 Here we go velocity acceleration and displacement. We spent a lot of time in physics 11 Dealing with that in physics 12. We're gonna assume for the most part that you know it I'm gonna spend one day on it We're gonna be using it over and over and over all year long So the first thing acceleration we defined this last year as a change in velocity Over a time interval and those you that had me last year when I ask you what's changing anything you'll say to me. Oh What is change in anything? Nicole my angel for a candy Final minus initial you see in math notation we get this acceleration equals Change in velocity over time And since change in anything is final minus initial final minus initial do you remember that or do you just read it right there? Mmm We can also write it as this a equals Vf minus vi Over T for what it's worth Emily technically it should be change in velocity over change in time There should be a delta there to remember that from last year But time is always a change in and so we get a bit sloppy and we almost always in physics drop the delta in front of the T because it's just implied This wasn't how you saw it introduced to you last year we rewrote it as this we got the v final by itself Except we're gonna be fussy this year vector vector vector Direction is gonna matter this year Vf equals vi plus at On your formula sheet, but I'll be honest if you're a Good student you'll probably just end up memorizing this one because you use it so often this assumes Uniform or unchanging acceleration if you have changing acceleration you need calculus the math gets ugly Where is there changing acceleration? Brett space shuttle launches as the fuel burns What happens to the overall mass of the spacecraft as the fuel burns? Gets lighter even though the engines are still putting out the same amount of thrust They're having to move less mass the space spacecraft actually accelerate faster and faster and faster and it's beautiful yucky math If we have uniform Acceleration we also can find average speed which I'll sometimes write as the average But if you want the fancy math term and this is what is on your formula sheet the horizontal bar means average How do you find the average how do you find the average let's suppose Brianna has 10 bucks and Emily has 15 bucks What are the average between them? How'd you get 1250 Emily turns out the average is Add V final and V initial and divide by 2 That also implies something it implies Cara that if here is v initial and here is v final and you graph them The average will occur exactly halfway between them if your acceleration is uniform So if you accelerated a constant speed and you start out at 10 meters per second and You hit final 50 meters per second 10 plus 50 is 60 by 2 you hit 30 meters per second exactly halfway through Then we have distance in Physics in physics 10 and science 10 you define distance as average speed times time D equals vt This is before we did acceleration. This was science 10 However, I just told you that the average is This so I plugged it right into there. Is that okay so far? Oh one more thing though V final is v initial plus at so you know what I can replace this v final with right here The initial plus at we can write it like this D equals the initial plus at plus the initial All over to time t. Oh Here's what I see Zay One v initial plus one v initial. I think those are like terms. They're not the cleanest like terms But those are like terms Zay. Do you know what one v initial plus one v initial is I? Can rewrite this as two v initials Plus a t all over to Times t so far so good Mitchell So far so good. I'm gonna multiply the t on to everything Tancy word distribution Front door bomber if you had mr. Rock upper math never understood that one, but whatever it works D equals I'll get to the it Plus a t squared and this is over two and this is over two The whole thing's over two, but instead Kara. I just broke it up. I got a very good reason for doing this Kara look at this first fraction. What's two divided by two? Kayla I was going Kara. I'm sorry Kara there Kayla Kayla What's this first fraction two divided by two? What happens to the twos? And Over here. I have divided by two, but instead of dividing by two I'm gonna write that as multiplying by a half because this is where it comes from Vi t Plus one half a t squared D equals Vi t plus a half a t squared Kayla that's where it came from you don't need to know that I won't ask you to you know redo that on a test But usually I'll try and show you where stuff comes from because I think that helps you both remember and understand the physics so Remember that one from last year Trevor D equals Vi t plus a half a t squared almost all of you memorized it because you use it so often so Let's put that in box number three here on the next page D equals Vi t Plus one half a t squared Oh, except now Sean I need to be vector fussy. That's a vector. That's a vector and that's a vector How do you think I was gonna read that like? Come on Can't make the font much bigger go die The last of the four