A LEVEL PHYSICS REVISION: ALL GRAPHS EXPLAINED

hey guys and welcome back to another a-level physics mechanics video this time we're going to go through the graphs so keep in mind um graphs are super important in animal physics they're going to come up again and again and again um but they're not always going to be the graphs I'm describing in this video so again in pretty much every single section every single major topic there is going to be a graph section because graphs come up all the time however the skills we talk about here are going to translate over to those other subjects anyway so for mechanics specifically here are the kinds of graphs that you can expect to come across so you're going to have the standard you're going to have displacement time graphs right displacement or distance it doesn't really make a difference so we can call it D or S and it's going to be time you also have your classic velocity or speed and time and then last but definitely not least we have the acceleration time graphs okay and these are again super super important time so why are these important well what you're going to be asked to do is interpret what the different shapes of these graphs mean you're going to be asked about gradients and also ask about areas under the curves so what I'm going to do is I'm going to draw a few different graphs for each one and then that way we can describe what it means so the first kind of most standard case is probably something along the lines of this a straight line okay so what does this show you well first of all let's talk about what the gradient of this would be so again this is a key skill you're going to have to know for pretty much all of a level physics because it comes up again and again so whenever you think about what the gradient of a graph gives you and again keep in mind they can give you any kind of graph and you expect to be able to work out what it gives you okay so that will make more sense as you go further into a level physics you'll see what I mean but when you work out the gradient what you do is you find the change in the Y and you find the change in the X and you divide them right so in other words if we were to look at the unit so speed is most commonly in meters and time will most likely be in seconds not always the case you also have kilometers per hour you also have miles per hour you also have kilometers per day or something similar to like you can have pretty much anything but the idea here is you're going to have a distance unit over a Time unit now what is distance over time well it's always going to be a velocity or speed so we're going to call it velocity but it could also be speed so if this was a distance time graph then you wouldn't have a negative section because distance can't be negative it doesn't have a direction to it so just be this positive bit so the speed is always going to be positive right if it has this negative part uh then this is going to be displacement which means the gradient will be velocity so this is the kind of skill you can use right just work out okay what units do I have and what variables do those equal to so again if you think about it it's if it's in meters and seconds then our answer is going to be meters per second well what does means per second remind you of reminds you of speed slash velocity okay so those are the key things to remember and what about the area under the graph well if we try and work out the area again we're going to do the same thing right to work out the area and again I'm not going to be specific but overall you're going to times the X and Y values right so if it's a rectangle you just times them if it's a triangle like this you do half and then times them but in terms of units you're basically just going to be doing meters Times by seconds right now if you think about it do we have an equation that is distance times time so basically the area just doesn't equal nothing it equals nothing so when I say nothing I don't mean it literally equals nothing I mean that it equals nothing that's important okay now again meters seconds is actually the units for moments but in this case we're not talking about like moments right or force or anything like that so sorry it can be also be impulse and things like that um but again this doesn't equal anything that we care about cool so knowing these two facts about the gradient in the area we're going to be given a bunch of different uh kind of situations so in this case the gradient it might say something like describe the motion of this object well the gradient is a straight line right so the gradient is constant so in this case you're talking about something that is accelerating or as it has a constant speed so it has constant velocity which means it's not accelerating okay so those are things you need to be able to describe likewise we can have pretty much the inverse of this graph and you can have it going okay imagine that's going through the origin actually you know what who cares about imagination right and again we have the exact same axes what about this well this is going to be a constant negative velocity student negative let's see and again it's not accelerating okay but what about what happens here well what happens when displacement equals zero well it just means it's back where it started and again you can try and think of some situations in which this might occur where you have a constant negative velocity or um constant positive velocity it's not dropping something okay because if you're dropping something it's