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:

Question

s(t) = −16t^2 + v_0t + s_0,
where v_0 is the initial velocity and s_0 is the initial position.

Find the instantaneous velocities when t =1 and t = 3.

Answer 1

Since it is "dropped" , the initial velocity is zero
and the initial height is 1454 ft
s(t) = -16t^2 + 0t + 1454

v(t) = -32t

v(1) = -32 ft/sec
v(3) = -96 ft/sec

Answer 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) = −16t^2 + v_0t + s_0, where v_0 is the initial velocity and s_0 is the initial position.

1. Find the instantaneous velocities when t =1 and t = 3 (I've already solved)

2. What is the name of the theorem that says there must be at least one solution to Part 1?

3. Find the velocity of the coin just before it hits the ground.