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1. Physics – 1D Kinematics - Acceleration: Hey, Moosa here. All right, let's talk about acceleration. Acceleration. Okay, So acceleration commonly misused term in the real world, and it drives me nuts. So here's more gonna get into before we even explain the equation of the Unitarian. Acceleration does not mean velocity. Okay, I hear all the time, and this is in real life or on TV or sports. You hear all the time. People will say things like they are really high acceleration when they're really referring to their speed, or the object that's traveling really fast can have a really great acceleration. And you just kind of cross. Why're what you're thinking about in terms of whether or not what you're saying actually makes sense, Here's the deal. Acceleration is the rate of change of velocity. It's the ability to change the speed that is actually there. So something that has a high acceleration doesn't necessarily mean that it's actually going fast. And something that's going fast doesn't actually mean that has a high acceleration. Okay, so the best definition for acceleration is the rate of change of velocity so somewhat with that kind of means rate of change of velocity, so rate of change of anything is that sing divided by time rate of change in velocity. So your equation for acceleration he's going to be change in velocity over time. But I could say things down a lion rate of change and mass, for example. That would be the change in mass over time, the rate of change in dollar bills in my pocket and I could be the That would be the change in dollar bills in my pocket over time. So get that terminology down. Okay, Next, As we already said, acceleration does not mean velocity. Okay, Now they are connected. As we already said, his accelerations change of all super time, but they're not the same thing. Also, positive acceleration does not necessarily mean speeding up it can, but it doesn't mean it speeds up just because positive what to talk about with that positive means in a second and then connected to that negative acceleration also does not mean slows down. It can, But it doesn't always. So let's get into that directional stuff here because I haven't done that really yet in the videos, Um, now is probably the best time to do it. So when we talk about direction. A lot of times will refer to say, Um, up, down left, right. But those aren't the only directional information, so let's get into just straight up. Directional stiff doesn't necessarily have to do with acceleration specifically, but of course, we'll connect it. So I put in two columns. I'll explain what that means in a minute. So we have our traditional up and down and our rates and left. We also have our cardinal system north and Self East West. You've got, um, positive or negative. That's why separate of Muti Combs. Actually, these values already here are typically defined as the positive values. These here are typically defined as your negative values. Now it's not necessarily always true. I could easily just defined down as positive, and that would just mean up is negative. So really positive. Negative just means opposite. Typically, modern convention has this column over here are by default your positive values and this comb over here in your negative values are there are plenty of other directional information that we could go ahead and state we could say, forward and backward. We can say in your out. We can use our coordinate system like positive X, y and Z were negative. X y z Typically, when we talk about the coordinate system, we're talking about these crosshairs here you're up and Daniel vertical access on the pages . Your Y axes in your left and right horizontal is gonna be your ex. And then you're up and down into and out of the board here. 1/3 dimension that I can't draw would be my Z dimension for high school physics in college level physics. Introductory level physics A k p. We typically just speak with two dimensions, but you'll see, especially the AP class later on in the year. You will have to, um, include the third dimension there as well. Okay, structural information ISO way. Let's get back to acceleration before you get too proud of myself. When you rewrite that equation, I'm gonna toss this up in the corner. Over here. Acceleration is going to be changing velocity over time, so let's get into the units next. My units for acceleration will be a change in velocity over time. So a standard unit for velocity is the meter per second. So I'm dealing with a meter per second per my standing unit for time is a second, so meter per second per second ends up equaling a meter per second squared meter per second squared is your standard unit of acceleration Now. You can, of course, have other units of acceleration, like kilometer per hour per second. So as long as it's a velocity unit divided by a time unit, it is an acceleration. But your standard unit is the meter per second squared. Got it good now, continuing along the acceleration thought without getting into numbers. Yet Let's just talk about that directional stuff that I talked about before. When we have a object with positive acceleration. As I said earlier, it doesn't necessarily mean it's speeding up. It simply means the acceleration. Acting on it is in the positive direction. I'm simply just give use positive. I'm gonna go ahead and say that the right is positive. So let's say I have a object here. Maybe it's a car I don't know, but some sort of object. That experience is an acceleration to the right. Okay, what causes that acceleration that's gonna get down on the dynamics part of physics. That's where we get into forces. So for Now let's just assume that something is accelerating to