WEBVTT
1
00:00:01.840 --> 00:00:04.610 A:middle L:90%
So in this problem we are given this table of
2
00:00:04.610 --> 00:00:08.859 A:middle L:90%
positions of a motorcyclist after acceleration, accelerating from rest
3
00:00:09.740 --> 00:00:15.039 A:middle L:90%
at different times, t in seconds and were asked
4
00:00:15.039 --> 00:00:25.350 A:middle L:90%
first to find the average velocity for each time period
5
00:00:26.940 --> 00:00:32.490 A:middle L:90%
. 1st 1 being from 2 to 4. Okay
6
00:00:32.490 --> 00:00:37.340 A:middle L:90%
, so the average velocity is the average rate of
7
00:00:37.340 --> 00:00:42.189 A:middle L:90%
change across the interval. In other words, it's
8
00:00:42.189 --> 00:00:54.259 A:middle L:90%
gonna be the Going to be S 2-11 over
9
00:00:54.939 --> 00:00:58.740 A:middle L:90%
T two minus T one right distance over time,
10
00:00:58.750 --> 00:01:02.509 A:middle L:90%
which will give us velocity. So From 2 to
11
00:01:02.509 --> 00:01:11.950 A:middle L:90%
4 We have 79.2-20.6 over four minus two,
12
00:01:14.739 --> 00:01:27.060 A:middle L:90%
which is 58.6 over two. So that's 29 0.3
13
00:01:29.540 --> 00:01:38.439 A:middle L:90%
feet per second. Okay, the next interval is
14
00:01:38.439 --> 00:01:45.489 A:middle L:90%
from 3 to 4 using the same formula, That's
15
00:01:45.489 --> 00:01:55.890 A:middle L:90%
79.2-46.5 over four minus three. And so we
16
00:01:55.890 --> 00:02:13.349 A:middle L:90%
have 32.7/1. So that's 30 2.7 feet for a
17
00:02:13.349 --> 00:02:22.759 A:middle L:90%
second. Okay, the next interval is 4-5,
18
00:02:24.039 --> 00:02:35.650 A:middle L:90%
So that's 1 24.8 minus 79.2 over five minutes four
19
00:02:36.740 --> 00:02:39.460 A:middle L:90%
. I must four is 1. So this is
20
00:02:42.439 --> 00:03:00.659 A:middle L:90%
40 five. No, this is Yeah, six
21
00:03:05.139 --> 00:03:12.460 A:middle L:90%
feet for a second. And then the final period
22
00:03:13.439 --> 00:03:21.400 A:middle L:90%
, final interval is from for 26, which we
23
00:03:21.400 --> 00:03:29.659 A:middle L:90%
can see from our table Would be 1 76.7-79.2
24
00:03:30.840 --> 00:03:38.259 A:middle L:90%
. So let's see here. 1 70 6.7-7
25
00:03:38.740 --> 00:03:47.360 A:middle L:90%
79.2 over six months four, Which is 97.5 over
26
00:03:47.370 --> 00:03:55.860 A:middle L:90%
two, Which is 48.75 feet for a second.
27
00:03:58.439 --> 00:04:00.949 A:middle L:90%
All right, so those are the average velocities.
28
00:04:02.139 --> 00:04:04.629 A:middle L:90%
Now. The next thing says to use the graph
29
00:04:04.629 --> 00:04:08.900 A:middle L:90%
of S as a function of T. To estimate
30
00:04:08.900 --> 00:04:12.740 A:middle L:90%
the incidents velocity when T equals three. So let's
31
00:04:12.740 --> 00:04:16.339 A:middle L:90%
go over here and graph this now. So I
32
00:04:16.339 --> 00:04:24.529 A:middle L:90%
go to my graphing dez most. Yeah. And
33
00:04:24.610 --> 00:04:35.149 A:middle L:90%
enter the data. 012 three 456, wow.
