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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