going to be accelerating and keep in mind they can get a bit more complicated than this so at the moment it's going straight through the origin but what if this displacement is zero was actually a um a ball hitting a floor then you might have something like this where it drops and then it starts up at the top again now why does that make sense well well it wouldn't actually do it it would go like this and then go back down again right well why does that make sense well again it's going to be bouncing off of the floor now again we haven't included the acceleration there so imagine that in like a weird alternate universe but then you can also have something like and this is where things get a bit more interesting you could have something like this What's Happening Here well again imagine this is just velocity and time well as you can see the velocity uh sorry the displacement and time well as you can see here the displacement is increasing fast and Fast and faster so the gradient is increasing if the gradient is increasing that means velocity is increasing which means this object is accelerating positively whereas the exact inverse of this would be something along the lines of it might go uh like very Steep and then go very smooth so it's beginning to decelerate so those are the kinds of situations you can find yourself in or any kind of like they can combine it right like it could start off linear and then flatten off which means the velocity is constant and then it slows down to a stop speaking of what happens if you just had a flat line on a displacement uh time graph that means it is stationary the displacement's not changing with time which means there's no velocity which means they're not moving now again let's do the same thing for velocity speed so again if we just considered something like this now again we're going to look at the gradient well again we're going to take the Y thing and divide it by the time well this is velocity in fact specifically it's the change in velocity over time which is acceleration it's pretty useful right acceleration is pretty good so in this case here the acceleration is constant and positive okay so keep in mind you're going to have to use those words as well so remember all of these um y axes that we're going to be talking about here they're all vectors right in terms of velocity displacement and acceleration which means you need to say if it's positive or negative because it has Direction now what about the area well in the area we'll be doing velocity times time right now the other way to look at that is it's meters per second times seconds which is meters but there is a problem with saying this right is you might say it's distance it's actually displacement now why do I say that well if you look at the graph that I've drawn on the left this velocity down here would be negative so if I work the area out of this region I'll get a negative answer you can't have a negative distance but you can have a negative displacement so bear that in mind is that in a velocity time graph if you're dealing with the Positive area which you mostly are the examiner or the question will just say calculate the distance traveled right because obviously you don't it won't be negative so the displacement is the distance however if it's below the x-axis then the displacement and distance are technically different numbers displacements will displacements will be negative distance will be positive still so keep that in mind it's just that in this top right region that we're dealing with the um displacement and distance are both the same okay and likewise we can have the exact same situations that we had over here so if we were to draw another graph and I'll try and draw them a bit smaller so we have a bit more space and again this is V against t then this is going to be a constant deceleration um something else to note is that deceleration is a bit of a wonky word technically it's still acceleration it's just negative so again because we're used to cars when cars slow down we say they're decelerating when they're speeding up we say they're accelerating in actuality in both ways in both cases they are accelerating right it's just that in one case the acceleration is negative the other case is positive like deceleration is just negative acceleration which is still acceleration and then obviously you might have something that's like uh an exponential increase right so it might be like this this is where the acceleration is constantly well maybe not constantly but it's constantly increasing right so it might not be constant depending on you'd have to differentiate this to work out if it is and then likewise you'd have the same thing which is where it's um slowing down as well yeah so hopefully that makes sense for that one and lastly but certainly not least we have the acceleration time graph um also uh actually one more graph I want to do with this one is if you have something like this that looks like a cross instead of a something like this it's obviously a constant velocity which means there's no acceleration okay this also means that when it comes to suvat we can only use suvat in this case if it's a straight line okay so please bear that in mind and that should make sense because Suva is a constant acceleration equation which means we can only do it when there's a constant acceleration so if it's a straight line or here if it's a straight line right it's just a is zero in this bottom case if it's across obviously it's a flat line across here then velocity