[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.75,0:00:02.61,Default,,0000,0000,0000,,We have seen multiple times in our life
Dialogue: 0,0:00:02.61,0:00:08.06,Default,,0000,0000,0000,,that distance can be viewed as rate times\Ntime.
Dialogue: 0,0:00:08.06,0:00:10.99,Default,,0000,0000,0000,,Now what I wanna do in this video is use\Nthis fairly
Dialogue: 0,0:00:10.99,0:00:15.73,Default,,0000,0000,0000,,simple formula right over here, this\Nfairly simple equation, to understand that
Dialogue: 0,0:00:15.73,0:00:20.14,Default,,0000,0000,0000,,units can really be viewed as algebraic\Nobjects, that you can kind
Dialogue: 0,0:00:20.14,0:00:24.36,Default,,0000,0000,0000,,of treat them like variables as we work\Nthrough a formula or equation.
Dialogue: 0,0:00:24.36,0:00:27.48,Default,,0000,0000,0000,,Which could be really, really helpful to\Nmake sure that
Dialogue: 0,0:00:27.48,0:00:33.00,Default,,0000,0000,0000,,our, that we're getting results in units\Nthat actually make sense.
Dialogue: 0,0:00:33.00,0:00:38.03,Default,,0000,0000,0000,,So for example, if someone were to give\Nyou a rate, if they were to say a
Dialogue: 0,0:00:38.03,0:00:43.36,Default,,0000,0000,0000,,rate of, let's say, 5 meters
Dialogue: 0,0:00:43.36,0:00:48.96,Default,,0000,0000,0000,,per second, and they were to give you a\Ntime, a time of 10
Dialogue: 0,0:00:48.96,0:00:53.22,Default,,0000,0000,0000,,seconds, then we can pretty, in a pretty\Nstraight forward way, apply this formula.
Dialogue: 0,0:00:53.22,0:00:57.77,Default,,0000,0000,0000,,We say well distance is equal to our rate,\N5 meters per
Dialogue: 0,0:00:57.77,0:01:03.44,Default,,0000,0000,0000,,second, times our time, times our time\Nwhich is 10 seconds.
Dialogue: 0,0:01:03.44,0:01:07.05,Default,,0000,0000,0000,,And what's neat here is we can treat the\Nunits,
Dialogue: 0,0:01:07.05,0:01:11.16,Default,,0000,0000,0000,,as I just said, like algebraic constructs,\Nkind of like variables.
Dialogue: 0,0:01:11.16,0:01:13.64,Default,,0000,0000,0000,,So this would be equal to, well
Dialogue: 0,0:01:13.64,0:01:16.01,Default,,0000,0000,0000,,multiplication doesn't matter what order\Nwe multiply in.
Dialogue: 0,0:01:16.01,0:01:17.76,Default,,0000,0000,0000,,So we can change them, the order.
Dialogue: 0,0:01:17.76,0:01:21.34,Default,,0000,0000,0000,,This is the same thing as 5 times 10.
Dialogue: 0,0:01:21.34,0:01:30.88,Default,,0000,0000,0000,,5 times 10 times meters per second, times\Nmeters per seconds, times seconds.
Dialogue: 0,0:01:30.88,0:01:32.59,Default,,0000,0000,0000,,And if we were to treat our units as these
Dialogue: 0,0:01:32.59,0:01:35.14,Default,,0000,0000,0000,,kinds of algebraic objects, and we could\Nsay, hey look,
Dialogue: 0,0:01:35.14,0:01:37.27,Default,,0000,0000,0000,,we have seconds divided by seconds, or you\Nhave a
Dialogue: 0,0:01:37.27,0:01:40.93,Default,,0000,0000,0000,,seconds in the denominator multiplied by\Nseconds in the numerator.
Dialogue: 0,0:01:40.93,0:01:42.66,Default,,0000,0000,0000,,Those are going to cancel out.
Dialogue: 0,0:01:42.66,0:01:47.37,Default,,0000,0000,0000,,And 5 times 10, of course is, 5 times 10,\Nof course is 50.