equations. We're going to use this unit is Awkward to derive right now. It actually pops out of work and energy in about two lines really really easily Comes from the fact that kinetic energy is a half and B squared So I'm not going to derive it right now. I'm just going to give it to you and it's this Vf squared equals Vi squared plus two a D and those are all vectors Although here the vectors end up not being quite as important because if you're squaring a negative often the negative vanishes Anyhow, but Do some examples now in physics 11 and in physics 12? I have two acronyms that I always use dope and defect Dope who had me last year. What does dope stand for do you remember? draw little Picture when in doubt dope You have word problem actually to do draw a picture and then defect was another acronym It was my approach and it stood for hey list your data Write down what you know find a formula that has everything And what you're looking for in it, but nothing else insert the numbers and Then crunch the answer. Well, I always say crunch the answer calculate I think was what my teacher used to say if I'm not sure what to do if I come to a new question my dolphin ID Usually it gets me through most of it So we're brushing off cobwebs from physics 11 example 1 a dragster has an acceleration of 18 meters per second squared Who remembers last year? What was 1g of acceleration? how big 9.8 this is not quite 2g's actually look this up dragsters have an acceleration of about this much I Know it's still at least from the internet. So I assume it's actually It begins from rest I Would almost always underline the word from rest because that tells me something very important. What does that tell me? Vi is zero how fast will the dragster be going after 2.1 seconds? So here's my question. What are they asking me to find in this question? first of all, I want to be careful Speed we're doing vectors and if you ever say velocity, I'm always going to say to you which one But this person said it correctly the first time I heard it back there Fine we're being asked to find the finals. So I write down that The reason I always write down what we're trying to find is I've learned over the years my question is no longer blank Brett I'm more relaxed. I'll do better. I've learned that with students over the years writing anything down always helps Now I'm going to defect I'm going to list my data So the first number as I read through here I see the number 18. Hopefully you clued in last year the value of Memorizing what units go with what because I don't actually look at the 18 I look at the meters per second squared and right away. What do I know that is Connor my friend 18 is what? You can write the units when you're deficking or not. I usually don't because I'm in a rush and on a test. I probably would it begins from rest Connor. What did this tell me? I'll write that down and Then I read through part a and what's this 2.1 Connor? Okay? So looking for an equation that has v final a v initial and t in it now in your homework When you get good at this Trevor I don't have a big issue if you jump straight to plugging in numbers on a test or on a quiz I will give you marks for writing out the correct formula Even if everything else is garbage so I'm going to build that habit into you in your notes And on a test and on a quiz. I'm going to always write out the formula. So I heard somebody mutter under their breath I'm pretty sure it's the final equals the initial plus a t which is going to be zero plus 18 times 2.1 18 times 2 is 36 18 times point one is 1.8 36 and 1.8 37 point eight someone want to check me Yes, I can do that in my head I grew up with other counts. Okay units meters per second. All right B How far will it have traveled after 2.1 seconds? Oh? by the way If you're looking for a rough guide as to how big your answer is If you double meters per second, it's roughly miles an hour And I'm assuming you've traveled to the states enough to know a little bit about miles per hour 60 miles an hour is 100 kilometers there. So doubling this It's about 80 miles an hour About 130 140 clicks give or take does that seem reasonable? Sure If I'd gotten 378 meters per second, and I doubled that to 600 miles an hour I'd be saying I don't think you go from zero to 600 in 2.1 seconds. So you can get a rough deal Brett, what's this asking me to find in part B? Mr. Redmond, huh? Got to be really fussy. It's not It is technically the displacement now having said that my big Sin my big mistake. I always mix up the words distance and displacement So I won't jump on you for doing that, but I'll put the vector here and go. Okay So now I have all my defect data listed right above me. I'm not gonna relist it I'm looking for an equation that has D and then some or all of these in it Don't all come up with the answer at once or anything Sorry, no, no, I want the equation. Let's try this again. Okay, right at the answer I'm looking for an equation that has D and some of these other stuff in it I have to assume you guys have forgotten everything Katie. I apologize if you