1
00:00:00,000 --> 00:00:00,377


2
00:00:00,377 --> 00:00:02,960
In this video, I want to talk a
little bit about acceleration.

3
00:00:02,960 --> 00:00:06,090


4
00:00:06,090 --> 00:00:08,130
And this is probably
an idea that you're

5
00:00:08,130 --> 00:00:09,600
somewhat familiar
with, or at least

6
00:00:09,600 --> 00:00:12,360
you've heard the term
used here or there.

7
00:00:12,360 --> 00:00:17,015
Acceleration is just the
change in velocity over time.

8
00:00:17,015 --> 00:00:25,370


9
00:00:25,370 --> 00:00:28,280
Probably one of the most typical
examples of acceleration,

10
00:00:28,280 --> 00:00:30,420
if you're at all
interested in cars,

11
00:00:30,420 --> 00:00:33,000
is that many times
they will give you

12
00:00:33,000 --> 00:00:35,510
acceleration numbers, especially
for sport cars, actually

13
00:00:35,510 --> 00:00:38,350
all cars if you look
up in Consumer Reports,

14
00:00:38,350 --> 00:00:40,600
or wherever they give the
stats on different cars.

15
00:00:40,600 --> 00:00:44,840
They'll tell you something like,
I don't know, like a Porsche--

16
00:00:44,840 --> 00:00:48,410
and I'm going to make up
these numbers right over here.

17
00:00:48,410 --> 00:00:53,020
So let's say that we
have a Porsche 911.

18
00:00:53,020 --> 00:00:55,960
They'll say that a Porsche 911,
they'll literally measure it

19
00:00:55,960 --> 00:00:58,672
with a stopwatch, can go
0 to 60 miles per hour.

20
00:00:58,672 --> 00:01:01,432


21
00:01:01,432 --> 00:01:02,890
And these aren't
the exact numbers,

22
00:01:02,890 --> 00:01:04,819
although I think it's
probably pretty close.

23
00:01:04,819 --> 00:01:08,130
0 to 60 miles per hour
in, let's say, 3 seconds.

24
00:01:08,130 --> 00:01:13,194


25
00:01:13,194 --> 00:01:15,610
So, although officially what
they're giving you right here

26
00:01:15,610 --> 00:01:17,150
are speeds, because
they're only giving you

27
00:01:17,150 --> 00:01:18,730
magnitude and no
direction, you can

28
00:01:18,730 --> 00:01:20,355
assume that it's in
the same direction.

29
00:01:20,355 --> 00:01:22,680
I mean, We could
say, 0 miles per hour

30
00:01:22,680 --> 00:01:27,320
to the east to 60 miles per
hour to the east in 3 seconds.

31
00:01:27,320 --> 00:01:29,740
So what was the
acceleration here?

32
00:01:29,740 --> 00:01:32,480
So I just told you the
definition of acceleration.

33
00:01:32,480 --> 00:01:34,930
It's change in
velocity over time.

34
00:01:34,930 --> 00:01:37,660
So the acceleration-- and
once again acceleration

35
00:01:37,660 --> 00:01:39,420
is a vector quantity.

36
00:01:39,420 --> 00:01:41,990
You want to know not only
how much is velocity changing

37
00:01:41,990 --> 00:01:44,870
over time, you also care
about the direction.

38
00:01:44,870 --> 00:01:46,370
It also makes sense
because velocity

39
00:01:46,370 --> 00:01:48,580
itself is a vector quantity.

40
00:01:48,580 --> 00:01:51,060
It needs magnitude
and direction.

41
00:01:51,060 --> 00:01:53,210
So the acceleration
here-- and we're

42
00:01:53,210 --> 00:01:55,210
just going to assume
that we're going

43
00:01:55,210 --> 00:01:58,720
to the right, 0 miles per
hour and 60 miles per hour

44
00:01:58,720 --> 00:02:02,834
to the right-- so it's going
to be change in velocity.

45
00:02:02,834 --> 00:02:05,000
So let me just write it
down with different notation

46
00:02:05,000 --> 00:02:06,583
just so you could
familiarize yourself

47
00:02:06,583 --> 00:02:08,479
if you see it in the
textbook this way.

48
00:02:08,479 --> 00:02:12,780
So change in velocity.

49
00:02:12,780 --> 00:02:17,930
This delta symbol right
here just means "change in."