Dialogue: 0,0:01:47.37,0:01:50.90,Default,,0000,0000,0000,,So we would be left with 50, and the
Dialogue: 0,0:01:50.90,0:01:54.54,Default,,0000,0000,0000,,units that we're left with are the meters,\N50 meters.
Dialogue: 0,0:01:54.54,0:01:55.75,Default,,0000,0000,0000,,So that's pretty neat.
Dialogue: 0,0:01:55.75,0:01:56.69,Default,,0000,0000,0000,,The units worked out.
Dialogue: 0,0:01:56.69,0:02:00.90,Default,,0000,0000,0000,,When we treated the units out like\Nalgebraic objects, they worked out so that
Dialogue: 0,0:02:00.90,0:02:06.43,Default,,0000,0000,0000,,our end units for distance were in meters,\Nwhich is a unit of distance.
Dialogue: 0,0:02:06.43,0:02:07.91,Default,,0000,0000,0000,,Now you're saying, okay, that's, that's\Ncute and
Dialogue: 0,0:02:07.91,0:02:09.31,Default,,0000,0000,0000,,everything, but this seems like a little\Nbit
Dialogue: 0,0:02:09.31,0:02:14.29,Default,,0000,0000,0000,,of too much overhead to worry about when\NI'm just doing a simple formula like this,
Dialogue: 0,0:02:14.29,0:02:18.02,Default,,0000,0000,0000,,but what I wanna show is that even with a\Nsimple, with a simple formula like
Dialogue: 0,0:02:18.02,0:02:22.49,Default,,0000,0000,0000,,distance is equal to rate times time, what\NI just did could actually be quite useful.
Dialogue: 0,0:02:22.49,0:02:25.57,Default,,0000,0000,0000,,And this thing that I'm doing is actually\Ncalled dimensional analysis.
Dialogue: 0,0:02:25.57,0:02:27.15,Default,,0000,0000,0000,,And it's useful for something as simple as
Dialogue: 0,0:02:27.15,0:02:29.37,Default,,0000,0000,0000,,distance equals rate times time, but as\Nyou go
Dialogue: 0,0:02:29.37,0:02:32.34,Default,,0000,0000,0000,,into physics and chemistry and\Nengineering, you'll see
Dialogue: 0,0:02:32.34,0:02:35.88,Default,,0000,0000,0000,,much, much, much more I would say hairy\Nformulas.
Dialogue: 0,0:02:35.88,0:02:38.09,Default,,0000,0000,0000,,And when you do the dimensional analysis,\Nit makes
Dialogue: 0,0:02:38.09,0:02:40.62,Default,,0000,0000,0000,,sure that your, that the math is working\Nout right.
Dialogue: 0,0:02:40.62,0:02:42.66,Default,,0000,0000,0000,,It makes sure that you're getting the\Nright units.
Dialogue: 0,0:02:42.66,0:02:45.96,Default,,0000,0000,0000,,But even with this, let's try a slightly\Nmore complicated example.
Dialogue: 0,0:02:45.96,0:02:49.17,Default,,0000,0000,0000,,Let's say that our rate is, let's say,
Dialogue: 0,0:02:49.17,0:02:52.93,Default,,0000,0000,0000,,let's keep our rate at 5 meters per\Nsecond.
Dialogue: 0,0:02:52.93,0:02:55.51,Default,,0000,0000,0000,,But let's say that someone gave us the\Ntime.
Dialogue: 0,0:02:55.51,0:02:57.86,Default,,0000,0000,0000,,Instead of giving it in seconds, they give\Nit in hours.
Dialogue: 0,0:02:57.86,0:03:01.92,Default,,0000,0000,0000,,So they say the time is equal to 1 hour.
Dialogue: 0,0:03:01.92,0:03:04.25,Default,,0000,0000,0000,,So now let's try to apply this formula.
Dialogue: 0,0:03:04.25,0:03:09.60,Default,,0000,0000,0000,,So we're gonna get distance is equal to 5\Nmeters per second, 5
Dialogue: 0,0:03:09.60,0:03:15.82,Default,,0000,0000,0000,,meters per second, times time, which is 1\Nhour, times 1 hour.