the right now. If initially it started off with zero velocity, then indeed, this object will begin to speed up as it travels to the race. So if I were to write this object again later on, the same constant acceleration is acting on it. Now. We'll have a velocity vector to the right, and if I iterated again even later on same concept stars, I'm trying to make my arrows all the same size. My velocity vector now is larger because it's continue, not acceleration. It's continuing to experience that change in velocity. So every given second that this acceleration acts on it, the velocity will increase by that amount. So in this case, posit acceleration does mean increases in speed. Let's get an example where positive solution does not mean increases in speed. No, that one's marker. What was that reddish marker that does not like to wipe up? Doesn't well, so what say my object experiences an acceleration to the red still, but now, in the beginning, it's actually traveling to the left originally. Okay, so perhaps this vehicle or object or ball or person, whatever was traveling like this and then an acceleration started act against it. That acceleration could be the breaks. It could be, Ah, thing pushing on It could be, Ah, maybe a bungee cord pulling on It doesn't matter. Something is trying to get it to change in speed in the right word sense. So if I were to draw this object in their moment in time and for the sake of simplicity, because it's moving toe laughing, their draught over here make you one of my equation. Soy. Have some more room with these markers to out of the way. If I would eggs rawness again a little bit later on seem acceleration to the right. This velocity vector would still possibly be toe left, but smaller until eventually. Uh, it gets to zero Now, think about this. But not object is no longer moving there. As long was that thing that was causing acceleration doesn't decrease or disappear, should say at this spot in time it can still have a rightward acceleration posit acceleration with no velocity. And all that does mean that that posit acceleration is there technically ah, high value. While we have no velocity, it also understand that the magnitude of acceleration doesn't necessarily have to do with the magnitude of the speed itself. And again, in this example, we have the speed going to the Left Excel vision to the right. Up until now, we're talking about a decrease in speed. Now, let's say this was a bungee that was pulling this object to the right hands. It slowed down that acceleration. Still there at this spot, right? It's now gonna start to increase in speed, back in the sense so far to redraw this to get another moment in time. This way, I'll drive down here. So it's not on top of itself. The speed will start to increase and increase and continued anchors. So the whole time that acceleration was to the right. But the speed changed. Now I do want to put a little disclaimer out there. If this was a bungee cord, there's a good chance of high likely chance. Actually, that acceleration doesn't stay constant. So banjo was just example I'm giving you just so you can understand why there would be an acceleration that cause it to stop and go back to the right when I get into freefall and then eventually into elastic cables and whatnot. I'll explain that a little bit better. All right, a couple more examples, real quick. So what happens when I have? Let's say the object is traveling to the right and there's an acceleration to the left. What will happen here? So its velocity story explosions Philip. Yet this will decrease in speed. So this is best known of the deceleration. So we have a positive loss in a negative acceleration and that sense of decelerates when we have so it's just a different example. We have the velocity to the rate of acceleration to the right, all the positive. We're gonna get acceleration. So let's get increase in speed. Let's go back with another deceleration example. I have my velocity till lap, so it's going negative, and I'm gonna have my acceleration to the right, so it's gonna be positive. In this example. It is decelerating. Well, it's traveling to the left and then finally, I have my velocity toe left negative and my acceleration to the left negative. This example is increasing in speed. So Ah, good rule of thumb is if the acceleration vector is playing the opposite direction. The vector of the velocity vector than the speed will decrease. And if the acceleration vector is pointed in the same direction, is the velocity vector will increase in that particular direction. I hope that you get this. I hope that you've got signed down because understanding how sign works in terms of vectors is incredibly important, especially early on in physics. A couple more things I wanna drop down your way before we wrap this video up you A M stands for uniform accelerated motion. It's a fancy way of saying acceleration remains constant in high school physics or AP physics. Almost every single scenario other than maybe when we get to the elastic step, almost every single scenario will would be dealing with you am uniform accelerated motion. And again, it's where the acceleration is constant, so understand that constant could mean one of really two things. Technically, it's one of only one thing, but I want to break it down the two possibilities that could mean the A never changes, so let's say a is two meters per second squared. It will remain that way forever. Throughout the whole problems will still be two meters per second squared all way down the line, but it also could mean not no acceleration. Also, it could be a zero. So whilst the acceleration is zero and that's not changing their still constant, a lot of students kind of forget that