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• 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 1

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

• we figured out that it would take an Airbus

• A380 about 78 seconds to take off.

• What I want to figure out in this video

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

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

• to 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 takes a little bit longer than expected

• to take off.

• But what is the minimum length of the runway

• given these numbers?

• So we want to figure out the displacement,

• or how far does this plane travel

• as it is accelerating at 1 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 right over here.

• As it accelerates to 78 meters per second,

• how much land does this thing cover?

• So let's call this, the displacement

• is going to be equal to-- So displacement

• is equal to-- You could 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

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

• the video on average velocity for constant acceleration--

• but if you have constant acceleration,

• and 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

• 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

• 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 0, all of that over 2.

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

• 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 the change in time is 78 seconds.

• We know our average velocity here

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

• 39 meters per second.

• Another way to think about it, if you want

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

• this plane has a constant acceleration

• starting with 0 velocity.

• It has a constant acceleration.

• This slope right here is constant acceleration.

• It should actually be a slope of 1,

• given the numbers in this example.

• And the distance traveled is the distance that

• is the area under this curve up to 78 seconds,

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

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

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

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

• But what an average velocity is, is some velocity,

• and in this case, it's exactly right in between 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 seconds.

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

• We have 39 times 78 gives us 3,042.

• So this gives us 3,042.

• And then meters per second times second just leaves us

• with meters.

• So you need a runway of over 3,000 meters

• for one of these suckers to take off,

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

• just for this guy to take off, which

• I think is pretty fascinating.

In the last video, we figured out

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# Airbus A380 take-off distance | One-dimensional motion | Physics | Khan Academy

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楊凱翔 posted on 2016/10/31
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