Posted by Mimi on Friday, April 3, 2009 at 4:32am.
If a ball is thrown in the air with a velocity 44 ft/s, its height in feet t seconds later is given by y = 44t  16t2.
(a) Find the average velocity for the time period beginning when t = 2 and lasting 0.5 second.
ft/s
(b) Find the average velocity for the time period beginning when t = 2 and lasting 0.1 second.
ft/s
(c) Find the average velocity for the time period beginning when t = 2 and lasting 0.05 second.
ft/s
(d) Find the average velocity for the time period beginning when t = 2 and lasting 0.01 second.
? ft/s
(e) Estimate the instantaneous velocity when t = 2.

Calculus  drwls, Friday, April 3, 2009 at 7:18am
This will not use calculus. It is an exercise to show how to use algebra to approximate the instantaneous velocity that you would get using calculus.
Just use the formula
y = 44t  16 t^2
multiple times.
For (a), y(2) = 88  64 = 24 ft
y(2.5) = 110  100 = 10 ft
Average velocity Vav
= [y(2.5)  y(2)]/0.5 = 28 ft/s
For (d), y(2.01)= 88.440  64.6416 = 23.7984
Vav = [y(2.01)  y(2)]/0.01
= (23.7984 24)/0.01 = 20.16 ft/s
Do parts (b) and (c) yourself and notice the trends in average velocity as the time interval gets shorter
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