A stone is thrown vertically upward from the top of the building.

Question

A stone is thrown vertically upward from the top of the building. If the equation of the motion of the stone is 𝑠(𝑡) = −5𝑡² + 30𝑡 + 200 , where 𝑠 is the directed distance from the ground in meters and 𝑡 is in seconds,

a. what is the height of the building?

b. what is the average velocity on the time interval [1 , 3] ?

c. what is the instantaneous velocity at time 𝑡 = 1 ?

d. at what time will the stone hit the ground?

e. what is the instantaneous velocity of the stone upon impact?

Answer 1

a What is the height at t = 0

b. [s(3) - s(1)] / 3

c. s'(1) = ?

d. 0 = -5t² +30t + 200

e. determine value of s'(t) for the t in d.