haven't but I have I've learned over the years Go ahead You could use Vf squared equals Vi squared plus 2 a D. I would not you know why Because in using Vf, I'm using my previous answer to find the new answer I'll only use a Calculated answer to find the second answer if I have to because if I got a wrong, I'm getting B wrong I think there is also an equation that has D in it that doesn't use anything calculated And I think it has the D by itself already which one Darn right we can just straight plug-and-shuck D equals Vi T plus a half a T squared I would not take marks off if you use Vf squared equals Vi squared plus 2 a D I would say be a better test writer than that. What did we say Vi was? Whoo God So this is gonna be point five Times eighteen times two point one squared Katie, what's the answer? 39.7 is that two or three sig figs that I'm good with that units Yep Is that right by the way? Yes turn the page How see how long will it take the dragster to reach a velocity of 126 meters per second? Okay, what's this bad boy asking me to find Connor once you done yawning long isn't a variable on my formula sheet I Agree with that So I'll do that What else have they told oh this time they've given me this Connor. What's this? Which one I Agree That's not enough to solve anything. I have to use some other data from the previous page I think we're still assuming that the initial is zero. I think we're still assuming that the acceleration is 18 Is there an equation that has D VF Vi and a in it Connor say yes Okay Watch one and do me a favor once you find it in your head Rearrange it to get the T by itself if you can if you can't that's fine, but we're gonna push you this year Yeah, I don't have them. I don't they're not numbered It's just the first one we did the actual VF equals VF is 80. Is that one? Rewrite it get the T by itself T equals VF minus Vi over a I am totally good if you go straight to this line in fact, I strongly encourage you to go straight to that line and And VF is a hundred and twenty six minus zero divided by 18 126 divided by 18 while I can divide by top by two that's gonna be sixty three. Does it work out evenly? Is it seven point zero even? Yeah This would be wrong by the way How many sig figs? That's one. We said from now on this year two or three. So I'm gonna go seven point zero T time seconds How far will the dragster have traveled once it hits a hundred and fifty three meters per second? I think they're asking me to find a displacement. I think they've given me a hundred to three. That's V final 153 I think the initial is still zero Acceleration is 18 Brett this time. Do I know the time? This time I have to use an equation that has D VFA and I in it This is where I would use the VF squared equals VI squared plus 2 a D equation Except can you do me a favor Brett? Can you get the D by itself in your head and just rattle it off to me? D equals Something squared blah blah blah You do it. I know I'm asking you to do some math in your head first week of second week of school I think isn't it VF squared minus? VI square you'd minus the VI squared over and then you would divide by I Totally agree VF 153 squared minus VI zero squared all over two times 18 more than one number on the top and on the bottom better go with brackets 153 Squared minus zero square. I said I need to type that divided by two times 18 yet 650 Is that two or three sig figs that I'm good with it? Meters units this particular dragster has a top speed of 162 meters per second and then Dragster driver opens his parachute deploys the parachute It takes 12 seconds for the dragster to come to a stop What's its average acceleration reason? I wrote Brianna average acceleration. I don't think it's constant I think initially the faster you're going the more the parachute pulls But when you're nearly slowed down the parachute often I've watched on TV is length and not hardly pulling at all But let's assume it's constant average acceleration otherwise yucky man What's this question asking me to find actually two things? It's got kind of a part a and a part b. So I'm gonna go a little one for part one Andrew, what's the first part asking me to find a Equals question mark. All right, let's work our way back through here. What's this 162? Sorry, I Disagree I don't think it's vf. I Think it's v initial. You know how I know I know what v final is. You know what v final is in this question Even though they haven't told me ah Zero vi is gonna be a hundred and sixty two by the way Adam. Are we speeding up or slowing down? I did Andrew. Are we speeding up or slowing down Andrew? So should our acceleration be positive or negative if we do this, right? I'm expecting a negative answer here. If not, I'll be a little concerned. Oh, I see another number 12. What's that? I Agree Andrew do we have an equation that has acceleration vf vi and t in it? Yeah, can you rewrite that equation getting the a by itself and go a equals? Yep. Yep. I totally agree on the provincial and therefore on my tests You would get a mark just for writing down the correct equation So