50
00:02:17,930 --> 00:02:21,580
Change in velocity over time.

51
00:02:21,580 --> 00:02:23,910
It's really, as I've
mentioned in previous videos,

52
00:02:23,910 --> 00:02:26,980
it's really time is
really a change in time.

53
00:02:26,980 --> 00:02:29,830
But we could just
write time here.

54
00:02:29,830 --> 00:02:31,710
This 3 seconds is
really change in time.

55
00:02:31,710 --> 00:02:35,282
It might have been, if you
looked at your second hand,

56
00:02:35,282 --> 00:02:37,740
it might have been 5 seconds
when it started, and then my 8

57
00:02:37,740 --> 00:02:40,850
seconds when it stopped, so
it took a total of 3 seconds.

58
00:02:40,850 --> 00:02:43,910
So time is really a
change in seconds.

59
00:02:43,910 --> 00:02:47,750
But we'll just go with time
right here, or just with a t.

60
00:02:47,750 --> 00:02:49,830
So what's our
change in velocity?

61
00:02:49,830 --> 00:02:52,780
So our final velocity
is 60 miles per hour.

62
00:02:52,780 --> 00:02:55,700


63
00:02:55,700 --> 00:02:58,700
And our original velocity
was 0 miles per hour.

64
00:02:58,700 --> 00:03:03,950
So it's 60 minus
0 miles per hour.

65
00:03:03,950 --> 00:03:06,400
And then, what is our time?

66
00:03:06,400 --> 00:03:08,500
What is our time over here?

67
00:03:08,500 --> 00:03:12,240
Well, our time is, or we could
even say our change in time,

68
00:03:12,240 --> 00:03:14,260
our change in time is 3 seconds.

69
00:03:14,260 --> 00:03:18,120


70
00:03:18,120 --> 00:03:22,890
So this gives us 20 miles
per hour, per second.

71
00:03:22,890 --> 00:03:24,310
Let me write this down.

72
00:03:24,310 --> 00:03:26,720
So this becomes,
this top part is 60.

73
00:03:26,720 --> 00:03:29,220
60 divided by 3 is 20.

74
00:03:29,220 --> 00:03:30,460
So we get 20.

75
00:03:30,460 --> 00:03:32,210
But then the units are
little bit strange.

76
00:03:32,210 --> 00:03:33,410
We have miles.

77
00:03:33,410 --> 00:03:40,800
Instead of writing MPH, I'm
going to write miles per hour.

78
00:03:40,800 --> 00:03:43,020
That's the same thing as MPH.

79
00:03:43,020 --> 00:03:45,800
And then we also, in the
denominator, right over here,

80
00:03:45,800 --> 00:03:52,040
have seconds.

81
00:03:52,040 --> 00:03:53,360
Which is a little bit strange.

82
00:03:53,360 --> 00:03:56,030
And as you'll see, the
units for acceleration

83
00:03:56,030 --> 00:03:57,390
do seem a little bit strange.

84
00:03:57,390 --> 00:03:58,490
But if we think it
through, it actually

85
00:03:58,490 --> 00:04:00,070
might make a little
bit of sense.

86
00:04:00,070 --> 00:04:01,632
So miles per hour.

87
00:04:01,632 --> 00:04:03,590
And then we could either
put seconds like this,

88
00:04:03,590 --> 00:04:06,332
or we could write per second.

89
00:04:06,332 --> 00:04:08,290
And let's just think
about what this is saying,

90
00:04:08,290 --> 00:04:10,040
and then we could get
it all into seconds,

91
00:04:10,040 --> 00:04:12,120
or we could all get into
hours, whatever we like.

92
00:04:12,120 --> 00:04:15,810
This is saying that every
second, this Porsche 911

93
00:04:15,810 --> 00:04:19,560
can increase its velocity
by 20 miles per hour.

94
00:04:19,560 --> 00:04:22,124
So its acceleration is 20
miles per hour, per second.

95
00:04:22,124 --> 00:04:24,040
And actually, we should
include the direction,

96
00:04:24,040 --> 00:04:26,200
because we're talking
about vector quantities.

97
00:04:26,200 --> 00:04:27,830
So this is to the east.

98
00:04:27,830 --> 00:04:32,220
So this is east, and then
this is east right over here--

99
00:04:32,220 --> 00:04:35,670
just so we make sure that
we're dealing with vectors.