is zero so it's stationary but in most other like any other place it's not stationary okay in terms of working out the area um honestly this can be really painful sometimes when it comes to a level physics because as you can see we sometimes have big fat curves right you also sometimes have U shapes you also have n shapes and things like that so how'd you do it well counting squares is the most popular example but you can also use something similar to like a trapezium rule which you may know from a level maths where you break up into a bunch of trapeziums find the areas of all of them add them together painful but necessary unfortunately um if you're thinking also if you think about uh integration you can only integrate if you know what the equation of the curve is so nine times out of ten we don't know that so with this uh this one's a bit more interesting uh what about the gradient of the acceleration time graph well it's acceleration over time specifically it's the change in acceleration over time which doesn't equal anything we care about right but what you can say is it's also the rate of change of acceleration so what I mean by nothing again is it's not it's not a physical quantity that we Define in a level physics so it's not something we necessarily care about however if they do ask you specifically for what it is it's just the rate of change of acceleration yeah and the area the area is actually a fairly interesting one you probably already know what it is right it's the uh it's just going to be acceleration times time which is velocity okay so it's kind of interesting so if you have like a flat cut um a flat line like this the area under it is the velocity that makes sense right because um it's just a fat line right however it also actually works if you have an increasing acceleration right the area under this curve here is also the velocity along this point which seems weird because obviously since it's accelerating the velocity is changing however keep in mind it would give you the average velocity okay because again it's if something's accelerating continuously right so the acceleration is constantly increasing then the average it will be the average velocity instead because the velocity is obviously constantly changing you won't have it instantaneously is uh what I'm getting at here um this is kind of a weird this is kind of weird however what they like to do sometimes is they might this is actually outside the scope of this particular spec point but they sometimes give you circular motion now in circular motion or things like resonance or oscillations then it's um common or it's it is included that the acceleration would change over time so it might be like a sinusoidal curve things like that but for the purposes of just standard mechanics we're pretty much only dealing with constant acceleration or no acceleration we don't normally deal with anything that looks like this okay okay so that was quite a long explanation of kind of the different kind of graphs that we can be dealing with and again we may come on to different types of graphs later on so for example when we do momentum there are graphs from momentum this is specifically the ones for things like Suva okay so again I've got some questions from different exam boards so a ball made from scrunched up papers dropped from rest at time T equals zero it reaches terminal velocity before it hits the ground which acceleration a gains time so first of all the reason why they've included the tunnel of velocity it means that air resistance is included okay so for example someone might in their ignorance say oh it's B Because acceleration is constant you're dropping its gravity nope keep in mind exam acceleration is a vector which means you're talking about the overall acceleration in reality if I drop something right so again let's say it's a piece of paper right that's my perfect piece of paper we're dropping it when it's not moving acceleration is equal to 9.81 downwards then as it speeds up you get this air resistance that begins to increase as velocity increases which means the overall acceleration will decrease with time so what we're looking for is an acceleration that starts at a value and dips so it won't be this acceleration wouldn't increase and then decrease it'll be more like this if so you can start at a value begins to decrease and then it levels off because eventually as this kind of uh upwards acceleration is increasing the velocity doesn't increase as quickly which means this acceleration doesn't increase as quickly so it actually tapers off towards the end so the answer is actually going to be C because here that's just G but then as the ball of paper speeds up the opposite acceleration is happening which is why the gradient decreases okay because again the more the uh velocity increases the more this kind of counter acceleration increases which means the velocity is not increasing as quickly which means this doesn't increase as quickly and then eventually it says it reaches terminal velocity what's terminal velocity is when the upwards acceleration so this value equals gravity which means you're no longer accelerating which means you will go off to zero which is exactly what C does none of these others actually go off at zero which might be the kind of key thing to eliminate you know it's not constant because air resistance isn't included okay you know it won't be constantly increasing right because think about it gravity would be constant what would be speeding it up what would be increasing