[ MUSIC PLAYING] This is a PVC tube about2. 5 meters in portion. Inside of it is aping-pong ball on one intent. We turned on a vacuumpump, which proceeds to suck out most of the breath. When that happens, the pipeis now a potential cannon. But how? Because we can puncturethe thin polyester encompassing, and all the pressureof the entire atmosphere will push the breath in andaccelerate the ping-pong ball.From merely this footage, can I figure out how fast the ping pongball shot out the end? Hello, I’m Dianna Cowern, developer of the YouTube channel Physics Girl, and welcome to lesson one ofDianna’s Intro Physics Class, also known as APPhysics One Review, also knownas Physics by Dianna. Today’s instruction? Kinematics. I requested a friend todefine kinematics, and he approximated that it wasthe motion of the human body. He was close. Kinematics is the physicsof action in general– how things move; not just humans. So that’s what weare doing today. So you can probably guess, kinematics is most important if you’re trying to move throughthe world without getting hurt. So today’s theme is to besafe or not to be safe. But picture don’t tell, they say, so let’s establish what kinematics by jumpingright into a question, which is, can you design a safe– can you design asafer bike helmet? I could have utilized thatearlier this week.To work up to the tools we need, the work requires numerical modeling. And so we begin ourmathematical modeling section.[ LAUGHTER] Here’s a simple scenario, a person mountain biking on a flat road .[ LAUGHTER] That does not look like a motorcycle. Let’s yield her some fuzz. Oh, geez .[ BIKE BELL RINGS] She’s going 10 rhythms a second. She’s a terribly steady, safe cyclist, which I predict is a nicething to say about person, person abiding. Side note here about units.You’re probably used to goingmiles or kilometres per hour , not meters per second. But the math is a loteasier in metric units, so there’s a reallysimple alteration, whatever it is you simply doubleyour rhythms per second, and you get miles per hour. So 10 meters per second isabout 20 km / hour. You can check that on Google. It’s not precise, butit’s pretty close. OK, our cyclist, shecould start anywhere, but we’re going to start herhere at slot equals zero. And we’ve shortened herto a stage corpuscle. Yeah, physicists do that a great deal. A second later, she’sgone another 10 rhythms. This is my time, andthis is my position. A second last-minute, another 10 meters.A second later, another1 0 rhythms. The graphwould look like this, where my horizontal axisis time, and my vertical axis isher position in meters. There she is. We’ve made a simple mathematicalmodel of her motion. Pause everything. Now is a key wonderfulmoment, because this isour first solid pattern of what we meanby numerical pattern. That’s what we talkedabout in the intro video to this whole class, the fact that physic determines numerical frameworks. And if you’re going, um, what? There’s no math now, I’m goingto say, what you talking about? Because math isn’t justxs and ys, three plus two equals six, whichisn’t even true.Just checking if you allare paying attention. Graphing is math. Geometry is math. OK, a graph is reallypowerful, because you can use it to predict the future. No joke. Predicting the future is waycommon in physic, like this. I depicted a linethrough these points. I can see where mymountain biker is going to be after six seconds. This strand predictsthe future for as long as she maintains leading thatdirection at the same speed. But let’s talk a littlebit about what a framework is and what it is not. It is a simplifiedrepresentation of what actually happened. Remember the stage corpuscle? That was a simplifiedrepresentation. Take, for example, cracking a wineglass with your expression, which is possible. I did it in an age-old videoa few years ago. I must be given to sing the resonantfrequency of the glass over and over.Really annoying. E voiced.[ HIGH PITCHED SOUND] And then the glass breach.