2. Suppose a coin is dropped from the top of the Empire State building in New York, which is 1,454 feet tall. The position function for free-falling objects is: s(t) = 16132 +vat+ so, where vEl is the initial velocity and s0 is the initial position. A. Determine the position and velocity functions for the coin. B. Determine the average velocity of the coin on the interval [1, 3]. C. Find the instantaneous velocities when 1' =1 and t= 3. Copyright 2021 Apex Learning. See Terms of Use for further intormation. Images of the TI84 calculator are used with the permission of Texas Instruments Incorporated, Copyright 2011 Texas Instruments Incorporated. AP Calculus AB Page 4 of 4 Test: Derivatives User Name: Instructor: Date: (print clearly) D. At what time is the instantaneous velocity of the coin equal to the average velocity of the coin found in part B? E. What is the name of the theorem that says there must be at least one solution to part D? F. Find the velocity of the coin just before it hits the ground