it's a great habit to get into and it's organized takes one second Andrew, what did you say vf was? I? Agree minus I agree Divided by 12 and oh good. That's gonna give me a negative answer. I have no idea what Bracket zero minus one sixty-two close bracket divided by 12 negative 13.5 Meters per second squared. Yeah. Yeah. Good good turn page. Let's talk about your tests Yo For a second half. Ah, wait a minute. It's a part two. How long do I have to travel? Thank you Thank you Andrew for pointing out my Negligence how long does it have to travel? I think now it's saying Now this is where English is bad because how long can refer to a time or it can refer to a displacement Do you think they want me to find the time here? Say no You know why? Because they told me the time here takes 12 seconds. I don't think that's the ant I don't think they want me to just write 12 seconds or we're done If I gave this to you on a test, I would rephrase this I would say how far does it have to travel before it comes to a stop and I may retype this I keep forgetting to and I do this every year note to sell So I think they want me to find a displacement Do I have all my data listed here, Nicole? Say yes, then I'm not gonna read defect. I got it all there All right, what equation hit? Sorry What equation can I use here? Better have a d in it. So I don't think I'm using vf equals vi plus at because that was like a d in it I don't think I'm using the average equals vi plus vf over two. I think I would use d equals vi T plus a half at square It's got the d by itself now the only issue here bread is that means I'm gonna use the a that I just calculated But I'm pretty sure I'm right and I maybe go back on a test to just double check I really want to make sure having said that on a test This is how I mark Brett Supposing you couldn't find the acceleration Supposing you couldn't do the first part, but you know how to do a second part if you wrote a note to me I can't find part a and you made up a reasonable acceleration you wrote assume a equals 19 meters per second squared and you solved it completely I would work out your answer to see if you did it right and I would give you full marks for part two I will always do that. Okay, the message is Never never ever leave a question blank Always write so so Brandon. We're gonna go like this D equals Vi t plus a half a t squared Vi is 162 Times 12 t plus a half a negative 13.5 12 squared Am I expecting a positive answer or a negative answer here? Which way are we traveling? Forward I think it's we're gonna get a positive answer. We're not traveling backwards yet. Jake. What'd you get? Oh? I thought you looked up cuz you were done Now what'd you get? Sorry, I don't think it's seconds cuz I don't think I'm finding T What am I finding? So what would the unit speed? Is it 972? if we're naughty D equals 972 meters No, ah 162 times 12 plus 0.5 times negative 13.5 Times 12 squared. There is some dissension. I'm getting 972 So if you got something do you get a bigger answer or a smaller answer? Smaller You put a negative there But no negative anywhere else right or you forgot the squared the two most common mistakes back at least once this year after a test You're gonna hear me say squared because about ten people wrote all the right stuff Forgot to do the squared and all got the same wrong answer and I'll notice the pattern when I'm marking it I'll come everyone keeps getting 17.1. That's not. Oh, don't tell me they forgot to hit the squared button on their calculators So don't do that Or Trevor I'll snap. I'll lose it. Can I turn the page now? Whoo-hoo. Let's turn the page You ready for your first shock? I Have based my tests in physics 12 on the used to be provincial that no longer exists And on the used to be provincial there was always listen up an essay question Emily's face just what? sort of the last question of every provincial was a Using principles of physics right to explain question. I Will be doing a bunch of those during the year with you Although I said essay you're gonna find I answer them with almost no English in fact often I'll do a good free body diagram or a couple of lines of work or My last line of defense is I'll make up reasonable numbers and just show that it works But on every one of your tests pretty much there is going to be a using principles of physics right to explain kind of a question Here is your first example of such a question Example three an object starts at rest and it accelerates east at a constant rate Accelerates in which direction Kara? I Have done this stupidly wrong so often as soon as they mention a compass direction I always in the margin draw a compass rose because the number of times I've done stuff wrong drives me crazy Takes one second. So there's my compass rose When it has traveled 10 meters it is moving at speed V check How fast will it be moving when it has traveled 20 meters? Select the best answer V More than 2v Exactly 2v less than 2v but more than V There's how we're going to do this You're going to vote Here's how you're going to vote if you're