[ GLASS Cracks][ Merriments AND APPLAUSE] And then, I can graphthis simplified simulate. Something like this, where ifI match that frequency right there, I get a reallyhigh amplitude response, and my wineglass shakesand shakes and shakes until it interrupts. There’s a lot more physicsgoing on than this graph demonstrates, but I can use it to pull outthe most important information. So this is streamlined. It is highly unlikelythat the cyclist biked through everysingle discern on this line.She might be a boringcyclist, but she’s also an fallible human. Kind of “ve been meaning to” her. She’ll speed up and slowdown, so her path will examine is that. But if we’re trying tofigure out, for example, how soon she’s going to getto the edge of a cliff– “Ahhh! ” bicycle rotations, girl, we don’t need to know her place atevery single nanosecond. A scientific simulation letsus dismis incidental details and tells us on averagewhat she’s doing. So hence, a mathematicalmodel is streamlined. Say it with me–simplified. But that being so, I can doa lot with this graph.For example, whatif she sped up? This “wouldve been” her gesture. A steeper course. What if she slowed down? This “wouldve been” her motion. Less engulf row. What if she started hereat x equals 30 and exactly sat on the path ingesting route mix? Well, this straight linewould be her action. What if she wasbiking backwards? This would be her motion, into the negatives. That’s pretty ineffectivefor prevailing a race. Her choice. This diagram gazes simple, butit contains so much information if we look at specificthings, like the gradient. Let’s just draw this again. La, la, la. OK, mathematically, descent is rise, like this, over run, likethis, which is often written as delta y over delta x.But now, our riseis delta x standing and our passage isdelta t, the time. So the slope of thisline is our change in position over our change intime, which equals velocity. I look at thisgraph, and I can tell how fast she’s going by lookingat the slant of this text. Let’s taken to ensure that with components. Here’s another digression. Throughout thiscourse, we’re going to pay close attention to legions. My high school teachertaught me this deception, and it’s calleddimensional analysis, and it cured me solveso many problems during my college examsat MIT–I kid you not. We are not going to write downan equation in this course without checking the unitsto see if they make sense.Physicists use dimensionalanalysis all the time to make sure that we’re notadding apples to oranges or tart to cake. Announces really good, though. So let’s think aboutour sections here. Delta x, which willbe meters, and time, which is likely to be seconds, equals– and the human rights unit of velocityare meters per second, because it’s a proportion of length. Checks out. Did you guys know about this? Dimensional analysis? Did you do that in likeyour high school class? It’s so useful. I cuss. Now, the diagram we drewis a model of her action, but the algebraicform of the graph is also a example of her flow, and it’s a potent one, because you canmanipulate algebra. Check it out–looking atthe slope of this graph, I’ve defined it asdelta x over delta t and announced that velocity.If I multiply both sidesby delta t, these cancel. Oops, only kidding. That doesn’t nullify. I have a new equation. Delta x equals v hours delta t. Just by doing that simple quirk, we can calculate her change in position. We have a new implement. This is a brand-new tool. Now, I can predictwhere my cyclist is going to be at anypoint in the future as long as she doesn’tchange her velocity. In the original diagram, wehave her changing her predicament by 10 rhythms every second. So her velocity is10 rhythms per second. I want to know where sheis seven a few seconds later. Let’s check the units.I’ve got secondsdivided by seconds. Those cancel out, andI’m left with meters. And she will be 70 rhythms down the road. There it is. We figured out howto pattern someone moving with constant velocity. Mission reached. Plus, we found that in aposition-versus-time graph, the gradient of thegraph is velocity. And we pulled out our firstsimple, helpful equation. Great. Now, is moving forward, there’sanother useful space to simulate this same motion, which will allow us to solve slightly harder problems. Instead of graphing her positionversus age, what if I graphed her velocity versus occasion? Oh, geez. So that’s velocity. This is time in seconds.She’s moving at 10 meters a few seconds, and you’ll notice that isa horizontal, flat thread. She’s probably more like this. But we’re going to modelit as a constant velocity. If you zoned outfor a second, you might notice thatour y-axis has changed. It is v now for velocity. It’s not x anymore for primacy. The horizontal axisis still t for experience. This is one second, twoseconds, three seconds. And now, I want to knowwhere she is at four seconds. And I make a rectangle here. Big old-fashioned rectangle. I want to get the area ofthis rectangle for a reasonablenes. You’ll verify why in a few seconds. Area equals portion seasons width.In this case, thewidth my rectangle is my time, four seconds. And the stature is