 So the name of the game for physics is you got to check your units right units is everything That's what physics is is applied mathematics. So if you know math Then you can do physics. All you have to know is understand the system you're in right so one of the questions my student had was this and this is You encountered this in grade 11 physics You encountered in grade 12 physics and you encountered in first-year university physics Okay, or college physics or whatever. So this is this is stuff that they cover All three years you get them. Okay, if you're lucky you get them in grade 11. You get in grade 11 But basically he had this Here's a graph This is time in seconds usually And this is velocity in meters per second Okay, and he had a graph like this and this is time. I forgot what the numbers were but two four Six eight Let's go ten seconds and let's make this. I think these were at five ten Negative five right and The question he had was this actually you know what he sent me the images Let me read off the question exactly that way I Don't make a little mistake and Ba ba. Oh, yeah, here we go. Oh, yeah, this is the graph nice. I should this went to 12. I guess here Let me erase those And then I'll close this guy and then open it up again because my computer Works over time so the fan noise will go up too high, right? Negative ten. So here's the question figure one Shows the velocity graph for particle having initial position X zero Okay, X zero and this is X zero. Okay, this is the X. Well, that's velocity zero But it's starting off a position zero at t equals zero seconds, right? And the question was this at what time or times is the particle found at X equals 35 meters Okay, so let me close this guy off That way the computer doesn't go crazy So the question is at what time is X this thing starts off at X is equal to zero at time is equal to zero at what time Do we find the position of this particle at 35 meters? Okay, so just imagine there's a position X here and once time You start the clock and The velocity of this guy is Increasing per second, right? So there's acceleration here Right, if you see this velocity and this is time in seconds Okay, what you see is an accelerating particle, right? So velocity is Increasing over time so velocity at time zero was zero at time one Was this guy here? Whatever that is I say 2.5 at time two is two seconds is five meters per second at three I'm assuming it'll be at seven point five meters per second at four seconds is going at ten meters per second okay, and Then what it does it starts slowing down at five seconds is back to seven point five But but but and it reaches a velocity of zero Right and then starts traveling in the negative direction. So if you're watching this thing this particle or this person, right? By the way, if I miss stuff Lance left hook Thank you for the follows and thank you for the subs if you decide to stop this channel, right? So there's this guy Let's assume He's running. I don't know how fast You know ten meters per second is only kilometers per hour that is right we can convert it Maybe we do a conversion to figure out if this is legit to assume. So it's a man Would it ten meters per second? Well, I used to run the 100 here. Well, we can we can do this Mental math, right? I used to run the 100 meters in track and field and the best time I had was like 11.8 Seconds or something right? I think the best time in the world is I don't think they've broken nine seconds yet Like nine point something seconds. I don't know if it's reached eight point something seconds yet, right? It will at some point I think but no one thought they would have broken 11 decades ago and then 10 decades ago and no one thinks that or when I was running anywhere last 15 years They will break nine but pretty sure they'll break nine, right? So if you can run 100 meters zero to 100 meters Let's assume in 10 seconds Then if someone's traveling at 10 10 meters per second, that's a legitimate Speed someone could be running at, right? Okay, so we could make it a person Okay, so this person starts running from x is equal to zero. This is their position zero right Equals zero starts running and they're running faster and faster right when they get to four seconds It takes them four seconds to reach a velocity of 10 meters per second and Then their velocity decreases. I should make this a little bit Shorter, right? So they're accelerating from here for four seconds, right four seconds And then they start decelerating Over the same four second period To zero So it takes them four seconds to reach maximum speed, right? Richard Zach, thank you for the twitch prime. So right and then for another four seconds They decelerate and usually if you're running 100 meters when you cross the finish line You're slowing down, but you can't stop right away. If you stop right away, you're gonna break bones, right? You're gonna tear muscles. You got to slow down Right, so you accelerate accelerate to your top speed and you slow down So for another four seconds this person Decelerates until they reach a velocity of zero, right? Here's a velocity of zero and then they start going in the other direction for two