Have you ever wondered how we are able to predict or calculate how high an object will go if I throw it into the sky? Or how far a car will go once I hit the brakes? Or how long it takes for a rocket to reach the sky? Well, that's where equations of motion come in. And today we're breaking down these powerful four equations step by step. Equations of motion are a set of formulas in physical sciences that describes how an object moves when they have a constant acceleration. and they connect four key quantities and we will discuss that in a second. We use these equations of motion to figure out how far an object goes, how long it takes, the speed or the acceleration with which it is traveling. These are the four equations of motion that we will be using. I will label each of these equations number one to number four. These are given to you on your data sheet or your formula sheet. But it's important to know what each variable in the equation means. So I first want you to notice that each formula has four different variables inside them. So for example, formula number one has VF, VI, acceleration and time. Formula number three has VF, VI, acceleration and displacement or distance. Each of these formulas have four variables and you should be familiar with these variables and what they are. So first of all, we've got VF which means final velocity in the context of equations of motion and the questions we will be covering. They can also refer to it as speed, the final speed. VI is initial velocity or speed. And for both of those variables, you know that you measure speed or velocity in meters/ second with a little negative one. Then a is acceleration and that unit is meters/s squared to a little -2. So remember acceleration is how is your velocity changing? Are you speeding up? Are you slowing down? Then of course we have displacement or change in position. This can also be referred to in our equation questions as distance or length. It's how far we are traveling. So that is the triangle X. And when we do vertical motion, up down motion. You will see this in grade 12. We swap out the triangle X for triangle Y. And the reason why is because obviously triangle X change in position in the X direction. That refers to horizontal mo movement. So think about along the X-axis. And change in Y is vertical movement. So along the Y-axis. And then last but definitely not least, we have time which is measured in seconds. Take note how I've put stars next to four of these variables. These are vectors. So if I refer to velocity, acceleration or displacement, those are vectors and you need to include a direction in your answer. However, if the question had to say calculate the final speed, you're still looking for VF. I know VF technically stands for final velocity, but it can also stand for final speed. And because speed is a scalar, we don't need a direction in our answer. But we'll get into that when we practice some questions. Now, how do you do questions requiring the use of equations of motion? My number one teacher tip for equations of motion is if you take a look at any of the equations of motion, you will see that each of them contain four unknown variables. So let's look at this equation for example. This is our first variable, second, third, and fourth. I know that there's a time here as well, but we've got time over here and time is repeated over here. So when we pick a equation of motion to use when answering a question, you want to make sure that you know three out of the four variables. So basically the fourth variable is your unknown and the other three you know it's given to you in the question. So the steps that will apply in this question is list your variables. So literally write out a list, choose the best suited equation based on what you have versus what you need. Always write the blank formula first. Substitute in get the answer and remember your units and your direction. So let's see a few. So over here I've got a car is traveling at 5 m/s and it starts to accelerate at 2 m/s squared for 3 seconds. What distance will the cover car cover in 3 seconds? So first of all, I've got the initial speed or initial velocity. So I've got vi is five. I've got the acceleration at 2 m/s squared. So acceleration is 2. And I've got the time is 3 seconds. I've got delta t. Triangle t. Remember triangle just means change in time. Change in time. So how did your time change? How many seconds past 3 seconds? What distance will the car cover in 3 seconds? Now although delta x generally stands for displacement or change in position essentially I'm still looking for delta x because that refers to a length a distance a displacement that's my unknown. So this is what I mean by step one read the question and list your variables. Then choose your best suited equation based on what you have. I have these three versus what I need. So see I have three out of the four variables. I'm looking for distance which is the fourth variable. Now yes you can maybe use this formula that doesn't give me distance. Some of my students say yeah but ma'am that will give me the final velocity and then I can use this one and then I can get distance. That is true but my advice is why use two formulas when you can use one. So the one that I would use because if you look at the list of things that I have been given the things that I have I don't have VF. So I'm going to try and avoid a formula that uses VF. So it won't be