Question

Suppose a coin is dropped from the top of the Empire State Building in New York, which is 1454 feet tall. The position function for free-falling objects is s(t) =−16t^2+v0t + s0.

Question: At what time is the instantaneous velocity of the coin equal to the average velocity of the coin found in Part B?

Part B and my answer was:
Determine the average velocity of the coin on the interval [1, 3].
s(3) = 16(3)^2+1454
= 1598
s(1)=16(1)^2+1454
= 1470

(s(3)-s(1))/(3-1)
(1598-1470/(3-1)=128/2=64ft/s

In order to solve the question, do i plug in different time values to find which is the closest? Any help would be appreciated.

Answer 1

find the velocity function from the derivative of s

v=s'=-32t+vo
set that equal to 64, solve for time t.

In your average velocity, you should have had a negative distance, which would have made a negative velocity (meaning downward). see the original equation for the negative sign.