positive of the answer your hand goes up as high as you can In fact, if you're absolutely positive, you can even stand on your chair if you're fairly sure Not sure Only voting because if I don't vote mr. Duicle notice that I never move my hand and he'll make fun of me and I will Okay, positive all the way to And really haven't got a clue So read the question and you're going to pick a B C or D ready Who says a is the correct answer? Who says B is the correct answer? Z jumps on the bandwagon with Matt Who says C is the correct answer many Who says D is the correct answer? Mitch did you vote? So Everybody look at Mitch Mitch. Do you think a is the correct answer? You haven't voted yet Are you sure or only partly? Yes positive? Maybe not so sure. Okay? I'll catch if you don't vote usually. All right So now here's the here's the rule You can either attack someone else's answer and convince me that they're wrong or you can defend your own answer and convince Me that you're right attack or defend. What do you got? Someone convince me that they're right or that someone else is wrong day What did you pick? You pick D now. Oh you left Matt behind you think D is correct convince me so you wrote this down you said well Vf squared equals vi squared plus 2 a D. Okay Okay, so what Zay is saying I started to make up reasonable numbers, which is a valid approach. He said I'm gonna pretend speed V Which is the initial was what you say. Oh, okay, so you started out here and you said if we're Vi is zero did you get that? A by itself or what did you do now? Let's make up some reasonable numbers Let's say that at 10 meters The speed it was traveling at 10 meters was pick a nice number Emily five So at 10 meters Five meters per second. What was its acceleration? I Don't care. I Could make the acceleration whatever I wanted to by changing the time So I'm going to pretend that it was accelerating at a lovely two meters per second squared And I'm just going to now crunch some numbers and see what happens. Okay, so how fast was it going? after 10 meters five How fast would it be going? After 20 meters well, it would be going vi squared Plus two times what did I say the acceleration was just trying to make up a number to see what would happen? To and here's the key. How far has it traveled? Starting at 10 ending at 20. How far has it traveled? Traveled 10 meters from vi to via that. Okay type in the right-hand side on your calculator and then don't forget to square root if C is right You should get exactly 10. What do you get? Sorry You're jumping on Zay's bandwagon. What did they what did you go with D? Let's see squared plus two times two times ten equals square root Are we faster at 20 meters? Yes. Are we twice as fast? No Says explain your answer using appropriate principles of physics. I wrote this here. I Wrote this here, so I would write assume V at ten is five a is five meters per second squared V 20 equals what did we say using those numbers? 8.06 meters per second Nicole if we'd use different numbers we'd get a different answer, but I don't think we get exactly twice as big What a three dots in a triangle like that mean? It's an abbreviation for therefore feel free to use it. It's nerdy By the way, hopefully you went like this in your mind It's speeding up. It can't be the same speed says accelerating That's actually a fairly tough one Sometimes Kara I'll plug in reasonable numbers like we just and that's a great and a lot approach and a lot of you Won't get beyond that. I will try and do some of these algebraically because I'm a nerd as well example for Two cars are at rest facing each other 300 meters apart, but we don't want anybody to die So we're going to assume they're in separate lanes car one accelerates at six meters per second squared up to a maximum speed of 30 meters per second car two accelerates at five meters second squared up to a maximum speed of 35 meters second How long to take the cars to meet? Assumed they are in different lanes, so there is no crash This is actually a fairly tough question You did this last year calling it relative velocity But the only way you did it last year was we had both had the cars already at their top speed the fact that they're accelerating at different rates makes us a fairly yucky question because You'd have to figure out how long it takes this car to accelerate how much time passes How much time passes for this car to accelerate? How far this car is traveled how far this car is traveled? I've talked a long time and I can tell you guys are kind of zoning out So I'm actually going to say don't worry about this one. This was kind of like an advanced bonus one The nerd within me likes it, but that's okay. What's your homework on a separate piece of paper preferably you can do numero, huh? three Four five is good Eight because I've been on a slide before Okay, and you will notice the answers are in brackets I will do that almost all the time or they'll be attached at the end But I will almost never give you homework without the answers let you check your answers I have one more thing for you