the acceleration downwards nothing if anything would be decreasing so it's between one of these two well it should end up at zero so it's not this one after that makes sense so again one more questions they are short questions but they're by no means easy they love to trick you and they love to backstab you in this one I can again a lot of students just pick this one because they're reading they're rushing they're like uh okay it's falling gravity constant done boom okay uh this is one of our first kind of graph questions so if you have a look it looks like a combination of a few different pieces so we have a metal ball released from rest it falls vertically towards the ground and figure 22 shows the variation with time tier of the displacement s of the ball so what's happening here what what is what is this right well it starts off at one point two five meters meters above the ground something like that and it drops and this is it speeding up because the gradient is getting bigger it's getting more negative so why is it getting negative well they're taking upwards as positive by the looks of it okay so since this thing's dropping it means the velocity is pointing downwards and then it hits the ground and instantaneously stops because it's bouncing off so it hits the ground goes to zero and then bounces off and then here the velocity is now positive and then it continues to decrease over time because obviously gravity is pulling it back down again ever since it has a negligible effect on the motion of the ball perfect the ball hits the ground at T equals 0.5 seconds as we can see during the Collision the ball is in contact with the ground for a time of 1.8 milliseconds the master ball is 56 grams again this part of the um question here these last two lines they're actually for a pot that we're not going to include in this bit because it's to do with impulse which is to do with momentum so I've taken that out and I'll put that into the other video it comes later so it just simply says describe and explain the variation of the velocity of the ball from T equals 0.2 to T equals 0.7 no calculations are required four marks okay this is really important the four Mark bit okay so here's what we need to do describe and explain means we need two described points with two relevant explanations right so what I'm going to do here is I'm going to put the a star for each described point and then we need to explain each point okay and there's a reason why I've done this and this is a reason why exam technique is so important with a level physics is unbelievable and this is why I also say bullet point in this question it's very easy for someone to write all of the correct things but only get two or three marks why because they've only described two things and they've only explained one or they've explained like three or four things and described one right or and this is the tragic thing someone gets four out of four but writes like six points eight points so they've wasted five ten minutes on a question that only needs four marks worth of stuff bullet point your answers and you'll end up writing for four marks like 12 words it's crazy okay and again if you look at the Mark scheme it's all bullet pointed they don't write in four paragraphs okay so if we need to describe points it says the variation in velocity so we need to say how it changes well if you look here it's negative and then positive so that's all we need to say okay so and it says explain it right so from 0.2 to 0.5 seconds that's what I'm going to write here so 0.2 seconds to 0.5 seconds the velocity is decreasing right is decreasing not just that it's negative one mark why well because it's falling right because the ball is accelerating downwards due to gravity two marks see how quickly that is two marks meant to take me two minutes 10-15 seconds bullet point okay be really really precise okay and then it says the variation right so what I might say is at 0.5 seconds what happens well the velocity changes right and you can even get fancy right instantaneously assuming you can spell it which I'm hoping I can changes from negative positive also keep in mind you can write a bit like a caveman this is not like proper English doesn't matter right at half a second velocity instantaneously changes negative to positive done that's it another mark now explain it well it's because it hits the floor and then bounces up this is because so because ball hits the floor and rebounds upwards there you go a lot of the time what happens is whenever I teach as physics students they write in four paragraphs and it looks very nice and yeah yeah and then they end up getting like two marks in this question even though what they're saying is 100 right it's just that they don't have the right points okay and that's kind of an unfortunate part about a level physics but you need the right points okay you need the correct to say the correct things at the correct times so please keep that in mind with this with a level physics Again by year 13 you're going to start bullet pointing everything okay you're gonna get six more questions for like experiment bullet point everything six bullet point six marks done that's all you need to do probably use an equation of motion to show that the speed of the ball is 4.9 meters per second just before it hits the ground okay so all we need to do s is 1.2 right I remember that it's actually not 1.2 so let's work it out so between 1 and 1.2 there's one two three four five so then we have 0.2 over five actually why am I even