100
00:04:35,670 --> 00:04:37,700
You're giving it a
direction, due east.

101
00:04:37,700 --> 00:04:40,350
So every second it can
increase in velocity

102
00:04:40,350 --> 00:04:41,690
by 20 miles per hour.

103
00:04:41,690 --> 00:04:42,605
So hopefully, with
the way I'm saying it,

104
00:04:42,605 --> 00:04:43,920
it makes a little bit of sense.

105
00:04:43,920 --> 00:04:46,390
20 miles per hour, per second.

106
00:04:46,390 --> 00:04:48,330
That's exactly what
this is talking about.

107
00:04:48,330 --> 00:04:50,240
Now we could also
write it like this.

108
00:04:50,240 --> 00:04:57,600
This is the same thing
as 20 miles per hour,

109
00:04:57,600 --> 00:04:59,670
because if you take
something and you

110
00:04:59,670 --> 00:05:02,640
divide by seconds, that's the
same thing as multiplying it

111
00:05:02,640 --> 00:05:04,070
by 1 over seconds.

112
00:05:04,070 --> 00:05:05,480
So that's miles
per hour-seconds.

113
00:05:05,480 --> 00:05:08,220


114
00:05:08,220 --> 00:05:10,320
And although this
is correct, to me

115
00:05:10,320 --> 00:05:12,410
this makes a little
less intuitive sense.

116
00:05:12,410 --> 00:05:13,750
This one literally says it.

117
00:05:13,750 --> 00:05:17,010
Every second, it's increasing in
velocity by 20 miles per hour.

118
00:05:17,010 --> 00:05:20,424
20 miles per hour increase
in velocity per second.

119
00:05:20,424 --> 00:05:21,840
So that kind of
makes sense to me.

120
00:05:21,840 --> 00:05:25,150
Here it's saying 20
miles per hour-seconds.

121
00:05:25,150 --> 00:05:28,220
So once again, it's
not as intuitive.

122
00:05:28,220 --> 00:05:30,790
But we can make this so it's
all in one unit of time,

123
00:05:30,790 --> 00:05:33,260
although you don't
really have to.

124
00:05:33,260 --> 00:05:35,240
You can change this
so that you get rid

125
00:05:35,240 --> 00:05:37,080
of maybe the hours
in the denominator.

126
00:05:37,080 --> 00:05:39,496
And the best way to get rid
of an hour in the denominator,

127
00:05:39,496 --> 00:05:41,080
is by multiplying
it by something

128
00:05:41,080 --> 00:05:43,110
that has hours in the numerator.

129
00:05:43,110 --> 00:05:47,200
So hour and seconds.

130
00:05:47,200 --> 00:05:50,990
And here, the smaller
unit is the seconds.

131
00:05:50,990 --> 00:05:54,380
So it's 3,600 seconds
for every 1 hour.

132
00:05:54,380 --> 00:05:56,770
Or 1 hour is equal
to 3,600 seconds.

133
00:05:56,770 --> 00:06:01,060
Or 1/3600 of an hour per second.

134
00:06:01,060 --> 00:06:03,060
All of those are legitimate
ways to interpret

135
00:06:03,060 --> 00:06:06,050
this thing in magenta
right over here.

136
00:06:06,050 --> 00:06:09,030
And then you multiply, do a
little dimensional analysis.

137
00:06:09,030 --> 00:06:11,400
Hour cancels with hour.

138
00:06:11,400 --> 00:06:19,330
And then will be
equal to 20/3600.

139
00:06:19,330 --> 00:06:23,840
20/3600 miles per
seconds times seconds.

140
00:06:23,840 --> 00:06:27,560
Or we could say,
miles-- let me write

141
00:06:27,560 --> 00:06:31,500
it this way-- miles per
seconds times seconds.

142
00:06:31,500 --> 00:06:34,690
Or we could say,
miles per second-- I

143
00:06:34,690 --> 00:06:37,280
want to do that in
another color-- miles

144
00:06:37,280 --> 00:06:38,375
per second squared.

145
00:06:38,375 --> 00:06:44,440


146
00:06:44,440 --> 00:06:46,030
And we can simplify
this a little bit.

147
00:06:46,030 --> 00:06:48,700
Divide the numerator
and denominator by 10.

148
00:06:48,700 --> 00:06:51,450
You get 2/360.