my velocity, 10 meters per second. The rectangle’s area isexactly the same equation that we just derivedfor her change in position, velocitymultiplied by period. Now some of you arescreaming, “Integration! Differentiation! ” And you are right. Those of you who have noidea what I’m talking about, it doesn’t matter. These are tools from themath announced calculus, and the tools arecalled integration and differentiation, which is all about areas under the arc. That’s why I’mbringing it up, but you don’t need tounderstand calculus to do physics, which is cool. So anyways, here’s the takeaway. The locality under thecurve is your delta x. Delta x is yourchange in position. It’s where you areminus where you started. So in this wholeproblem, we are only graphed the same exact motionas the previous problem, but this time, we switchedfrom statu graphs to velocity diagrams. Why did we do that? Why did we convert programme? Well, you’re going to see.We just showedthat the rectangle, that area under thecurve, is displacement. So now, we can usethat displacement for rather complicated actions. So let’s go on.Let’s do it. What if her velocityisn’t constant? What if she’s accelerating? Say she’s driving on the highwaystarting at 20 meters a few seconds, but then she startsto accelerate. And seconds later, she’sgoing 30 meters per second, about 60 miles an hour.Let’s are of the view that sheaccelerates moderately smoothly, mostly a constantacceleration, and it made her fourseconds to do that. That’s her action. To find her distanceduring those four seconds, I’ll reiterate what I didfor the last graph and calculate thearea under this bow. Look, a rectangleand a triangle. I’m going to use elementarygeometry, my dear Watson. Let’s begins with the rectangle. I can write thechange in position for that part of her motionis just her starting velocity, because that’s theheight, which I’m going to write as av with a little zero, and I’m going tocall that v sub not.I’m putting a zeronext to that velocity because she’s changingvelocity, so this is her initial velocity. And the province under thisrectangle is v not epoch t. In such cases, v sub notis 20 and t is 4, so the field of the rectangleis portion occasions width. 20 days 4 is 80. My seconds nullify. 80 meters. Let’s think about whatthat means for a second. If she weren’taccelerating, the rectangle is the distance she would havetraveled, just like before. She would have gone 80 meters. The triangle up now, though, this is new. It’s the addition toher travel distance because she’schanging her velocity. She is accelerating. Let’s look at the areaof this triangle, which is equal to herchange in position while she’s accelerating. Well, the area of a triangleis just one half cornerstone experiences height, and we’re going tosee something really cool.The locate is time, and the heightis the difference between 20 and 30 meters per second. That’s her change invelocity, or delta v. Doing the math inour principals real quick, the alter between2 0 and 30 is 10, times 4, days a half, is 20 meters. So how far did our cyclistgo in those four seconds? Well, “shes gone” 80 plus 20 is 100 meters. The rectangle, that’sour v not day t. The reform of positionbecause of her acceleration, that’s 1/2 t ages delta v, and so how do Ichange my velocity? By accelerating. Acceleration is change invelocity over change in time. Let’s make surethe units work out. The contingents of velocity aremeters per second divided by time, which is seconds. I get a brand-new group, which ismeters per second per second, or rhythms per secondsquared, and we get a new part for acceleration. It’s not a extremely instinctive unit.So for some context, things would fall on Earth with an acceleration of 9.81 meters per second squared if there was no air. The acceleration you’d feelin a vehicle going from zero to 60 in three seconds, 8.9 metersper second squared, which is noteven as much as gravity. We can look at the accelerationof the mantis shrimp’s claw, which is an insane 3,000 meters per second squared, which is ridiculous, as comparedto fast humans guiding, who accelerate at about three tofive meters per second squared.And the theoreticalfastest my ping-pong ball can intensify in the tubeis about 49,000 rhythms per second squared. We’ll see how fast itactually intensified, though, when we get to that question. We can use theseshapes to be drawn up with an equation fordistance traveled. Here’s something recreation. I’m going to do mythird favorite deception. I’m going to substitutesomething in. Notice these two equationsthat I wrote down– the area