2. 1D Motion / Kinematics

Kinematics Equations

# Kinematics Equations

Patrick Ford

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Hey, guys, you need to know how to solve motion problems involving in acceleration. So what I'm gonna do in this video is introduced you before equations of motion or sometimes called the Kinnah Matics equations that you absolutely need to know. But more importantly, I'm gonna show you when and how to use each one of these equations. So this is really important for you to learn practice and master because it sets the stage for the rest of physics. So let's check it out. So I remember for constant velocity, when the acceleration is equal to zero for motion problems, the only equation we could use is V equals Delta X over Delta T. We had another version of this equation that we called the position equation. But really, these two things were just two versions of the same equation. Well, a lot of times in physics you'll find that the acceleration is not zero. And in those cases you're gonna need form or equations called the Equations of motion or sometimes called cinematics equations or uniformly accelerated motion equations. Now, uniformly accelerated motion just means that the acceleration must be constant. And that's what you absolutely need to know about these equations. You can only use them when the accelerations constant. Now a lot of textbooks will show the derivations and the proofs and all that stuff, which you don't really need to know. But you should memorize them. So I have them listed in this table here. So we're gonna talk about each one of these equations. So it's over the first one, which is that VI equals vi not plus 80. This equation actually comes from an equation that were pretty familiar with. It comes from a acceleration average is equal to Delta V over Delta T. So you can manipulate this equation toe look like this in the same way we can manipulate the vehicles Delta X toe look like the position equation. It's the same idea. So we have the next one here, which is nothing really nothing special about it. V squared equals V not squared, plus to a Delta X. This third equation here have written in two different ways because you'll commonly see it written in those two different ways they look the exact same. The only difference is that this Delta X over here can sometimes remember it could be expanded and rewritten as X minus X initial, and they just move this thing to the other side. So again it means the same exact thing. You'll often see them sort of written interchangeably like that. So now the last one over here is Delta X equals V, not plus V over two times t. And this one has a little Astra's because in order to use this, I strongly recommend that you look at your ask your professors because some textbooks and professors might not allow you to use this. But basically what this equation says is this V Notch plus V is actually just the average of two velocities. So this is really saying here is Delta X is equal to the average times T, which we actually already know. Okay, so that's really it. So what? The important thing you need to know about these equations is that all of them have some combination of all of these five variables, and you need to know which equations have what variables in order to get the right answer. So let's go through each one of them really quickly. So we have V equals V not plus 80 So you have V, not A and T, but Delta X is missing some to write the little sad face there. Now we have V V, not A and and Delta X. So that means this is V V, not A and Delta X, but it's missing time. And now for these two equations for number three, whatever form you're using, this has Delta X has V, not T, and A So this is Delta X V, not T and A. But it's missing the final velocity. And now finally, we've got Delta X equals V not pose v times t s o. That means it has Delta X V, not SVT. But it's missing the acceleration. So notice that there's a pattern here. Every single one of these equations is missing. One of the variables except the only one that I have it all in common is the initial velocity. So, guys, what you need to know about these five variables here is that to solve any motion problem, whether it's a car or rocket or whatever it is with these equations, you're always going to need three out of the five variables to solve. So the whole game here. All these problems is figuring out which of these five variables you have in which three you can figure out in order to pick the right equation to get whatever you're missing. So in order to show you how that works, let's just go through this example. Together we have a racing car that is starting from rests. It accelerates constantly, which means that we're able to use the, um equations, which is good. We have 160 m track and the car crosses after eight seconds. We're gonna figure out what's the acceleration of the car. So all of these problems, we can always follow these list of steps to get the right answer. Basically, we're gonna start off by drawing the diagram and listing off our variables. It's a great visual way to figure out what we have and what we need. So you've got the initial velocity you're saying starts from rest. We got this car here, it's gonna travel, and it's gonna cross the finish line, and then it's gonna be moving. Uh, probably, you know, with some final velocity over here. So let's list off our variables. So start off with Delta X then we've got V knots. We've got V A and T now, basically, now that we've drawn and listed the five variables, let's just identify what we know and what our target is. We're told that the track is 160 m, so that's the length that's 160. The time is gonna be, uh, crosses the finish line after eight seconds. So that's the time that's t equals eight. And so what are we trying to find? We're trying to find the acceleration. So this is gonna be our target, Variable A. That's gonna be the question, mark. So that's what we've got here. But notice how we Onley end up with two out of the five variables. Now, whenever this happens, there's gonna be a clue inside of the problem that's going to give you that third one. So let's look at here. We have a racing car that starts from rest and accelerates constantly. So what you need to know there is from rest means that the initial velocity is equal to zero. It starts off with a V not of zero. So that's that third variable that you need so RV not is equal to zero, and now we have three out of five variables. So we're good to go. We can pick an equation. So now the next step here is we have to pick an equation without this ignored variable. So let's take a look what happened here. I was given three variables. Whether numbers or words in the problem, I'm asked for one of them, but this final velocity I have no information about its not asked, and it's not given. So this is called the ignored variable. Over here, it's a variable that has not asked for or given. And so whenever you are picking the equation, you have to pick the equation that contains the variable you're looking for. So, for instance, I'm gonna pick an equation that contains acceleration. But it excludes the ignored variable here. So basically, I'm gonna pick an equation that does not have V inside of it. So let's take a look at our list and figure out which equation that is. Well, the first one has V, so it's not gonna be that one second one says v squared. So it's not gonna be that one. The third one has a But it does not include V, which is good and just to be, you know, thorough. The fourth equation has v plus v not over to. So that's also bad. So notice how this always will give you just one equation to to use. So from this list here, we're gonna pick equation number three. Delta X is Vienna, T plus one half A T squared. So now let's just go ahead and fill out all the variables. So all the numbers we got 1 60 initial velocity zero times eight. So that just goes away. Plus one half. Now we have a you know, we have eight square notice How we're Onley ended up with one unknown variable. That's the acceleration. That's what we want. And then we just rearranging solve. So this one half goes to the other side. Eight square goes to the other side. So I have 160 times two divided by eight squared equals the acceleration. You go ahead and plug that in. What you're gonna get is 5 m per second squared. So that's our answer over here. Moving on to part B. So actually it was part a so part B. Now we're going to be looking for what? The cars velocity is at the finish line. So in other words, we're gonna be looking for what the final velocity is. This is actually the ignored variable in part A. So we're looking for the final velocity over here. You can go through the list of steps. We already have the diagram. We have the five variables. We actually know what this acceleration is Now. Now it's just equal to five target variables. V. So actually, there is no ignored variable anymore because we have four out of the five. That's what makes these problems easier is that as you continue to solve, you figure out more and more the variables. So really, we could start off with anyone of the equations, and the easiest one is gonna be the first one. So I'm looking for the final velocity. So I need V notes, plus a times t. I know V not. That's just equal to zero. I have the acceleration from the first part, and I have time. So I'm just gonna plug this stuff in really straightforward. I've got V equals zero plus and then I've got five from my acceleration and then eight seconds. So we end up with a final velocity of 40 m per second. Alright, guys. So that's it. We're gonna get a lot more practice with this. That's it for this one. Let me know if you have any questions.

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