Dialogue: 0,0:03:15.82,0:03:17.19,Default,,0000,0000,0000,,But what's that gonna give us?
Dialogue: 0,0:03:17.19,0:03:20.41,Default,,0000,0000,0000,,Well the 5 times the 1, so we multiply the\N5 times the 1.
Dialogue: 0,0:03:20.41,0:03:22.90,Default,,0000,0000,0000,,That's just going to give us 5.
Dialogue: 0,0:03:22.90,0:03:25.77,Default,,0000,0000,0000,,Well then we have to, remember we have to,\Nthe units algebraically.
Dialogue: 0,0:03:25.77,0:03:27.65,Default,,0000,0000,0000,,Where we're going to do our dimensional\Nanalysis.
Dialogue: 0,0:03:27.65,0:03:35.57,Default,,0000,0000,0000,,So it's 5, that we have meters per second,\Ntimes hours, times hours.
Dialogue: 0,0:03:35.57,0:03:38.67,Default,,0000,0000,0000,,Or you could say 5 meter hours per second.
Dialogue: 0,0:03:38.67,0:03:41.00,Default,,0000,0000,0000,,Well this doesn't look like a, this isn't\Na, a,
Dialogue: 0,0:03:41.00,0:03:42.97,Default,,0000,0000,0000,,a set of units that we know, that, that\Nmakes
Dialogue: 0,0:03:42.97,0:03:45.49,Default,,0000,0000,0000,,sense to us, this doesn't feel like our\Ntraditional units
Dialogue: 0,0:03:45.49,0:03:48.35,Default,,0000,0000,0000,,of distance, so we wanna cancel this out\Nin some way.
Dialogue: 0,0:03:48.35,0:03:49.95,Default,,0000,0000,0000,,And it might jump out of you, well if, if\Nwe can
Dialogue: 0,0:03:49.95,0:03:52.07,Default,,0000,0000,0000,,get rid of this hours, if we could express\Nit in terms
Dialogue: 0,0:03:52.07,0:03:55.24,Default,,0000,0000,0000,,of seconds, then that would cancel here\Nand we'd be left with
Dialogue: 0,0:03:55.24,0:03:58.90,Default,,0000,0000,0000,,just the meters, which is a unit of\Ndistance that we're familiar with.
Dialogue: 0,0:03:58.90,0:04:00.41,Default,,0000,0000,0000,,So how do we do that?
Dialogue: 0,0:04:00.41,0:04:04.71,Default,,0000,0000,0000,,Well we'd wanna multiply this thing by\Nsomething that has hours in
Dialogue: 0,0:04:04.71,0:04:07.15,Default,,0000,0000,0000,,the denominator, and seconds in the
Dialogue: 0,0:04:07.15,0:04:10.33,Default,,0000,0000,0000,,numerator, times essentially, seconds per\Nhour.
Dialogue: 0,0:04:10.33,0:04:13.16,Default,,0000,0000,0000,,Well how many seconds are there per hour?
Dialogue: 0,0:04:13.16,0:04:19.54,Default,,0000,0000,0000,,Well, there are 3600, let me do this in a,\NI'll do this color, there are 3600 seconds
Dialogue: 0,0:04:19.54,0:04:27.51,Default,,0000,0000,0000,,per hour, or you could even say that there\Nare 3600 seconds for every 1 hour.
Dialogue: 0,0:04:27.51,0:04:30.88,Default,,0000,0000,0000,,So when you, now when you multiply, these\Nhours will
Dialogue: 0,0:04:30.88,0:04:35.54,Default,,0000,0000,0000,,cancel with these hours, these seconds\Nwill cancel with those seconds,
Dialogue: 0,0:04:35.54,0:04:38.38,Default,,0000,0000,0000,,and we are left with, we are left with 5\Ntimes
Dialogue: 0,0:04:38.38,0:04:43.23,Default,,0000,0000,0000,,3600, what is that, that's 5 times 3000\Nwould be 15000.
Dialogue: 0,0:04:43.23,0:04:46.13,Default,,0000,0000,0000,,5 times 600 is another 3000.
