) = 12s 4s³, f(3) = 3

f(s) =