of this triangle, 1/2 terms delta v, and then, this over hereis just a simple definition of acceleration.Notice, both of theseequations have a delta v. I’m going to revision thisone be doing what I did before brought forward by the delta t. These cancel, and I see thatdelta v is just acceleration times time. It’s a simple littlealgebraic substitution. When I find twodifferent equations have something in common, perhaps I can compound them. And if I push thisin here, I get something really interesting. I get that the area ofthe triangle, this here, due to my accelerationis now 1/2. Bring it up–1/ 2 timesdelta v, at, and then another t, at squared. Now, I’m going to putall this together. I’m going to put togetherthe area of my rectangle and the field of my triangle. That’s 1/2 at squared plus–where’s the other one? V not t. And in this problem, exactly what we we doing? We were doing the change inposition, which has two articles. It has how far I would havegone if I wasn’t accelerating and how far I wentbecause I accelerated.And recollect, I don’t need both. Maybe I have a case whereI’m not intensifying, and this term goes away. Maybe I have a case where Ihad zero initial velocity, and this expression goes away. I could have a casewhere I’m doing both. I could have a case whereI have an initial velocity, and I’m accelerating. And then, I need both. Now let’s rewritethis, but we’re missing one key term, the initial berth. My initial position here waszero, so I didn’t need that. But if I supplement it tothese two words, I get post equals initialposition plus initial velocity hours era plus 1/2 days acceleration times time squared. You may have already seenthis equation a cluster. We announce this theequation of action. Ahhh! Where you are iswhere you started plus how far you disappeared due toyour initial velocity plus how far you extended due to thefact that you’re accelerating.I bet you never understoodthis equation so well. We have , now, onesimple, captain equation– the equation of motion. This equation is important. Write it down. Tattoo it on your appendage. And we are only extracted it. We simply look back the range undera velocity versus meter diagram to find displacement, and from that, we derivedthe equation of gesture. That’s pretty cool. You can use this to derive allthe other equations you have in your bible or mislead sheet. Now then there, if youwant to memorize them .[ MUSIC PLAYING] And I been in a position to solve myping-pong-ball question. How fast is the ping-pong ballgoing when it leaves the tube? I merely need two amounts, the interval the clod traveled, which I measured using thenice tape measure on screen and I got 2.29 rhythms, and the time, which I measured byknowing this was filmed at 18,000 encloses per second. So each chassis is1/ 18,000 of a second. And I get about 0.0121 seconds. So my median velocity is 2. 29 meters over 0.0121 seconds length over period, whichequals 189 rhythms per second.If we expect constantacceleration, my final velocityis twice that, then, at 379 rhythms per second, whichis over 800 miles an hour. Dude, that’s fasterthan the speed of sound, whichdoesn’t seem right. So I redid the sametype of measurements, 4.5 centimeters of tube, which onlytook three chassis, and I came 270 rhythms per second, which is a lot more reasonable. So why significant differences? Well, it’s not actuallyconstant acceleration. There’s a bunch ofcomplicated things going on, including the factthat air is racing in , not just pushing the clod. It’s also pushing itself. But I did measuring anincredibly high acceleration of 47, 000 metersper second squared for the first 10 centimeters. Can you think of how I did that? And voila. Now, my final question is, canyou build a safer bike helmet? OK, say you’ve gota mountain biker.She’s wearing ahelmet, and she operates into a tree going around1 0 rhythms per second, about 20 km / hour. And she loses her balanceand falls off the bicycle. I’m a so much better careful cyclist. I want to know whather face feels. Precisely, I want toknow what the acceleration of her head experienced. Her head comes to a completestop in the distance that part of herhelmet deteriorates, which we’ll liberally sayis about 10 centimeters. Now, I don’t have anyfancy laser manoeuvres, I exactly have her accelerate andthe helmet fold span, 10 centimeters. If I precisely plug this intomy equation of action, which we’ll write again, this expression goes away, because her initialposition is just zero.I know her initial velocity. I don’t know her epoch, and Idon’t know her acceleration. I have two