0:00:00.810,0:00:02.500
In the last video,[br]we figured out

0:00:02.500,0:00:06.875
that given a takeoff velocity[br]of 280 kilometers per hour--

0:00:06.875,0:00:09.250
and if we have a positive[br]value for any of these vectors,

0:00:09.250,0:00:12.580
we assume it's in the forward[br]direction for the runway--

0:00:12.580,0:00:16.860
given this takeoff velocity,[br]and a constant acceleration of 1

0:00:16.860,0:00:20.260
meter per second per second,[br]or 1 meter per second squared,

0:00:20.260,0:00:22.380
we figured out that it[br]would take an Airbus

0:00:22.380,0:00:28.240
A380 about 78[br]seconds to take off.

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What I want to figure[br]out in this video

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is, given all of these[br]numbers, how long of a runaway

0:00:33.110,0:00:36.080
does it need, which is a very[br]important question if you want

0:00:36.080,0:00:39.020
to build a runway that[br]can at least allow

0:00:39.020,0:00:40.699
Airbus A380s to take off.

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And you probably want it to[br]be a little bit longer than

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that just in case it takes a[br]little bit longer than expected

0:00:45.300,0:00:45.890
to take off.

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But what is the minimum[br]length of the runway

0:00:48.350,0:00:51.450
given these numbers?

0:00:51.450,0:00:53.870
So we want to figure[br]out the displacement,

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or how far does[br]this plane travel

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as it is accelerating at[br]1 meter per second squared

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to 280 kilometers per[br]hour, or to 78-- or where

0:01:05.150,0:01:07.630
did I write it[br]over here-- to 78.

0:01:07.630,0:01:10.840
I converted it right over here.

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As it accelerates to[br]78 meters per second,

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how much land does[br]this thing cover?

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So let's call this,[br]the displacement

0:01:23.940,0:01:26.760
is going to be equal[br]to-- So displacement

0:01:26.760,0:01:31.760
is equal to-- You could view[br]it as velocity times time.

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But the velocity[br]here is changing.

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If we just had a constant[br]velocity for this entire time,

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we could just multiply[br]that times however

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long it's traveling, and it[br]would give us the displacement.

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But here our[br]velocity is changing.

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But lucky for us,[br]we learned-- and I

0:01:46.740,0:01:50.880
encourage you to watch the video[br]on why distance, or actually

0:01:50.880,0:01:54.370
the video on average velocity[br]for constant acceleration--

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but if you have[br]constant acceleration,

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and that is what we are[br]assuming in this example--

0:02:02.600,0:02:06.572
so if you assume that your[br]acceleration is constant,

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then you can come[br]up with something

0:02:08.030,0:02:10.030
called an average velocity.

0:02:10.030,0:02:13.210
And the average velocity, if[br]your acceleration is constant,

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if and only if your[br]acceleration is constant, then

0:02:16.420,0:02:20.020
your average velocity[br]will be the average

0:02:20.020,0:02:23.740
of your final velocity[br]and your initial velocity.

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And so in this situation,[br]what is our average velocity?

0:02:27.234,0:02:28.650
Well, our average[br]velocity-- let's

0:02:28.650,0:02:30.320
do it in meters per[br]second-- is going

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to be our final velocity,[br]which is-- let me calculate it

0:02:32.880,0:02:34.450
down here.

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So our average velocity[br]in this example

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is going to be our[br]final velocity, which

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is 78 meters per second,[br]plus our initial velocity.

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Well, what's our[br]initial velocity?

0:02:46.860,0:02:48.870
We're assuming we're[br]starting at a standstill.

0:02:48.870,0:02:52.330
Plus 0, all of that over 2.

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So our average velocity in this[br]situation, 78 divided by 2,

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is 39 meters per second.

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And the value of an average[br]velocity in this situation--

0:03:03.780,0:03:06.590
actually, average velocity[br]in any situation--

0:03:06.590,0:03:08.800
but in this situation, we[br]can calculate it this way.

0:03:08.800,0:03:10.300
But the value of[br]an average velocity

0:03:10.300,0:03:12.400
is we can figure[br]out our displacement

0:03:12.400,0:03:21.020
by multiplying our average[br]velocity times the time that

0:03:21.020,0:03:24.340
goes by, times the[br]change in time.

0:03:24.340,0:03:28.190
So we know the change[br]in time is 78 seconds.

0:03:28.190,0:03:30.260
We know our average[br]velocity here

0:03:30.260,0:03:37.100
is 39 meters per second,[br]just the average of 0 and 78,

0:03:37.100,0:03:38.770
39 meters per second.

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Another way to think[br]about it, if you want

0:03:41.020,0:03:42.580
think about the[br]distance traveled,

0:03:42.580,0:03:44.590
this plane is[br]constantly accelerating.

0:03:44.590,0:03:48.350
So let me draw a[br]little graph here.

0:03:48.350,0:03:52.370
This plane's velocity time graph[br]would look something like this.

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So if this is time and this[br]is velocity right over here,

0:03:56.480,0:03:58.280
this plane has a[br]constant acceleration

0:03:58.280,0:03:59.510
starting with 0 velocity.

0:03:59.510,0:04:01.540
It has a constant acceleration.

0:04:01.540,0:04:03.962
This slope right here is[br]constant acceleration.

0:04:03.962,0:04:05.420
It should actually[br]be a slope of 1,

0:04:05.420,0:04:07.260
given the numbers[br]in this example.

0:04:07.260,0:04:10.180
And the distance traveled[br]is the distance that

0:04:10.180,0:04:13.300
is the area under this[br]curve up to 78 seconds,

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because that's how long it[br]takes for it to take off.

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So the distance traveled is[br]this area right over here, which

0:04:19.700,0:04:22.630
we cover in another video, or[br]we give you the intuition of why

0:04:22.630,0:04:26.640
that works and why distance is[br]area under a velocity timeline.

0:04:26.640,0:04:31.350
But what an average velocity[br]is, is some velocity,

0:04:31.350,0:04:34.930
and in this case, it's exactly[br]right in between our final

0:04:34.930,0:04:36.700
and our initial[br]velocities, that if you

0:04:36.700,0:04:39.520
take that average velocity[br]for the same amount of time,

0:04:39.520,0:04:44.540
you would get the exact[br]same area under the curve,

0:04:44.540,0:04:47.060
or you would get the[br]exact same distance.

0:04:47.060,0:04:48.980
So our average[br]velocity is 39 meters

0:04:48.980,0:04:51.290
per second times 78 seconds.

0:04:51.290,0:04:55.640
And let's just get our[br]calculator out for this.

0:04:55.640,0:05:04.220
We have 39 times[br]78 gives us 3,042.

0:05:04.220,0:05:07.600
So this gives us 3,042.

0:05:07.600,0:05:10.010
And then meters per second[br]times second just leaves us

0:05:10.010,0:05:11.580
with meters.

0:05:11.580,0:05:16.030
So you need a runway[br]of over 3,000 meters

0:05:16.030,0:05:18.000
for one of these[br]suckers to take off,

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or over 3 kilometers, which is[br]like about 1.8 or 1.9 miles,

0:05:24.030,0:05:25.990
just for this guy[br]to take off, which

0:05:25.990,0:05:28.525
I think is pretty fascinating.