34
00:04:35.540 --> 00:05:02.660 A:middle L:90%
And then zero yeah. 4.9 20.6 46.5 79.2 24
35
00:05:04.939 --> 00:05:17.860 A:middle L:90%
0.8 And 1 76.7. So here's our graph of
36
00:05:18.000 --> 00:05:25.600 A:middle L:90%
this data. Okay. Here's our graph of the
37
00:05:25.600 --> 00:05:30.029 A:middle L:90%
data. So we want to find instantaneous velocity when
38
00:05:30.029 --> 00:05:35.660 A:middle L:90%
T equals three. Okay. So what we need
39
00:05:35.660 --> 00:05:41.360 A:middle L:90%
to do is is draw the graph through this data
40
00:05:42.339 --> 00:05:44.259 A:middle L:90%
. Okay, so let's get the best fit here
41
00:05:44.639 --> 00:05:47.829 A:middle L:90%
. That data looks like it is either exponential or
42
00:05:47.829 --> 00:05:54.350 A:middle L:90%
a second order parabola happening to us here. Okay
43
00:05:58.339 --> 00:06:09.139 A:middle L:90%
, so let's say that why one approximately equal to
44
00:06:09.149 --> 00:06:20.959 A:middle L:90%
a X squared plus, but this should be a
45
00:06:23.240 --> 00:06:30.160 A:middle L:90%
that's one down there plus B X. Right one
46
00:06:31.540 --> 00:06:35.620 A:middle L:90%
plus. See okay, and look at that that
47
00:06:35.620 --> 00:06:39.759 A:middle L:90%
data, it's right on that curve, doesn't it
48
00:06:40.740 --> 00:06:43.699 A:middle L:90%
? We have a very very good fit our squares
49
00:06:43.699 --> 00:06:46.050 A:middle L:90%
.9999. We have a great fit here. Okay
50
00:06:46.050 --> 00:06:48.459 A:middle L:90%
, so if I blow this up a little bit
51
00:06:49.339 --> 00:06:53.649 A:middle L:90%
. Right, So that I'm here at three.
52
00:06:54.839 --> 00:07:01.060 A:middle L:90%
Oh okay. Okay. Well so we know that
53
00:07:03.040 --> 00:07:18.779 A:middle L:90%
that the instantaneous velocity at T equals three is the
54
00:07:18.779 --> 00:07:27.240 A:middle L:90%
limit as T goes zero over the change in the
55
00:07:27.240 --> 00:07:39.569 A:middle L:90%
distance? Over the change in time as well as
56
00:07:39.569 --> 00:07:48.720 A:middle L:90%
our horizontal X goes 23. Okay, well we
57
00:07:48.720 --> 00:07:53.060 A:middle L:90%
look at our graph here for a second. What
58
00:07:53.060 --> 00:07:57.319 A:middle L:90%
can we see about our graph? Oh, we
59
00:07:57.319 --> 00:08:03.839 A:middle L:90%
can see that if three is here at 46 a
60
00:08:03.839 --> 00:08:15.459 A:middle L:90%
half. Okay then at was at three mm we're
61
00:08:15.459 --> 00:08:18.060 A:middle L:90%
looking at this tangent line right of this curve here
62
00:08:20.740 --> 00:08:24.660 A:middle L:90%
and so look at this territory are for a minute
63
00:08:24.339 --> 00:08:31.379 A:middle L:90%
. Okay then at four. All right, that
64
00:08:31.379 --> 00:08:41.269 A:middle L:90%
tangent line would be about where would be about 75
65
00:08:41.269 --> 00:08:46.159 A:middle L:90%
, wouldn't it? Okay, so let's use that
66
00:08:48.139 --> 00:09:00.919 A:middle L:90%
. So instantaneous velocity Would be 75 46.5 Over four
67
00:09:00.919 --> 00:09:09.159 A:middle L:90%
months 3, Which would be 28.5 feet per second
68
00:09:09.740 --> 00:09:11.070 A:middle L:90%
. And if you want to be more accurate zoom
69
00:09:11.070 --> 00:09:16.309 A:middle L:90%
in closer and use a smaller and smaller interval so
70
00:09:16.309 --> 00:09:20.889 A:middle L:90%
that you take this limit right here to get an
71
00:09:20.889 --> 00:09:24.159 A:middle L:90%
even more accurate instantaneous velocity