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Current time:0:00Total duration:5:29

Video transcript

in the last video we figured out that given a takeoff velocity of 280 km/h 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 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 runway 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 given these numbers so we want to figure out the displacement or how how much how far does this plane travel as it's accelerating at 1 meter per second squared to 280 kilometers per hour or 278 or where did I write it over here 278 I converted it over right over here as it accelerates to 78 meters 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 could view it as velocity times time but we the velocity here is changing so we don't have just if we just had a constant velocity for this entire time we could just multiply that times however long is 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 why it well actually the video on average velocity for constant acceleration but if if you have constant acceleration and that is what we are assuming that is what we are assuming in this in this example so we're if we 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 if we have a you know in this situation actually a verge félicité any in any situation but in this situation we can calculate this way but the value of an average velocity is we can figure out our displacement by multiplying our average velocity by multiplying our average velocity times the time that 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 39 meters per second just the average of 0 and 78 39 meters per second another way to think about it that if you want think about the distance traveled this plane is constantly accelerating so let me draw a little graph here this plane this planes 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 zero velocity has a constant acceleration this slope right here is it's constant acceleration it should actually be a slope of 1 given the numbers in this example and the distance traveled is the distance that it 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 time line but what an average velocity is is some 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 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 so get our calculator out we have 39 times 78 78 gives us three thousand 42 so this gives us three thousand 42 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 is pretty fascinating