unknowns. Now, there’s probably somefancy equation in your bible you could just plugand chug, but to me, that passes no feeling forwhat’s actually going on. So let’s do this. I have this equation for x, but I have uncharteds, a and t. So how can I find one of them? Well, I is a well-known fact that I startedat 10 rhythms a few seconds, and I stopped at zero.So my change in velocityis 10 rhythms per second. So let’s assume aconstant deceleration. We’ll precisely graph it. That means you gofrom 10 to zero. This symbolizes I knowmy median velocity, because it’s just halfwaybetween 10 and zero. It’s five rhythms a second. So my norm velocity isfive meters per second. And I know I was at the averagevelocity for 10 centimeters, or 0.1 rhythms. So then, I knew howlong it took me to stop. I know the time, becausevelocity is change in position over change in time. All I have to do isrearrange to get the time. This comes up here.This goes down here. X over v. I knowthis is 0.1 meters, and this is5 rhythms per second. And I see that the timeit made me to stop is– let’s go over here– 0.05 of a second.Now, her acceleration. Well, it’s thechange in velocity, which is 10 rhythms persecond, over change in time, which is 0.05 seconds. And I get 500 metersper second squared. That’s about 50 timesthe acceleration you would feel from gravityhere on Earth’s face. So that’s a lot. But it’s survivable. You may have heard ofthis sort of comparison for acceleration called gs.So for example, my friendDestin from the path Smarter Every Day gotto go up in an F16, and he knew 7 ks. Hoping it happens one day. The highest ever recordedgs experienced by a human were 216 gs. Want to hear something crazy? The mantis shrimp punch– that’s the majesticcreature that I made a entire Physics Girlvideo about–its claw accelerates up toaround 15,000 ks. So now, you’rethinking to yourself, thank goodness shewas in a motorcycle collision and not swiped bya mantis shrimp. So we observed the bikeaccident is survivable, but you might stillget a concussion. So how do you makeyour helmet safer? Well, if you increase thedistance you need to stop, say if you have an inflatablebike helmet that gave you another 10 centimeters, well, that’s like how the rumple region, thefront of a automobile that crumples when you’rein a disagreement, helps you feelless acceleration. So you can work out theinflatable helmet problem. Go Google inflatablebike helmets. Figure out what thecrumple zone of a helmet would be and workout the acceleration.Send me the answer if you do it. I believe in you. So that’s our firstlesson on kinematics. When they wants to see you what youlearned on YouTube today, here are your twoimportant takeaways– If you can turnyour physics problem into a diagram ora illustrate, get it on. If you can find youraverage velocity in problems linked to 1D constantacceleration, use it. And here are all theproblems we did today. You know why? Because the only wayto really learn physics is to work troubles. So here’s your homework. Go work all these problemsagain on your own. For real. I’m not kidding. Go do them. You are also welcome to find a ton more onedimensional motion kinematics troubles online. So if you find any otherinteresting difficulties, pole them in the comments.We’ve just stroke onthe basics of kinematics. Because if youstick with physics, stranger things happen. For sample, inthis whole lesson, we assume that time passes atthe same rate for everybody, that one second for thecyclist is equal to one secondfor the tree she reached. It’s not fakephysics we are only did, but it’s a lessprecise approximation. If you want to bereally precise, term actually delivers moreslowly if an objective is moving. And you really notice itwhen that object is traveling close to the speed of light. That’s real physics. You get coolthought experimentations, like where 1 twinleaves earth for 2 weeks and comes back to find thattheir twin has aged 40 times. If you continue onto take physics and take a classon special relativity, you’ll learn about thatcraziness and a whole lot more. And I hope you dostick with physics. And now a send foryou from a special guest. Hi, my word is Simone.I run a YouTube channelnamed after myself, because I couldn’t thinkof anything more fun. But little known factis that I actually used to examine physics in college. I did drop out afterjust a year, which is a little bitof a parenthesis, but I love physics, andI am just so excited for you to learn more about it, because what better style to understand the world thanthrough the magic of numbers? Good luck.[ MUSIC PLAYING ].