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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

  • 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

  • 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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空中客車A380起飛距離|一維運動|物理學|可汗學院。 (Airbus A380 take-off distance | One-dimensional motion | Physics | Khan Academy)

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    楊凱翔 發佈於 2021 年 01 月 14 日
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