 Hello, my name is Brad Langdill and I want to talk to you about algebra, which is so important if you're doing physics, you're going to have to have some basic algebra skills to even get started. So let's review some of those things you should have picked up back in your introductory class of physics, maybe Science 10 if you're in Alberta. A couple of things we're going to look at, basic rules of algebra, opposite operations undo. What you do to one side you've got to do to the other side as well. So I want to go through some questions from a document I give my kids, it's that algebra review, it's on the website www.ldindustries.ca. Let's try a couple of problems. We've got v equals d over t is our formula. I'm telling you that v here is 20 meters per second. I'm not going to put in the 20.00, but I am going to put in the units. You're going to see why here a little bit later on. I'm told that my displacement is 45 meters and we're asked to solve for the time, this variable in the denominator. So how are we going to get that time by itself? We're going to use an opposite operation. This is 45 divided by t, so I'm going to do the opposite. I'm going to multiply by t. And what I do to one side I'm going to do to the other. The reason I'm multiplying by t is because that t on the top and the bottom will now cancel out on the right hand side. All I've got left is 45 meters. And on the other side I'll have t multiplied by 20 meters. Now that might not seem like it did anything. You didn't get t by itself. Well, it's okay. You can get rid of the 20 meters per second by dividing both sides by 20. The reason we're choosing division here is because this is t multiplied by 20. So I have to divide by 20 to move it to the other side and cancel it out. And what's left over here is a t on the left and on the right 45 meters divided by 20 meters per second. Now why did I leave those units in there? Well, look, you can use this as a check. A meter divided by a meter per second is equivalent to a second. That's what's left over when you cancel those out. And because time is measured in seconds, you can be sure that you did this properly. So I type in my calculator 45 over 20 and I'm getting 2.25 meters, 2.25 seconds. That'll be 2.3 seconds to significant digits. So here's our first one solved. Now you know what, check out what we actually just did here. The only thing we really did, if you want to see the shortcut, is we just took the velocity, that variable that was on the left-hand side in the numerator, and it just switched places with the variable and the denominator on the right-hand side. That's all that happened. So you can use that as a shortcut if you like. I guess if you use the shortcut, hopefully you understand the algebra behind where it came from, so that you're not just cheating your way through. But this is certainly a little faster than going and showing all those steps. All right, let's take a look at the next one. We've got the accelerated motion formula. Acceleration is final velocity minus initial velocity divided by time. By the way, you don't have to know what any of these variables mean to do the math. It can be anything you want. We're just worry about the math here, really, not the physics. 23 meters per second is my acceleration. My final velocity was given as 5.2 meters per second. I'm trying to find the initial velocity and the time is 1.5 seconds. So it's a lot like the last one. I'm going to start off by getting rid of this 1.5 seconds. And to do that, I'll multiply both sides by 1.5. That'll cancel out the 1.5 seconds on the right. And on the left, that'll give me a value of, check on the calculator here, 34.5. Now let's think about our units. We have a meter per second squared multiplied by a second. One of the seconds will cancel out with one of the seconds. So we're left with a meter per second as our unit here. If you're not sure about the unit conversions at this point or the canceling out, not a big deal if you're still getting the steps, that's fine. All right, now we got to get this VI by itself. There's a few ways you can do it, but here's the way I think this is easiest. Again, just opposite operations, I'm going to subtract 5.2 meters per second from both sides. So that's going to give me, on the left, 34.5 minus 5.2 is 29.3, and the units again are meters per second. Now here's the thing, don't forget about what you have left over on the right-hand side. You don't just have a VI, you have a negative VI. And that's actually important because you want to solve for what positive VI is. You've got a negative one more time with the opposite operations. What I'm going to do here is you can do it two ways. You can think of this as either multiplying by negative one, or if you're thinking opposite operations, divide by negative one. Either way you do it, whether you divide by negative one or multiply by negative one, you're essentially just going to switch the sign on whatever you had on both sides. I'm going to get 29 meters per second to two significant digits. So all I did was basically take the negative sign off this side, move it over there in that last step. You don't only do that in the last step, don't do that earlier. Okay, so there's number one and number four. I want to show you two more here. Here's a little bit more complicated of a formula, but again I'm going to substitute in, including my units. I've got the displacement. I'm looking for the initial velocity. I'm told the time, which is 12.5 seconds, plus one half of the acceleration, which is 13.55 meters per second. Meters per second squared. Multiply by the time again. Okay, so I'll put that time in again, and it's squared. All right, now this looks pretty intimidating, but it's not too bad. The first thing I'm going to do is I'm just going to evaluate what this term is. This is all one term, all one number, that I can simplify down and make it look a lot prettier. So one half, 4.5 times 13.55 times 12.5 squared. That whole term is about 1058.6. Now I'm going to leave it as just 1058.6 on my page, but I'll keep that number in the calculator. And if you keep in track, actually what we have here now is a meters, is the unit. The second squared canceled with the second squared. Okay, that's equal to 30 meters equals Vi times 12.5 seconds. All right, now I need to keep getting that Vi by itself. So I'm going to subtract 1058.6 meters from both sides. So 30 minus that number that I had there. So I can either just type it in again or if you push second answer in the TIED model calculators, the answer will be whatever was in the last line. So this is 30 minus that number, which is negative 1029 about. So I'm going to write negative 1029. Still meters is initial velocity times 12.5 seconds. And again, opposite operations. Now I'll divide by 12.5 seconds. So the initial velocity is whatever that number there was divided by 12.5. So I'm getting negative 83. Well, I guess it doesn't round 82 meters per second. Well, of course, we want three sig digs. So I guess I'd say 82.3 meters per second. So there's one that's a few more steps, but the basic idea is the same. We're just using those opposite operations. I hope that was helpful for you. If you have more questions on algebra, definitely check out the website. There's more resources there at www.ledindustries.ca.