displacement velocity and acceleration going to be the topics of this lesson we're getting into chapter two of my new General Physics playlist and this is a chapter on Motion in one dimension now some might call that kinematics in one dimension either way so the key is we're going to focus on one dimension we're going to actually start doing some real physics so chapter one was all about equipping us with some of the tools we need to do physics like units and vectors but now we're going to start doing some actual physics my name is Chad and welcome toad ad prep where my goal is to take the stress out of learning science now if you're new to the channel we've got comprehensive playlists for General chemistry organic chemistry General Physics and high school chemistry and on Chads prep.com you'll find premium Master courses for the same that include study guides and a ton of practice you'll also find comprehensive prep courses for the DAT the MCAT and the oat all right so we're going to start with displacement so and first thing you need to know is that displacement is a vector not a scaler and you might remember that that means it has both magnitude and Direction so whereas scalers have only magnitude so it has both magnitude and Direction and we can contrast this with distance so distance has only magnitude it's just a scalar it doesn't have a direction associated with it so you might think of displacement as the change in position which is why it's often symbolized as Delta X now in Motion in one dimension we're only going to consider motion happening in one dimension largely so and and X is kind of the easiest first Dimension to introduce but technically displacement could be defined as say Delta y if it's in the y direction and things of this sort so however it's customary to introduce it simply as Delta X for displacement here and technically again it's displacement in the X Direction but in this particular chapter Motion in one dimension we're only going to be consuming uh uh we're only going to be considering one dimension and it'll be the X Dimension typically all right so displacement symbolize Delta X and the SI unit is meter it has units of length here and again want to contrast it with distance here so we've got two different uh paths here they both start at the origin and they both end up at the point 3 0 and so as a result the displacement is exactly the same in both cases you might think of displacement again as the straight line distance between your initial starting point and your final destination so and whether you actually take the straight line path doesn't matter displacement doesn't care it only matters where you start and where you end up where you start and where you end up and if it's the same in both cases then the displacement is going to be the same as well all right now the distance is definitely going to be different here notice the straight line path would be the shortest possible distance and its magnitude in this case would be the same as the magnitude of the displacement so however in this case here we can see that this distance traveled is actually going to be longer on that pathway even though the displacement is exactly the same so want to make sure you got that distinction again displ is a vector has both uh magnitude and Direction so distance is just a scalar with no Direction associated with it all right so if we took a look and said what is the displacement here so well in this case in going from the origin to 30 that's a displacement of three and assuming this was in units of meters we could say meters but we don't the units aren't given so we don't really know but it's three and we might say in the positive X Direction so notice it's not just magnitude we got to give a direction here and here it was in the positive X Direction it wasn't in the negative X Direction it was in the positive X Direction and notice I put this on a kind of classic cartisian here so but for the purpose of this problem we might just get rid of the y- axis and stuff like this although I really want to set this up for dealing with both the X and Y directions in the next chapter so uh why it's introduced this way cool same thing here if I said calculate the displacement it'd be exactly the same it' still be three in the positive X Direction so second we're going to move on to Velocity here and just like displacement velocity is a vector it has both magnitude and Direction now in this case I might tell you that I'm going down the freeway doing 65 miles hour so and that sounds like a velocity in a customary everyday vernacular we might actually call that a velocity however physics is really specific because I didn't include a Direction with that that is actually not a velocity it's not a vector it is simply a scaler and the scaler equivalent we call speed so speed is the scaler I can say I'm doing 65 mph yep yes you are that's uh magnitude no Direction but if I say I'm doing 65 miles hour due north that now is a vector quantity has both magnitude and Direction and that would be considered a velocity all right so uh we like to use miles per hour uh in driving and things of this sort but the SI unit is me/ second you might recall that that's a derived unit unit of length over time and that's actually how velocity is defined so the technical definition of velocity is an equation it's the change in position over the change in time you might recall that change in position that's displacement so it's really the displacement over the change in time now it works out quite often that you know your given time period you say from Time Zero to time 10 seconds well then delta T is going to be 10 seconds and so sometimes people leave this Delta off but it technically is a change in time because what if you didn't start at Time Zero what if you had some big journey and you decided Well from this point in the