The height, in metres, of an object that has fallen from a height of 180 m is given by the position function s(t)=-􏰀5t^2 􏰂+180, where t 􏰃>0 and t is in seconds.

a. Find the average velocity during each of the first two seconds.
b. Find the velocity of the object when t 􏰀=4.
c. At what velocity will the object hit the ground?

1 answer

s(t) = 180-5t^2
(a) avg velocity is total distance/total time.
s(2) = 180-5*4 = 160
160m/2s = 80 m/s

v(t) = ds/dt = -10t
v(4) = -40

180-5t^2 = 0
t = 6
That is, at t=6, the height is zero -- it hit the ground.
Now you just plug 6 into v(t)