uh get our calculators out because a level physics is just a calculator so the way you work this out is um go away you take the difference so from 1.2 to 1 and then you divide it by the number of steps so one two three four five so it goes up in 0.04 so this would be 1.24 right this is 1.24 meters also just so you know with your mock exams and your end of unit tests a lot of times in schools they use really low quality ink or they like change the scale of stuff so to me this looks pretty damn clear but a lot of schools that I've kind of acquired and like a lot of pupils that have given me their past papers and stuff or their mock exams these diagrams look really unclear so if you have glasses I would recommend just asking your teacher to make it bigger specifically for you um because again these can come towards your mock grades which is used for University anyways uh you the initial velocity is dropped from rest velocity is what I'm trying It's the final loss is what I'm trying to work out acceleration of course is just gravity because there's no air resistance and time is we do have the time it's 0.5 seconds so we can actually use any Suva equation we like um but I like to just use V squared equals U squared plus 2as because it's already um rearranged for me so V is just equal to square root two 9.81 1.24 whip out that calculator again square root two times nine point one point two four [Music] four point nine three which is about and again technically this isn't like velocity right because again just um you're going to have a good question here shouldn't it be negative your answer is yes right because they've taken upwards is positive so if I followed their convention and followed these uh values I would get a negative answer so the answer should technically be negative 4.93 the reason why it's positive is because it says the speed okay which means it doesn't have a direction which is approximately 4.9 and then lastly um possibly the most annoying thing that you have to do in a level physics draw a suitable tangent and you have to do this to basically every damn graph that you ever get which is annoying um if it helps I've done this like 200 times and I still find it annoying so yeah so the rebound speed of the ball is 3.5 so people say oh how do I call Rebound speed think about it right this is the rebound here so the rebound speed is just the gradient of this part it's not like a new physical quantity now drawing the actual thing this is where things are going to get a bit interesting because this doesn't work very well so we need to find the steepness of basically this so I could draw that might be somewhat reasonable okay so yeah and I'm going to take it from 0.7 and the reason why I've done it from here is was the rebound speed would be that instantaneous part here so I've drawn it right from the beginning now again you do get a lot of leniency with this so don't worry too much about it to make sure your line is straight and if I've read that off like so again I'm just drawing a guideline I know which line I'm following which is why I'm allowed to go up and down well I say aloud I'm not but so 0.64 0.68 0.72 so the difference in this is 0.72 minus zero so yeah and this would be 0.7 minus 0.5 which is 0.2 okay so 0.72 um and yeah this is a three mile question I've already done it right it's it's not too bad so without you really like I'm not just that unfortunately a little physics you're going to be drawn a hell of a lot of tangents whoops 18 over five so 3.6 meters per second which is about 3.5 not too shabby at least I find anyway once again we have another multiple choice so you might think oh man that seems kind of easy but again if we look at the grass in fact I'm going to zoom out slightly so you can see all of them at once actually that's better so we have a velocity Against Time object so we need to work out the what the displacement time graph would look like so again we should remember that the gradient of a displacement time graph is equal to the velocity so let's have a think in this first part here the velocity is constantly increasing which means in the first part this gradient should be constantly increasing and then when it gets to this flat part the velocity is constant right which means we should have a constant gradient so this part should look like a curve up and then this part will be a flat part so which one shows that it's part C that would be my logic in doing this okay um just be very careful right so this is increasing that which means the gradient of the displacement should be increasing the only one that actually shows that is one of these two and hang on a minute uh is one of these two and then when it goes straight again so when I said constant gradient I actually drew the wrong thing I meant it's going to be like a flat line like that not flat a straight line so it's actually going to be D not C uh brain fart there but yeah consecrating with me a constant increase of displacement okay so again very easy to make a mistake between those two but again you should be able to eliminate these two by the fact that the displacement isn't constantly increasing in either of those so the gradient's not constantly increasing then all you need to do is a it's a 50 50 Choice from there so that's my strategy and multiple choice questions is eliminate the impossible and it increases your odds by quite a bit and then yeah look at which one actually matches it so is it a constant increase or is it flat what's happening but yeah that's it for this video