Journey to the End or you know something like that so it is you know proper to put the Delta there although if you see it left off on occasion no it just means they're starting from time zero so but technically this would be position final minus position initial over time final minus time initial the change in anything is always final minus initial and again if you've got time final minus time initial where the initial time is zero that's why it just turns into the time Final in such cases while you'll see it written sometimes improperly uh just like that you might even see me do it on occasion all right so there's your definition of velocity and again it has both magnitude and Direction so but there a couple different situations we might deal with when it comes to Velocity we might deal with constant velocity so and constant velocity means your velocity is not changing so and keep in mind this means you're still moving but your speed is not going up or down down if you will and I said speed I just want to make sure you realize the magnitude of your velocity is not changing and so it's just like you're cruising down the road doing 65 mph down the freeway and that speed is not changing that would be constant velocity so but it also means that your direction is not changing so it turns out that if your magnitude is not changing but your direction is like you're you're taking a turn at a constant speed that actually is not no longer considered constant velocity we have a a whole section on like rotation motion and things of this sort where we'll deal with such situations and so uh sometimes you can have your speed not changing and your velocity changing as in such cases where you're you're on a curve all right so but we might still in this section we're going to be dealing with really largely Motion in one dimension and so we don't have to worry about going around a curve and stuff just yet uh and so in this case when we deal with constant velocity the other option is going to be a varying velocity where the velocity is changing so what we're going to find is the only the only situation we're really going to consider is one the the velocity is varying uniformly it's either increasing or decreasing at a constant rate we'll find out that rate is what we call acceleration but we'll get there in a little bit so but that's the only other situation we're going to deal with and so we'll find out in such cases that it's advantageous to try and calculate the average velocity so and just like if you want to calculate the average of two things well you take like say you want to take uh the average of my weight today and my average of my weight tomorrow well you take my weight today and my weight tomorrow and add them together and divide by two and that's a essentially what we're going to do here as well in dealing with say a varying velocity is you're just going to take the initial velocity and the final velocity and add them together and divide by two or add them together and multiply by a half same diff you'll see it written both ways so another equation that'll be customary when dealing with a varying velocity on occasion as well all right so we've introduced a couple equations one was the definition of velocity and one is just convenient to use when we're dealing with a varying velocity so and now we're going to introduce some really simplistic motion diagrams uh the last lesson in this particular chapter is going to be all about motion diagrams we'll give a little more comprehensive treatment to it so but here we're definitely going to talk about some really introductory motion diagrams where we're plotting position on the y- axis versus time and I know this is a little confusing CU you're like you're plotting the X position on the Y AIS yes yes I am and it is customary sorry I didn't invent the rules here so but we're plotting the position in the only Dimension we're concerned with the X dimension on the y- axis and then time on the x-axis well we can see in this first graph we've just got a horizontal line notice that means that the position never changes as time progresses so well if you got no change in position that means you've got no displacement and if you got a big zero for your displacement well then your velocity is zero as well you might recall that slope is defined as rise over run or the change in the Y over the change in the X well in this case the change in the Y and the change in the x is going to correspond to the change in position over the change in time well the change in position over the change in time that is your definition of velocity so the slope on this position versus time graph is velocity and so if you've got a horizontal line that means your slope is zero indicating that your velocity is zero another way to recognize that all right the next one here so we've got a nonzero slope now so it is a positive slope it's uphill and in this case that's going to correspond to a positive velocity so also because it's a straight line it's a constant slope and again on a position versus time graph your rise over your run is your change in position over change of time it is your velocity and so if you've got a constant slope you've got a constant velocity now you might being tempted to be like well sh the velocity was constant back here well yes constantly zero but I definitely want to distinguish between a velocity that is Zero versus an actual constant velocity and you should see that you know in this case with a positive slope it means your position's going up as time progresses you're moving forward it's often customary in dealing with Motion in one dimension to Define your direction as just the positive X Direction versus the negative X Direction and so the the sign often is your direction so to speak so in this case we have a positive slope that is a positive velocity which in this case would