- What is acceleration?
- Airbus A380 take-off time
- Airbus A380 take-off distance
- Why distance is area under velocity-time line
- What are velocity vs. time graphs?
- Acceleration vs. time graphs
- What are acceleration vs. time graphs?
- Acceleration and velocity
How long of a runway does an A380 need? Learn how to calculate the minimum runway length needed for an Airbus A380 to take off. This tutorial uses principles of constant acceleration and average velocity, demonstrating how these concepts apply to real-world physics. Created by Sal Khan.
Want to join the conversation?
- I don't understand when you say the plane doesn't move a full meter in the first second, rather a half meter. Could you please explain for me more in details. Thanks(13 votes)
- After 1 second it has accellerated to a velocity of 1 m/s. Because it is uniformly accelerating, it thus has moved slower than 1m/s during this first second. On average it has moved (starting velocity + final velocity)/2 which is (0+1)/2=1/2 m/s. Therefore in the first second it has moved 1/2 m.(30 votes)
- why is average velocity the half of the final velocity?(11 votes)
- Becouse initial velocity (when plane starts his movement) is 0, and final velocity (when plane take off) is 78 m/s. So to find average velosity we should sum initial and final velocity and divided it by 2 (becouse we have only 2 magnitude of velocity). If it was more magnitudes, for example 3, we sum all 3 magnitudes of velocity and divide it by 3. Sorry English not native language =) Hope it helps(22 votes)
- Can you please explain why we divide Vf-Vi by 2 to find the average velocity?
Don't we have to divide Vf-Vi by the total time it took to reach to Vf to find the average velocity?(8 votes)
- Let's say that you have something starting at 0 m/s and slowly accelerated so that in 1000 seconds it is going 10 m/s. What seems like a more reasonable average velocity 5 m/s (Vf-Vi/2) or 0.01 m/s (Vf-Vi/1000)?(5 votes)
- If displacement= velocity*time,i.e, 78*78. why is the velocity halved?(5 votes)
- Displacement = AVERAGE velocity * time.
FINAL velocity is halved in order to get average velocity (if initial is 0)(5 votes)
- if acceleration is not constant then what should we do?(3 votes)
- I saw the velocity-time slope is constant and it didn't become steeper or lower. Doesn't it mean that the acceleration is 0? I don't know why it is 1m/s^2(3 votes)
- The slope of a velocity vs time graph being constant only means that the acceleration is constant not that it is 0. The slope of a velocity vs time graph is the acceleration so if the slope is 0 then the acceleration is 0 but if the slope is not 0 them neither is the acceleration.(5 votes)
- Where is the first video? where we calculate the 78 seconds answer(3 votes)
- It's the last video in this Unit and Lesson. In Physics Library inside the science library, you go to unit 1 lesson 3. There should be the video "Airbus A380 take-off time." That should be the video.
This is the youtube video:
- Where did you get the two(3 votes)
- Couldn't you just times ( d= t x v ) and divide by 2 to get the average?
For example: (78 seconds * 78 m/s) = (6084 / 2) = 3042(2 votes)
- But how can area under the curve be equal to distance?How come area is equal to distance?(1 vote)
- look at the units. The units of this "area" are speed (on the y axis) and time (on x axis.
So this "area" does not have the units of usual area (ie m>2)
But it has the uniits m/s x s = m
ie it has the units of distance.
maybe dont think about it as area in the normal way, but as a tool for calculating distance.
you could call it the 'zone below the curve' for example. :)
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.