Dialogue: 0,0:04:46.13,0:04:51.96,Default,,0000,0000,0000,,So that is, it's equal to 18000, and the\Nonly units that
Dialogue: 0,0:04:51.96,0:04:57.79,Default,,0000,0000,0000,,we're left with, we just have the meters\Nthere 18 oh, it's
Dialogue: 0,0:04:57.79,0:05:03.31,Default,,0000,0000,0000,,18000, 18000, 18000 meters, right?
Dialogue: 0,0:05:03.31,0:05:04.54,Default,,0000,0000,0000,,And so, this is, we're done.
Dialogue: 0,0:05:04.54,0:05:08.30,Default,,0000,0000,0000,,We've now expressed our distance in terms\Nof units that we recognize.
Dialogue: 0,0:05:08.30,0:05:13.96,Default,,0000,0000,0000,,If you go 5 meters per second, for 1 hour,\Nyou will go 18000 meters.
Dialogue: 0,0:05:13.96,0:05:17.02,Default,,0000,0000,0000,,But let's just use our little dimensional\Nanalysis muscles a little bit more.
Dialogue: 0,0:05:17.02,0:05:18.54,Default,,0000,0000,0000,,What if, what if we didn't want the answer
Dialogue: 0,0:05:18.54,0:05:20.55,Default,,0000,0000,0000,,in meters, but we wanted the answer in\Nkilometers?
Dialogue: 0,0:05:20.55,0:05:22.00,Default,,0000,0000,0000,,What could we do?
Dialogue: 0,0:05:22.00,0:05:27.57,Default,,0000,0000,0000,,Well we could take that 18000 meters,\N18000 meters, and if
Dialogue: 0,0:05:27.57,0:05:30.70,Default,,0000,0000,0000,,we could multiply it by something that has\Nmeters in the
Dialogue: 0,0:05:30.70,0:05:36.19,Default,,0000,0000,0000,,denominator, meters in the denominator,\Nand kilometers in the numerator, then
Dialogue: 0,0:05:36.19,0:05:39.76,Default,,0000,0000,0000,,these meters would cancel out and we'd be\Nleft with the kilometers.
Dialogue: 0,0:05:39.76,0:05:42.76,Default,,0000,0000,0000,,So what could we multiply it so we're not\Nreally changing the value?
Dialogue: 0,0:05:42.76,0:05:45.35,Default,,0000,0000,0000,,Well we want to multiply it by essentially\N1, so
Dialogue: 0,0:05:45.35,0:05:49.48,Default,,0000,0000,0000,,we wanna write equivalent things in the\Nnumerator and the denominator.
Dialogue: 0,0:05:49.48,0:05:55.73,Default,,0000,0000,0000,,So 1 kilometer is equivalent to 1000\Nmeters.
Dialogue: 0,0:05:55.73,0:05:58.54,Default,,0000,0000,0000,,So one way to think about it, we're just\Nmultiplying this thing by 1.
Dialogue: 0,0:05:58.54,0:06:01.67,Default,,0000,0000,0000,,One kilometer over 1000 meters.
Dialogue: 0,0:06:01.67,0:06:03.26,Default,,0000,0000,0000,,Well, one kilometer is 1000 meters.
Dialogue: 0,0:06:03.26,0:06:05.67,Default,,0000,0000,0000,,So this thing is equivalent to 1.
Dialogue: 0,0:06:05.67,0:06:07.97,Default,,0000,0000,0000,,But what's in need is when you multiply,\Nwe
Dialogue: 0,0:06:07.97,0:06:12.45,Default,,0000,0000,0000,,have meters cancelling with meters, until\Nyou're left with
Dialogue: 0,0:06:12.45,0:06:16.57,Default,,0000,0000,0000,,18000 divided by 1000 is equal to 18, and
Dialogue: 0,0:06:16.57,0:06:20.01,Default,,0000,0000,0000,,then the only units we're left with is the\Nkilometers.
Dialogue: 0,0:06:21.02,0:06:23.98,Default,,0000,0000,0000,,And we are done, we have re-expressed our
Dialogue: 0,0:06:23.98,0:06:27.56,Default,,0000,0000,0000,,distance instead of in meters, in terms of\Nkilometers.