WEBVTT

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In the last video,
we figured out

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that given a takeoff velocity
of 280 kilometers per hour--

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and if we have a positive
value for any of these vectors,

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we assume it's in the forward
direction for the runway--

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given this takeoff velocity,
and a constant acceleration of 1

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meter per second per second,
or 1 meter per second squared,

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we figured out that it
would take an Airbus

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A380 about 78
seconds to take off.

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What I want to figure
out in this video

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is, given all of these
numbers, how long of a runaway

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does it need, which is a very
important question if you want

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to build a runway that
can at least allow

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Airbus A380s to take off.

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

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

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to take off.

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But what is the minimum
length of the runway

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given these numbers?

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So we want to figure
out the displacement,

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or how far does
this plane travel

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as it is accelerating at
1 meter per second squared

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to 280 kilometers per
hour, or to 78-- or where

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did I write it
over here-- to 78.

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I converted it right over here.

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As it accelerates to
78 meters per second,

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how much land does
this thing cover?

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So let's call this,
the displacement

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is going to be equal
to-- So displacement

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is equal to-- You could view
it as velocity times time.

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But the velocity
here is changing.

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

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we could just multiply
that times however

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

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But here our
velocity is changing.

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But lucky for us,
we learned-- and I

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encourage you to watch the video
on why distance, or actually

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the video on average velocity
for constant acceleration--

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but if you have
constant acceleration,

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and that is what we are
assuming in this example--

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so if you assume that your
acceleration is constant,

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then you can come
up with something

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called an average velocity.

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And the average velocity, if
your acceleration is constant,

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if and only if your
acceleration is constant, then

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your average velocity
will be the average

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of your final velocity
and your initial velocity.

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

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Well, our average
velocity-- let's

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do it in meters per
second-- is going

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

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down here.

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So our average velocity
in this example

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is going to be our
final velocity, which

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is 78 meters per second,
plus our initial velocity.

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Well, what's our
initial velocity?

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We're assuming we're
starting at a standstill.

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Plus 0, all of that over 2.

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

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is 39 meters per second.

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And the value of an average
velocity in this situation--

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actually, average velocity
in any situation--

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but in this situation, we
can calculate it this way.

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But the value of
an average velocity

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is we can figure
out our displacement

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by multiplying our average
velocity times the time that

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goes by, times the
change in time.

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So we know the change
in time is 78 seconds.

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We know our average
velocity here

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is 39 meters per second,
just the average of 0 and 78,

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39 meters per second.

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Another way to think
about it, if you want

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think about the
distance traveled,

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this plane is
constantly accelerating.

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So let me draw a
little graph here.

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This plane's velocity time graph
would look something like this.

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So if this is time and this
is velocity right over here,

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this plane has a
constant acceleration

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starting with 0 velocity.

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It has a constant acceleration.

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This slope right here is
constant acceleration.

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It should actually
be a slope of 1,

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given the numbers
in this example.

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And the distance traveled
is the distance that

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is the area under this
curve up to 78 seconds,

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

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

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we cover in another video, or
we give you the intuition of why

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that works and why distance is
area under a velocity timeline.

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But what an average velocity
is, is some velocity,

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and in this case, it's exactly
right in between our final

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and our initial
velocities, that if you

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take that average velocity
for the same amount of time,

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you would get the exact
same area under the curve,

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or you would get the
exact same distance.

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So our average
velocity is 39 meters

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per second times 78 seconds.

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And let's just get our
calculator out for this.

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We have 39 times
78 gives us 3,042.

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So this gives us 3,042.

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And then meters per second
times second just leaves us

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with meters.

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So you need a runway
of over 3,000 meters

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for one of these
suckers to take off,

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

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just for this guy
to take off, which

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I think is pretty fascinating.