 Hey everybody, welcome to Tutor Terrific. Here we're looking at our fourth lesson of our unit two on physics in my physics course and this lesson we're gonna be using the big three kinematic equations in one dimension in some complicated problems more complicated than we saw in our last lesson for sure Where these problems and these equations would be very useful to you. All right So how do we use these a lot of students know them, but they don't know how to use them because they don't know where to start Well, let me explain you see the problem in front of you You don't see it here But let's say you have a problem in front of you You know that you have these big three equations and this little runt here, which is a version of the second equation If you acceleration happens to be zero these equations by the way Do not forget that they are used only when a is a constant You cannot use them when you have variable acceleration values throughout your trajectory like would be in the real world But this is a simplification to sort of teach you like we do in physics all the time how to do things So back to the question. How do we use these to solve problems? Where do we begin? Well, when you have the problem in front of you I want you to start by writing down all the quantities Given to you in the problem in a list You make a list like this given and you write down or sometimes we say known quantities I say given and you write down under here all of those Quantities and their values with units, okay? Then you write down the quantity Usually just one for the easier problems, but maybe more than one that the problem asks for in another list And we call that wanted and I list those down here with values and units And I make a note of other unknown quantities not asked for in the problem under this wanted list I know they're not technically wanted But I still make a list of everything unknown under here and I usually circle or box the one that is actually asked for by the problem or the part of the problem and then Once you have that down, it's much easier to figure out the roadmap Of which equations can be used and in what order to get the values for the desired quantities Usually for easier problems, you would just pick an equation that has all the given info in it plus just one Unknown quantity so you've got all the other variables known and one unknown so you can actually solve it and you'll For example, if I had the final velocity the initial velocity and the time for the trajectory I would and I was asked for acceleration I would certainly use the first equation because I know three of the four quantities in it That's an example of a roadmap really It's just a decision that you make which will allow you to use math properly to solve for an unknown quantity For easy problems, it will be the quantity asked for for harder problems That you might have to use one equation to get something you need in another equation to solve for a desired quantity. That's common We're going to start with some easier problems though in this lesson So we have a car that accelerates from 13 meters per second to 25 meters per second in six seconds flat What was his acceleration assuming it's constant we have to assume that in all of these problems? So that's the problem you have it in front of you now. Let's make a List of given quantities, okay? I'm given the initial Velocity 13 meters per second. I'm given the final velocity 25 meters per second. How do I know those are vf and v not well the wording of the problem and the units of the value Okay, accelerates from this meters per second to this meters per second meters per second is reserved in these big three For the V's for the velocities, so we know that when we say from a certain velocity That means that's the starting velocity v not and when it says to another velocity We know it's the final velocity vf. Okay 6.0 seconds. What would that be? That would be t the time, okay? So those are the things we are given so we're going to put them in the given list like this 25 meters per second for final velocity You might notice a difference here between my V and this vf Identity don't need to see the necessity for the final because the initial has its own subscript that Distinguishes it so but you can use it if you'd like it's not necessary These are the three things the three things that were given. Okay, what do we want it? We're wanted to provide the acceleration value now I'm going to also make note of the quantities that we also don't know and we might not need but we could need to solve them Perhaps to get to the a and that would be the initial position and the final position X not an X we were not given any of that information at all as far as how far it traveled Doesn't look like we're asked for that. It's we're really asked for the acceleration. So I boxed it here now the roadmap which equation involves these three known quantities and The unknown quantity we desire v v not t and a well the first one The first one in the list does that okay? So we will plug in now after we solve for a these three known quantities Okay, so here's what that looks like solving for a first to avoid any sort of complications by putting numbers in there That's what I recommend We solve for a first by subtracting the v not to the other side So we get this then we will divide both sides by t and then we'll get this aha So I'm this is physics guys Most physics classes in high school require some facility with algebra Some require Algebra 2 to be passed before you take it So I'm assuming you have some good facility and algebra with plain old variables So now a is solved for so we will plug in the three quantities at this point a will be vf minus v not Over t 25 meters