seconds Because the velocity is now negative. So if this is our positive direction and in physics what you do whenever you're laying down a problem You give a certain direction You make a certain direction positive and the other direction negative, right? It's very directional. It's vector-based Right, so physics. There's a lot of vectors and vectors is basically Magnitude and direction Okay, so this person starts going in negative velocity direction and we're talking just a two-dimensional System so for another two seconds, which this person runs back and this is two seconds two seconds So the question was this okay, and this is you know, you don't have to draw this But it's a good idea to know what's happening in this system, right? And that's the that's the key with physics It's math applied mathematics. So what you're doing is you're taking Your math abilities the powers that you have you're looking at a physical situation in the world This happens to be kinematics right kinematics is bodies in motion I guess things in motion, right? You can have a whole bunch of other different types of systems you go into that physics deals with electromagnetic magnetic gravity Particle physics quantum mechanics anything you want, right? This is kinematics. It's one of the simpler physics Well, these types of problems anyway situations that we have sending rockets to the moon is Kinematics it's also got gravity in there and different formulas that you have to end up using So the way it works is this The question was this at what point or sorry at what times Is this person? 35 meters away from when they started, right? The wording of the problem wasn't and that's one of the Issues with teaching physics and stuff like this the wordings of problems aren't the best way, right? If you take the integral of the function of the ground, you get the distance moved You will yeah, if you take if you take the If you take the integral you get the acceleration you take the derivative you get the Distance right the derivative kicks you down one dimension or One unit the integral will kick you up. You get the acceleration through the integral. I believe Right, so for example if we have here, let me bring up some kinematics Bring up my kinematics formula skin mathematics Formulas and that's what you need for physics, right in your formulas, okay? So take a look at this velocity distance Here Let's do this here. I'm going to do this with a different color Since you brought it up. We'll deal with it right now Okay, we're gonna take a lot of tangents. No integral gives distance. Oh integral gives distance Look at the formula integral gives distance. Oh Yeah, I'm going the other way pooper me The area under philosophy girl. Yeah, the area under velocity. That's the way we're gonna use it, right? The area under velocity the function is initially a function of speed. So yeah, so let me write down the formulas here I always get things backwards. So here's velocity the formulas you have velocity finals the velocity initial plus 80 and The distance is equal to I'm just going to write it down v initial t plus one half a t squared Right, so these are two the equations you have for kinematics and here's the other ones here Let me write down the other ones as well. Let me bring up chat. So I'm not missing anything Here's the other you basically have four formulas you deal with in Kinematics, okay? Here's the other one v squared v final square is equal to v initial squared plus minus plus to a d and Distance is equal to v. Oh, no, we already got that one. Why is it give me two of those ones? Oh minus Yeah, we use this one distance is equal to One half One half v final plus v initial plus v initial Plus v initial times t Now back in the day they used to make us memorize these but I don't memorize these or Later on you didn't really memorize these. Okay, did I forget a distance? Did I forget a distance? Distance right here this one changes in distance VIT is the constant term of belief this one. So basically if you take the derivative of this guy Right the derivative of this guy is it's just a quadratic function, right? Thanks for the correction by the way gang. I mean for sure correct me when I'm wrong. Please, please It's how I improve right so if you take the derivative of this if you take in a derivative of a any type of quadratic You're 5 x to the power 3 plus 2 x squared All you do you kick the power down to the bottom and subtract one from it, right? Take it down one notch. So this one would be 15 x squared plus 4 x, right? So this one the power is one so that kicks down and that becomes here. Let me write it down Write this guy down here. So D is equal to V initial one times V initial is just V initial We're the equivalent of it. We're the equivalent of it, right? Oh You want the C out here? That's right Haven't done this forever. You want the C out here? But we're not gonna do an integration. I'm not there yet. Thank you for that Oh, hold on. How come this didn't get approved? Sorry about that put in rooster the automata zaps things out, right? So the one comes out multiplies that and this becomes t to the power of zero plus one half times two comes down a t