00:01
Okay, so we have a ball that is thrown into the air from rest and is thrown with the initial velocity of 34 feet per second.
00:07
And we know that its height is modeled by the equation 34t minus 11t squared.
00:13
And we want to find the average velocity for these four distinct time periods.
00:19
And after that, we want to find the instantaneous velocity at time equals two.
00:24
So what we're going to do is rely on the fact that position over time is, is voluble.
00:30
Velocity because velocity is the rate of change of position with respect to time.
00:36
So we're going to treat this like a slope problem.
00:39
So we have, for all these different time periods, we can find their height using the y equation and divide that by that difference in time to get those average velocities for each time period.
00:52
So the first period we have is from two seconds to 2 .01 and then 2 to 2 .005 and so on.
00:58
So the first thing we do is is plug in each time value into our y and then we will find those y values and then find the slopes, if you will, or those average slopes for each period and then go from there.
01:16
So y of 2, plug that in.
01:17
You get 24 feet.
01:18
Then we do y of 2 .01, which is 23 .8989.
01:23
Y of 2 .005 is 23 .949725.
01:29
Of 2 .002 is 23 .979956.
01:33
And lastly, y of 2 .001 is 23 .98989.
01:39
So with these y values, we're now going to plug that in to this slope equation, this v equation right here.
01:47
And we're going to keep in mind that the time stamp of 2 or 2 comma 24, if you're thinking of it as a point on the graph, that's always going to be our y1 and t1.
01:57
So if we scroll down here, we see that we have our four time periods and the respective slopes...