per second minus 13 meters per second over six seconds now with proper sig figs You get 2.0 meters per second okay when you do your rounding properly and I've circled that so I am Communicating that that is my final result. Oh, so it takes Oh, and that would be the improper units there So I'll put a squared there 2.0 meters per second squared is the acceleration All right, let's look at another problem. Okay, this is a two-part problem It doesn't necessarily mean it's harder just means it's gonna take more time than a problem that asks for one thing Let's say in this problem is being asked to design an airport For small planes. Okay, it's an engineering problem civil engineering question one kind of airplane that might use this airfield much reaches speed of Before takeoff of at least 27.8 meters per second Okay, it can lift off with a good 27.8 meters per second and the plane can only accelerate at 2.0 meters per second squared Part a says if the runway is 150 meters long can this airplane reach through a square the required speed for takeoff You might think wait well it it said it could reach that no it said that this plane needs to reach that Can it do it if the runway is 150 meters long if it can only accelerate at this? Acceleration value that's what the question is asking so the road map Might be a little tricky at first because that's we need our given and wanted Tables and so we have those here are given or our known values are the initial position of zero now How do how do I know that? Well whenever I'm given a length of my trajectory? Which would be the plane accelerating on the the airway the airstrip? I can always assume that the initial position is zero and the final position is a hundred and fifty And so that's exactly what's been done here zero for x not and 150 meters for x final, okay? Also If an airplane is taking off it is assumed that it starts at rest because well It has to taxi to the runway and wait its turn and then it can start accelerating So it's going to be at rest right as soon as the takeoff begins So zero meters per second for v not we do not know the final speed that this plane Can reach in a hundred and fifty meters, but we do know its acceleration that it's capable of 2.0 Meters per second squared now it could have a smaller acceleration Well, we're going to use the maximum acceleration because of this the nature of the question Can this plane reach the required speed that lets us know that maybe this runways too short So we're going to use that maximum acceleration in this problem, and we're going to find v so which equation? allows us in this set to Find v given the known quantities here, okay? The third one does and that's because We don't have any time information so time would be another unknown quantity you to include in the wanted list And I don't know it And so I can't use either of the first two equations right now because t is another unknown variable By the way, the second equation would be useless to us for another reason our wanted value v final is not in it And so we would stay away from that anyway, so we're going to use the third equation Okay, it's one equation that can get us our answer right away So our goal right now is to solve for the final v luckily it's already on its own It's already isolated all we have to do is square root the other side to get the values Now let me show you how things can get kind of messy when you plug in your values before you finish solving I've got v squared over here, and I'm going to start plugging in the other values over here now if you look all the units are A little crazy, okay, and so when I multiply them together I get meter squared per second square now for some people That's kind of Stressful, and they've never seen that unit before they don't know or can't remember that it relates to v squared So I always solve for the the quantity first in variable format before I plug things in to reduce complications, but let's look here at how they plug things in zero for v naught understood and Two is just in the equation and the a is acceleration. They didn't Type that second zero, which is a significant figure in this problem Not sure why but that's what was done and then times a hundred and fifty meters, okay? Which gives us six hundred meter square per second square We have to take the square root of that and we will get twenty four point five meters per second now technically We'd have to write twenty five meters per second, but Because we don't have a decimal after that one fifty however Most books and most texts and most teachers allow you to be off by one or two sick figs I'm not so good at good on that, but that's what we can find in most textbooks now This is not our answer. Okay, our answer was a yes or our question was yes or no Can this plane reach the required speed for takeoff it can reach twenty four point five meters per second? It requires twenty seven point eight meters per second to be able to lift off So no it cannot take off from this runway So part B asks well, okay, then what is the minimum length the runway must have? Okay, so now we're gonna we're gonna modify for this different question our known and wanted table because now we're asked for a length meaning a new x final, okay, and We are told that when we do this The final velocity will be twenty seven point eight meters per second. We're gonna set our Velocity that we know To twenty seven point eight meters per second We're gonna set the unknown to our final x because it's a totally different type of question so I modified my table now and My known quantity is my final velocity and everything else is already the same and my wanted is x the final Distance the final displacement of the plane before it takes