that having an exhibition being constant doesn't mean that acceleration has to be something other than zero. It can be zero. So understand, if there is no acceleration acting on the object, it's still undergoing you. And the last thing I want to get into this is more like foreshadowing for dynamics down the line. Uh, can we possibly have an acceleration acting on an object if the velocity isn't changing? Can we have acceleration with No, I'm sorry. If the magnitude of velocity isn't changing, I e the value. So can an acceleration exist if the magnitude of the objects speed does not change, a lot of people want to say no. And then some of you are watching and you're kind of knowing notice. I'm leaning you into this. Probably realized answers, Yes, but you might be struggling and know how or why. And so the answer is yes, yes, there can be an acceleration without the magnitude of lossy changing and acid with the fact that vectors have one of two things. They have magnitude and direction. We can change the direction of an object without its magnitude changing. And this is actually the basics behind circular motion. If I haven't object trying to travel around in a circular path, naturally, it does not want to do this. Naturally, that object wants to go forward. So in order for it to turn in this circular path, something needs the bullet inward. And that is a centripetal acceleration that we're gonna get into in a couple of units, couple videos down the line. But if I were to draw this object again another moment in time, its velocity vector so far, the levels of the in this a its velocity vector. At this moment, time will be the same, but its point in a different direction. So there's something that's moving in that other direction. If we got rid of that acceleration, it would just shoot straight forward. We're not trouble. Your path. Okay, that's it for now. Next video. I'm gonna go through you am a little bit more. Break down the equations that you're gonna be using a little bit more and start to break into some numbers. Okay, That's it. Thank you.
2. Physics – 1D Kinematics - Uniform Accelerated Motion: no muscle here, Right? Stuck about you ate em. Or more specifically, the U AM equations. Remember you A m stands for uniform accelerated motion, which means the acceleration will stay constant and a given scenario again. Remember, Constant does not necessary mean something. It could also be zero. It just won't be changing. Uh, in Kinnah Matics. It's really helpful to identify when we're in a you A m situation because we've got these magical equations that we can use that will allow us to find every other equation. Let me write down the equations we know so far, and then I will break down the new ones. So so far, we've learned average velocity is changing displacement over time. That's one of my you a EMS. We've also learned acceleration is changing velocity over time. Now, that's technically you am, But we're gonna write it in a different format to help us in our future problems. I'm gonna come back to that in a second. I want to talk about this average velocity 12 before I move on and show you the other equations. Average velocity again means the average velocity, right? And so if we know the total distance traveled. Untold timer told displacement all the time we could find that average velocity. But there's another way to find average velocity. What if we know the syriza velocities throughout the motion? Let's say we know the glossy. In the beginning, we'll call that view one. We know the elastic. Later on, the two etcetera, etcetera we confined that average velocity by doing the average of anything, just like we do the average say to find our grade on average velocity is give me the sum of each thing that could do that whole Sigma V. But I'm just gonna say v one plus V two dot, dot dot divided by the number of things. So in this case, that too. So if I knew object started off a 10 meters per second and then traveled that 20 meters per second and I wanted to know the average velocity just at the two divided by two, that would be 15 meters per second average of 10 and 2015. I have three velocities given I say v one plus B two plus two B three now divide by three. So just like you could find the average of anything else. You can still find a use that same method to find the average velocity for V. So just this is kind of a new equation. It's more like a math new equation. I don't know if it's really new, but you could think of it as as new. Um, yeah. And then acceleration the other format that we see this in. And I just could come from next to each other because they're not really new equations is just rearranging this. We're gonna expand this delta out, remember, Just getting raised this on the story to side over here. Never. Delta V is change in velocity. Remember, Delta always means final minus initial. So go to save the F minus the I or V two minus V one or V four minus B one. Whatever it is the change in that particular velocity. So I'm gonna expand this equation out, Turn this into VF minus the eye over time. So acceleration is equal to VF minus V I over time. And then I'm gonna isolate the F because a lot of times we want to find our final velocity after accelerations been acting on it for a certain amount of time. So to do that, I'm gonna multiply both sides by my time, not gonna show you the steps and rearranging equations every single time. But early on, I will on and that'll maybe l rewrite this for you. And then all you reason rewriting this final format. So so far, we have eight times t well, equal VF minus V I and I gotta get rid of that red mark it eight times t equals V f minus of the I. I want to get the FBI itself. Zinoman Adv EI Edible Sides To show