- [Voiceover] In the last video we figured out
that given a takeoff velocity of 280 kilometers per hour,
and if we have a positive value for any of these vectors,
we assume it's in the forward direction for the runway.
Given this takeoff velocity and a constant acceleration
of one meter per second, per second,
or one meter per second squared, we figured out
that it would take an Airbus A380
about 78 seconds
about 78 seconds to take off.
What I wanna figure out in this video is given all
of these numbers, how long of a runway does it need,
which is a very important question
if you wanna build a runway that can
at least allow Airbus A380s to take off,
and you probably want it to be a little bit longer
than that just in case it take a little bit longer
than expected to take off.
But what is the minimum length
of the runway
given these numbers?
So we wanna figure out the displacement,
or how far does this plane travel
as it is accelerating at one meter per second squared
to 280 kilometers per hour or to 78,
or where did I write it over here?
To 78, I converted it over,
right over here.
As it accelerates to 78 meters per second,
how much land does this thing cover?
So we can say,
so let's call this the displacement,
is going to be equal to,
so displacement is equal to
you can view it as velocity times time.
But the velocity here is changing,
if we just had a constant velocity for this entire time
we could just multiply that times however long
it's traveling and it would give us the displacement.
But here our velocity is changing.
But, lucky for us, we learned and I would encourage you
to watch the video,
the video on average velocity
for constant acceleration.
But if you have constant acceleration,
and that is what we are assuming,
that is what we are assuming in this example,
so if you assume that your acceleration is constant,
then you can come up with something
called an average velocity, and the average velocity,
if your acceleration is constant,
if and only if your acceleration is constant,
then your average velocity will be the average
of your final velocity and your initial velocity.
And so in this situation, what is our average velocity?
Well our average velocity
let's do it in meters per second
is going to be our final velocity, which is,
let me calculate it down here.
So our average velocity in this example,
velocity average in this example is going to be
our final velocity which is 78 meters per second,
plus our initial velocity.
Well, what's our initial velocity?
We're assuming we're starting at a standstill.
plus zero, all of that over two.
So our average velocity in this situation,
78 divided by two is 39 meters per second.
And the value of an average velocity
in this situation,
actually, average velocity in any situation,
but in this situation we can calculate it this way
but the value of an average velocity
is we can figure out our displacement
by multiplying our average velocity,
times the time that goes by.
Times the change in time.
So we know that the change in time is 78 seconds
we know our average velocity here is
39 meters per second,
just the average of zero and 78, 39 meters per second.
Another way to think about it
if you want to think about the distance traveled,
this plane is constantly accelerating.
So let me draw a little graph here.
This plane's velocity/time graph would look
something like this.
So that this is time, and this is velocity,
right over here.
This plane has a constant acceleration,
starting with zero velocity
has a constant acceleration.
This slope right here is constant acceleration,
it should actually be a slope of one,
given the numbers in this example,
and the distance traveled
is the area under this curve
up to 78 seconds,
'cause that's how long it takes for it to take off.
So the distance traveled is this area
right over here,
which we covered in another video,
or we give you the intuition of why that works,
and why distance is area under a velocity/ time line.
But what an average velocity is
is some velocity,
and in this case it's exactly right in between
our two, our final and our initial velocities,
that if you take that average velocity
for the same amount of time
you would get the exact same area
under the curve,
or you would get the exact same distance.
So our average velocity is 39 meters per second,
times 78 second, so this gives us
3,042 and then meters per second times second,
just leaves us with meters.
So you need a runway of 3000,
over 3000 meters for one of these suckers
to take off, or
over three kilometers, which is
like about 1.8 or 1.9 miles,
just for this guy to take off,
which I think is pretty fascinating.