off, okay, so we're gonna find the proper displacement now Which equation allows us to do this? Well as you could see time is still not involved and All the normal well all the part a variables even though they're switched around are involved in this table So it means we will still use the third equation the third time independent equation But we will solve for x final this time So algebraically we would have to subtract v not squared to the other side and then divide by 2a And that's what we have here What we can do though is we can leave the x not here because it's zero It can be completely ignored because it's zero, okay? And also another way to look at this is x minus x not would be the displacement or the length of the runway So when we plug in our velocities final minus initial And make sure you square them in this equation Divided by two times the acceleration we would get 193 meters so we could see that this run we needed to be almost 200 meters long to accommodate this plane All right last Simple problem in this set of questions on this lesson How long does it take a car to cross a 30 meter wide intersection? After the light turns green if the car decelerates from rest at a constant two meters per second seems like that is the acceleration of the day, okay? We are looking at a question. That's asking us How long okay? How long is different than how far? Okay? How long is about time? So just keep that in mind. Let's take a minute to make our list of given and wanted quantities first, okay? Here's our equations always put those on the screen for you, but let's make our given and wanted list to begin Okay, so we're given the length of the intersection, okay? 30 meters so it means the initial position is zero meters and the final position is 30, okay? So you'll see that right here also Car to cross an infrared section after the light turns green if the car accelerates from rest when you see the word from rest That means your initial velocity is zero meters per second zero meters per second Then it gives us the acceleration 2.0 meters per second squared like this, okay? So there's our acceleration now. What do we want to define how long so we're wanting the time? So the time is unknown and it is desired There's something else. We don't know and that's would be the final velocity But I'm going to leave that alone right now and ask you which equation Would allow us to find t given this information x not x V not and a We want t that would be the second equation the second equation allows us to find that Time but as you can see this equation is quadratic in time It has a constant a t to the first power term and a t to the second power term So some people might be worried that they have to factor it or I'll have to use the quadratic formula fear not There are two zeros that we can plug in the initial velocity is zero So the second term becomes zero and the initial position is zero So the first term is zero as well So this is still quadratic, but all the lower order terms are gone So watch what happens when I solve for t We start with here We've got x equals one half a t squared without the zeros Then we will continue to solve for t by multiplying both sides by two to get rid of that one half and Dividing both sides by a so it's 2x over a over here and just a t squared by itself Then the last thing to do is just square root both sides And then we get t equals the square root of 2x over a ah now Let's plug in the known quantity see how much easier it is to plug in stuff when you solve for variables first As long as you plug in zeros and cancel out any terms that are zero things become very very simple Now we could just plug in chug as my chemistry teacher long ago once said I keep that traditional We're going to plug in chug here 2 times 30.0 meters for x Divided by a 2.0 meters per second squared gives us a time of 5.48 seconds we look back at our initial quantities. We're doing dividing we can have three sig figs Perfect, so that's the time it takes to get through this intersection Now you can always check your work on all your problems If you wanted to do that if you had time on a test for example, all you do is take your answer and plug it back in To check and make sure you get the other given quantities back so one example would be to plug things in to Get the final velocity so we could plug it into the first equation and get the final velocity 10.96 meters per second, which is another unknown and Then we can find the final distance And check that it's equal to 30 like that the problem gave us in the first place x equals x naught plus v naught t assuming an average velocity there That's the runt down here Assuming there is no change in velocity. You would have to do an average velocity since we know it changes Which would be one half times the two velocities Some together that would give us the average and you get exactly 30 meters when you do that That's one way to check your answer. There's many ways But always check to make sure your answer is reasonable just by looking at the value. Okay, so Five and a half seconds. That's about how long this takes that seems rather slow But 30 meters wide is a decent size intersection What's really slow about this is the acceleration most cars do accelerate faster than that That's like a really slow like a like a semi or something So that's doesn't seem super reasonable But if you got point one second for example or a hundred seconds you'd think okay That's not reasonable at all. Then you'd have to go back and check your work Okay, so those are the two ways you can check your work on these types of problems All right guys. Thanks for watching this video the final lesson five is coming next for now. This is Falconator signing out