that my final velocities get equal to my initial velocity plus the product of the acceleration active Janek Times a time which that exception is acting on it. Let me raise this and then rewrite this because that's the important format right there. All right, cool. So so far we have one. We have to. I'm gonna introduce two more and again. Technically, we can call that this guy care. Third, we can even call it a closed all to be over TV. So two new ones change in distance is equal to my initial velocity. Times time plus 1/2 80 squared. I don't like that black market either. I got upgrade my markers and then we've got the F Square equals V I square plus to a delta d I could go and derive these equations for you. There really just combinations of these other equations. I'm not gonna go. If you do that, you're welcome to look it up or check it out in a textbook if you that is something that interests you. But for the sake of this lesson, I just want to talk about these two equations. This equation lets us determine the displacement and object has traveled. Notice that we don't know the final velocities. Here. We have initial velocity. We have time. We have acceleration. We don't have the final velocity. We could determine the displacement as long as we know its initial velocity, its acceleration in the amount of time acting on it. A couple things I want to point out. A lot of times will change these eyes, toe ones or the letter A just means the first velocity. Sometimes we even put a little circle there for not the original velocity down here. We'll see. The ABS can change two twos or bees, etcetera. There they want to point out. Here is this is plus 1/2 a T squared. But if the acceleration is negative, we do have to include that negative in the equation. So it'll end up subtracting this term. That should make sense because it in the beginning, if it wasn't accelerating in the negative sense its velocity will make a trouble. Agreed distance. But now, well, it's troubling this way. If there's something acting against it, it's gonna slow down. It's not to travel as far as it would have without that acceleration. Also, pay attention, this equation here, too, if a zero and and I'm not gonna cross it off for the sake of not one to rewrite it. But if it was zero, this whole term would be gone. And then we just be Delta D equals V. I t Now think about this. If I were to rearrange this for V, I, it would save EI is equal adult a D over tea or the velocity is equal to change in this place in overtime, and that is my original equation. Of course, this is average glossing. This is initial velocity, but in this example. It would be the same because there would be no acceleration acting on it. You don't mind really the same thing. We're just adding this extra bit. So if you're one that likes the memorize equations or if your teacher and move so makes you memorize some of these equations, you might want to just memorize this and realize that in the scenario in which there is no acceleration, it's this equation appear your call on. Then we've got this last bottom equating here. VF squared equals V. I squared, plus two a. Delta D Think about it. What's missing in this equation? Yeah, you'll see that there's no time variable here, and so that's there to allow that equation. Well, that was the cell for other variables without having the knowledge of time. So I keep referring to all these different variables. Turns out that there are basically five variables that you really ought to pay attention to any time you're dealing with enigmatic problem and these air known as the motion variables . We've talked about all of them already. I'm just gonna indicate them right now, So my motion variables, we've got time. We've got displacement. You've got my initial velocity, My final velocity and my acceleration Displacement is best written has dealt the deep We could expand this two d f minus D i or ex af minus x i or Y f minus x I Technically, maybe they're six motion variables, but more often than not, what we care about is that changing distance. Every now and again, we will have an initial value not at zero so expanded this into my final initial helps. We could also replace this with average, depending on if we know both of them or Delta the number average. The and Delta V were not the same thing. So you have to be smart about it. If you want to do that. Here's the thing. Here is the thing that you really need to understand the most about these about all of this stuff doing with you am equations as this. If you know three of any of these five, you can use these equations to find all the rest. So any single word problem that you do If you know three of those variables, you can find everything else. And guess what you're gonna know at least the variables. There's no way we're going to give you a problem that doesn't have at least three variables in it because it won't be something that you can complete. So when you read a problem, it might make sense. In fact, I encourage every single time you do a cinematic problem just right. Thes motion variables down and go through while you read it and see if you can identify these variables because all you need is how many one No. Two, no three of these variables to find every other one. This is genuinely that simple. Now, it might look like a lot of these equations air kind of overwhelming in a little intimidating. But in reality, you get these equations down and you remember these five variables and you identify these five variables. All you got to do now is find a proper equation that fits. Plug it in, solved. Got it. All right. I think that's it for the, um, equations. Next video. I will be going over a bunch of example problems. Check it out. Thank you.