Question

a ball is thrown into the air by a baby alien on a planet in the system of alpha centauri with a velocity of 20 ft/s. its height in feet after t seconds is given by y = 20t - 28t². a. find the average velocity for the time period beginning when t = 3 and lasting .01 s: -148.28 .005 s: -148.14 .002 s: .001 s: note: for the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator. estimate the instantaneous velocity when t = 3. -148 question help: video

Explanation:

Step1: Recall average - velocity formula

$v_{avg}=\frac{y(t + \Delta t)-y(t)}{\Delta t}$

Step2: For $\Delta t = 0.002s$

$y(3)=20\times3 - 28\times3^{2}=60 - 252=-192$
$y(3 + 0.002)=20\times(3 + 0.002)-28\times(3 + 0.002)^{2}$
$=60+0.04-28\times(9 + 0.012+0.000004)$
$=60.04-(252+0.336 + 0.000112)$
$=60.04 - 252.336112=-192.296112$
$v_{avg}=\frac{-192.296112+192}{0.002}=\frac{-0.296112}{0.002}=-148.056$

Step3: For $\Delta t = 0.001s$

$y(3 + 0.001)=20\times(3 + 0.001)-28\times(3 + 0.001)^{2}$
$=60 + 0.02-28\times(9+0.006 + 0.000001)$
$=60.02-(252+0.168+0.000028)$
$=60.02 - 252.168028=-192.148028$
$v_{avg}=\frac{-192.148028 + 192}{0.001}=\frac{-0.148028}{0.001}=-148.028$

Answer:

-148.056
-148.028