149
00:06:51,450 --> 00:06:53,300
Or you could get,
this is the same thing

150
00:06:53,300 --> 00:07:04,210
as, 1/180 miles
per second squared.

151
00:07:04,210 --> 00:07:05,980
And I'll just
abbreviate it like that.

152
00:07:05,980 --> 00:07:10,040
And once again, this 1/180
of a mile, how much is that?

153
00:07:10,040 --> 00:07:11,457
You might want to
convert to feet.

154
00:07:11,457 --> 00:07:13,040
But the whole point
in here is, I just

155
00:07:13,040 --> 00:07:14,830
wanted to show you
that, well, one, how

156
00:07:14,830 --> 00:07:16,230
do you calculate acceleration?

157
00:07:16,230 --> 00:07:18,480
And give you a little bit
of a sense of what it means.

158
00:07:18,480 --> 00:07:20,021
And once again, this
right here, when

159
00:07:20,021 --> 00:07:22,240
you have seconds squared in
the bottom of your units,

160
00:07:22,240 --> 00:07:23,531
it doesn't make a ton of sense.

161
00:07:23,531 --> 00:07:25,980
But we can rewrite
it like this up here.

162
00:07:25,980 --> 00:07:35,650
This is 1/180 miles per second.

163
00:07:35,650 --> 00:07:40,310
And then we divide by
seconds again, per second.

164
00:07:40,310 --> 00:07:43,550
Or maybe I can write
like this, per second,

165
00:07:43,550 --> 00:07:46,079
where this whole thing
is the numerator.

166
00:07:46,079 --> 00:07:47,620
So this makes a
little bit more sense

167
00:07:47,620 --> 00:07:49,410
from an acceleration
point of view.

168
00:07:49,410 --> 00:07:52,490
1/180 miles per
second, per second.

169
00:07:52,490 --> 00:07:55,400
Every second, this
Porsche 911 is

170
00:07:55,400 --> 00:08:01,400
going to go 1/180 of a
mile per second faster.

171
00:08:01,400 --> 00:08:03,150
And actually, it's
probably more intuitive

172
00:08:03,150 --> 00:08:05,483
to stick to the miles per
hour, because that's something

173
00:08:05,483 --> 00:08:07,720
that we have a little
bit more sense on.

174
00:08:07,720 --> 00:08:10,210
And another way to visualize it.

175
00:08:10,210 --> 00:08:12,960
If you were to be
driving that Porsche,

176
00:08:12,960 --> 00:08:15,580
and you were to look at the
speedometer for that Porsche,

177
00:08:15,580 --> 00:08:17,620
and if the acceleration
was constant--

178
00:08:17,620 --> 00:08:20,030
it's actually not going to
be completely constant--

179
00:08:20,030 --> 00:08:22,030
and if you look at
speedometer-- let me draw it.

180
00:08:22,030 --> 00:08:30,069
So this would be 10,
20, 30, 40, 50, 60.

181
00:08:30,069 --> 00:08:32,360
This is probably not what
the speedometer for a Porsche

182
00:08:32,360 --> 00:08:32,859
looks like.

183
00:08:32,859 --> 00:08:36,520
This is probably more analogous
to a small four cylinder car's

184
00:08:36,520 --> 00:08:37,530
spectrometer.

185
00:08:37,530 --> 00:08:39,740
I suspect the Porsche's
speedometer goes much

186
00:08:39,740 --> 00:08:41,321
beyond 60 miles per hour.

187
00:08:41,321 --> 00:08:42,820
But what you would
see for something

188
00:08:42,820 --> 00:08:45,880
accelerating this fast is,
right when you're starting,

189
00:08:45,880 --> 00:08:48,080
the speedometer
would be right there.

190
00:08:48,080 --> 00:08:51,480
And that every second it would
be 20 miles per hour faster.

191
00:08:51,480 --> 00:08:53,700
So after a second
the speedometer

192
00:08:53,700 --> 00:08:54,810
would have moved this far.

193
00:08:54,810 --> 00:08:56,310
After another second
the speedometer

194
00:08:56,310 --> 00:08:57,436
would have moved this far.

195
00:08:57,436 --> 00:08:59,310
And then after another
second the speedometer

196
00:08:59,310 --> 00:09:01,081
would have moved that far.

197
00:09:01,081 --> 00:09:02,830
And the entire time
you would have kind of

198
00:09:02,830 --> 00:00:00,000
been pasted to the
back of your seat.