to the power of one and then that just kicks the derivative of a constant which is what the C is is just zero, right? So plus zero if you want so this becomes D the derivative of D which is velocity so D DD over DT, I guess that's a symbol of that which is velocity math explicit So I can see why it block blocked it. Oh, that's why it does it So this becomes the derivative of D relative to T is meters per second basically is velocity is equal to V initial and velocity is now v final plus a half kills the two AT right that Is this Right, so if you take the derivative of that you get that DD over DT Okay, cool Can I raise this now because we want to find the area right if you want the If you want to take the integral you're gonna go the other way stop But we're not gonna do the integral really I don't I've forgotten how to do integrals Okay, I would have to look at all up. So let me erase all this the brown anyway. Let me kill this guy Clean up our space a little bit. We might leave the formulas up there So here's what we've got right and One thing you have to appreciate with physics is units is everything. It's the units that matter HM So units is everything okay, so right now the units of the y-axis is meters Per second the units of the x-axis is time never mind What is this is physics, right? He was cleaning his throat Okay, so yeah In the distance formula you would add a constant equivalent to where you start. He's assuming it's zero where I suppose Yeah, we're starting at zero right so x is equal to zero so The y-axis is meters per second the x-axis is seconds so in general If you get a question like this where they say at what time is This a runner 35 meters away from where they started Assuming constant acceleration huge constant accelerations one of the key factors, right? Now if you're looking for time Right, if you're oh, sorry. We're 35 meters. Yeah, we do that If you're looking for a distance, then you look at your units you go. Okay. How do I? use The distant property of our graph to get the meters out Well, if you multiply these two guys the seconds will kill the seconds and you get meters right that's one way you can think about the Physics problems that you get whenever you get a physics problem look at what units Specifically you're looking for or your marker units and take a look at your setup to try to figure out What you could do with the units to get your appropriate Unis that they are referring to or wanting, right? So for this problem What you need to do if you multiply those two guys to get the meters You read Narnia. I haven't read it yet. I've read parts, but I haven't read it yet And I haven't watched the movie either. I've read the CS Lewis I've read the other the trilogy that he had the The more adult sci-fi trilogy CS Lewis had and that I loved that was amazing, right? They hid the I forget what they were called There was trippy it was very cool. It was very cool So take a look at this So for this problem, the only thing you needed to do is figure out at what area Under the curve is equal to 35 meters I'm not gonna lie. Don't lie The golden compass the golden compass The golden compass is Narnia. Isn't it the hidden the hidden secret or something and Pallelangra or something CS Lewis To that for this don't get a single thing above all this now check this out here Daska check this out to find out how far this runner has traveled All you need to do is find the area Okay So here let's find out after four seconds This is two three after four seconds How far this runner is from where they started? Okay, so if you want to find the area here check this out That's an area of a triangle. This is the right angles here, right area of a triangle Is equal to one half base time site. This is something you do in grade eight You do this, right? So this is check like this question is a university first-year university physics question The only mathematics you need Okay, it's basically grade eight or grade nine math as long as you understand What the system is telling you as long as you understand the units, right? There's a little bit more to it, but the only math that you're really using you're not even using these guys Like we're not we're not even going to use these guys, right? We're just going to use area under the graph. I Teach high school math. Yeah, but I'm not a teacher in an institution. I do private I wouldn't function in an institution. Well, so let's find the area here The area there is going to be four times ten so one half four times ten One half of four is two two times ten is 20 20 meters Right, so in the first four seconds This runner has traveled 20 meters Okay Let's figure out how far this runner has traveled up to eight seconds, right? So another four seconds Okay This is again for the total distance from there to there and again the height is 10 and that's a triangle again Well, it's the same thing as this so from there to there Decelerating that's another 20 meters. So here's 20 and if you count it to here, that's 40 meters total That the runners traveled in eight seconds, right? Now they were asking the question was at what time or times is the runner 35 meters away from their original