that one it won't be that one and it won't be this one. So based on what it looks like I have, this one seems to be the best option and it is. So write down your blank formula first. Writing that down gets you a mark. Then you substitute. So in the place of vi I put five. In the place of time I put three plus half. In the place of acceleration a I put two. And again in the place of time I put three. Don't forget to square it because my formula says I'm a square time. And I'm looking for the displacement. Very important. These variables vi and t they are squashed up next to each other which means we know that it's vi multiplied by t you know variables are squashed up next to each other in a formula it means multiplication then I may use my calculator and I get the distance to be 24 m now because I want distance and not displacement I just have to put a unit I don't have to put a direction so where do you get your marks formula substitution answer with units now what did I mean in number one where I said be careful of implied variable variables. In my second example, I have rocket powered sleds are used to test the human response to acceleration. If a rocket powered sled is accelerated to a speed of 444 m/s in 1.8 seconds, then what is the acceleration and what is the distance that the sled travels? I want you to pause the screen and see if you can try this first. Here are the formulas that you can choose from. Okay, so there's essentially two parts to this question. They're first asking me what is the acceleration and then what is the distance. So I'm going to do the first part first. But before I even get into that, let's list the variables. So they say a rocket powered sled is accelerated to a speed of 444 m/s. So what this means is, and I want you to think about it like this, they are accelerating this rocket powered sled. They want to test the response, human response to acceleration. So how quickly can humans respond to acceleration? So they're taking the slate and they're accelerating it to 444 m/s um in 1.8 seconds. So it takes 1.8 seconds for the slate to reach that speed. What is that 444? Is that vi VF or is it a I hope immediately you rule out acceleration because as you should know acceleration has a unit of m/s squared and they're actually asking me to calculate acceleration. So how can that be acceleration? So it's not acceleration. Where a lot of students go wrong is determining whether that is VI or VF because of how the question is phrased. They want you to to determine that 444 is in fact your final velocity. Then what would your initial velocity be? You have to assume that you're starting from rest. You're starting from a zero velocity from rest from not moving. And then it takes 1.8 seconds to allow the rocket to reach the rocket sled to reach 444 meters/s. And how long did it take? It took 1.8 seconds. So there there's the three variables that I know. That's what I know. What am I looking for? Well, firstly, acceleration and thereafter distance, which is delta x, triangle x. I'm going to look for acceleration first. So again, I'm going to try and pick a formula where I get the answer in one go. So I'm looking for acceleration. I've got VF, I've got VI, and I've got time. This one looks like a pretty good option. That's the one I'm going to go for. So you write your blank formula first, your naked formula, your empty formula because as you know that always gets you a mark. Then you substitute in the place of VF I've got 444. In the place of VI I've got zero. Acceleration is what I'm looking for. And time is 1.8 seconds. So acceleration is 246, 67 m/s squared. Now please take note that's the unit they want acceleration. And because acceleration is a vector, we know that we need a direction. So you can say in the positive direction or forwards. Now there's an interesting thing happening here because I still need to find distance. And technically this is all part of the same question. So if you want to use this acceleration answer to help us find distance in the next question, then please do not round off acceleration when using it to help me find distance because it's within the same question. So if they were to break up this question, let's say they call this 2.1, find the acceleration, then that's your answer over here. Round off, done. And then 2.2, find the distance. Then you may use the rounded off version because it's a new question. But here it's just one big old question. So if you're going to use acceleration to find distance, please use the non-rounded off version. So I'm going to find distance and I'm actually going to try and find it by avoiding acceleration. Is it possible? I think it is possible. So if you make use of this formula over here, you're looking for distance. So this is your unknown. That's your question mark. You know vi, you know vf, and you know time. So, I'm going to use this one because then I don't even need to use acceleration. So, my initial velocity is zero. My final velocity or speed is 444. I divide that by 2, close it in brackets, and the time that I take, 1.8 seconds, and that should give me the distance that my sled will travel and I get 399.60 m. I hope that this has been helpful. Please check out the very next video for more practice questions on equations of motion. Let's do it together. I'll see you there. Bye everybody. And subscribe if you haven't yet. I love adding more students to my YouTube family. Bye everybody.