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April 16, 2014

April 16, 2014

Posted by **Mimi** on Friday, April 3, 2009 at 4:32am.

(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 7:18amThis 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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