position, right? Well, their original position was here 35 meters would be like if that's 40 would be like here This is 35 meters. Oops 35 meters, right? So the runner is 35 meters away from where they started twice both on the way Here they hit it once and when they're running back they hit it twice So there's twice that they're 35 meters away. So all we have to do is figure out The area of the graph where the sum of the area is equal to 35. So let's check this out Let's do the area for this six After six seconds this part is 20 right Let's figure out what the area is in this part right, the area on this part is two times Five right because from there to there is five So two times five divided by two that's an area of triangle Area triangle is equal to one half base times height, which is equal to let me kill these guys And this looks scary, but all we doing is just geometry, right? So one half the base is two times two times five, right? This kills this so that's another five meters here, right? So 20 plus five is 25 we wanted to figure out 35 but we haven't figured out the area area. So what's the area here? The area here is two times five right from there to there is five. It's just a box So two times five is 10. So that's 10 So 20 plus 10 is 30 35. Oh six seconds this runner is at 35 meters away, so it takes some six seconds to go from here six seconds right The kicker is he goes to the top and comes back. So six seconds Is the first time he hits 35 meters away from where he was and then what we're gonna do is figure out When else is he six seconds away or sorry when else is he 35? meters away, so let's figure out the area here This was five times two because six to eight is two divided by two Which is five again. So this part is five right so that's 40 meters and Then we got a he's got to come back, right? This is negative velocity, which means in the negative direction Is it true that the math can answer almost everything almost? Oh Almost you can quantify almost anything. How much do you love ice cream on a scale of one to ten? You just quantified your love of ice cream, right? So let's figure out. This is backwards from where you went. Let's figure out the area here This is again five and from eight to ten is two seconds. Well, that's the same as that, right? So the area here again is one half Times base times height this kills this. So that's five Right, but it's negative five because it's negative velocity right, so if you subtract five From 40 because that's what the total area was all the way here Right, that's 40 meters that way five meters back. That's 35. So also at 10 seconds Ten seconds, he's at 35 so it took him four seconds To go there and come back again, right? That was the first problem we Did first year University a month in he had this problem, right? You make it look so easy. I wish it was my teacher It's It's just I have the background for it, right and some of these problems aren't easy for me like we did one problem where We got it wrong and then we have to figure it out We knew the answer and we sort of went okay. What is it about the system that we're not understanding? Right, so let me show you. So is that okay? This is again. We just used our knowledge of Physics what the graph means and that's really the knowledge aspect of it. There's a really any mathematics here You know that this is velocity That's time and the area under the graph based on the units meters per second times seconds gives you Eliminates the seconds and gives you meters, right and then we use this geometry to figure out the area, right? math is abstract enough to apply to many many situations both real and made up physics moving around Four dimensions, etc. It can't answer philosophical questions like moral problems. It can only quantify Quantified not qualified very well said the masquerade but it can get you to a level where you can With the quantifying whatever system you're looking at you can hopefully make the right decision right this is what if you watch science fiction Vulcans, right what is good? the what's the Vulcan say The needs of the many outweigh the needs of the few right which I don't agree with I think that's crazy, right? that's extreme firm Form of majority rules, right, but in certain situations it applies Right, and then the Vulcan Star Trek it comes up a lot where they have to you know One person has to sacrifice their lives to save a whole planet or something for sure that applies, right? You can also conclude that it's eight seconds for the entity because eight seconds for the entity because 35 to 40 minus five is four seconds. So half of that Is two seconds 35 to say oh, yeah, that's right. That's right The only things that I'm from Sweden. So the terms and stuff you guys use make me confused Yeah, and that's the language the natural language, right? You know how to speak Klingon. No, I don't know people do Let me erase this let's do another problem, right? I guess we're just gonna do physics Unless you have math questions if you have math questions, they'll lay it on us and we'll try to deal with it, right? so Let's do another one here. Here's another problem we had This was the second problem that went