mean we're moving forward in the X Direction in the positive X Direction whereas had we had a downhill slope a negative slope that would be a negative velocity which again in Motion in one dimension would mean we're moving backwards in the negative X Direction so to speak all right finally we've got a situation where we've got a slope that is not constant in this case and because your slope is not constant again the slope is equal to your velocity if the slope's not constant your velocity is not constant we'd call this a varying velocity now one thing to note you can tell here that anywhere along this graph here your slope is positive the entire time and you can see just in terms of X versus T you say well what's actually happening here um well your position is going up as time progresses that's true so this thing is moving forward but we can also see a little more than that and so in such cases where your velocity varies it's often customary to talk about what's known as the instantaneous velocity so let's say I want to know what's the instantaneous velocity right at that point along the way and it turns out what you do is you draw a line tangent to your curve right at that point so and the slope of that tangent so and again slope on your position versus time graph equals velocity the slope of that tangent line is the instantaneous slope at that point and is equal to the instantaneous velocity at that particular Point well we can see on this graph all along the way the slope is getting more and more and more and more and more positive which means the velocity is getting more and more and more positive and if the velocity is getting more and more positive that means this object whatever it is is moving faster and faster and faster in in the positive X Direction cool that's velocity so the third term we're going to Define here is acceleration so and just like displacement and velocity acceleration is a vector not a scalar and so it has both magnitude and Direction now in the case of displacement it was the vector and we kind of said something like distance could be the scalar version uh with velocity we said velocity is Vector and then speed was the scalar we're going to have no scalar equivalent for acceleration acceleration is a vector it has both magnitude and Direction now if you look at the definition of acceleration so well first let start with the unit it's a derived SI unit of met per second squared so we can kind of see where that comes from based on the definition so now acceleration again being a vector I probably should have been using this a little more liberally I'm I'm really bad about remembering those arrows sorry I forgot them on both displacement uh as well as on uh velocity so but acceleration is equal to the change in velocity over the change in time that is the textbook definition for acceleration all right so to have an acceleration you have to have a velocity that is changing and students often struggle with the difference between velocity so and acceleration now if you have a velocity it means you are moving that's that's it if you have an acceleration it means not only are you moving but most of the time it means that your speed is changing now technically mean that your direction is changing but we'll deal with that in a whole other unit for now it's going to mean not only that you're moving but that how fast you're moving is changing so a lot of people think of of velocity and acceleration in similar fashion they think like oh I'm moving really fast you know that must be I'm accelerating or you know something like this again it's not about how fast you are moving or how slow you're are moving if you're moving you have a velocity period it's is your speed changing so think about it this way so a lot of people think of like you know if I was going down the road on a motorcycle at 3 300 mil hour that'd be crazy right so the wind blowing in my face and all sorts of craziness going on and they would think it you know because it's such a a rush and and and such a kind of forceful experience they might associate a little more to it than they should but think about the same thing if you were doing 300 miles an hour sitting on an airplane so taking a nap so and now you don't have the wind in your face and stuff like that and so I want you to think of that situation for here to start because that's the one I want to want to go with I I don't want the the adrenaline of of riding a motorcycle and the wind hitting you in the face and all that stuff as part of this discussion I just want a nice calm airplane ride now here's the deal if you're flying through the air at a cruising velocity of 300 m/ second in some particular direction and I said me second 300 miles hour in some particular direction so as long as it's just constantly 300 miles per hour you have a constant velocity you do not have an acceleration so and it should feel very calm in your your ride however think about taking off in that airplane so as you're taking off that plane is not only moving but it needs to get to a velocity that's fast enough to generate enough lift on the wings to get that plane into the air and so it's not only just moving it has velocity but it has a velocity that is speeding up faster and faster and faster as it goes down the runway and that's what throws you back in your seat so and the key is you have a velocity that is changing in this case it's increasing and so you have an acceleration and so often times you can distinguish between when you have an acceleration and when you don't is if you're being thrown back in your seat so to speak that's key you have an acceleration whereas if as all as you're moving is constant velocity you're not really being thrown back in your seat and the reason I want to you know not use the motorcycle analogy is a lot of people feel like oh I'm riding the motorcycle at 300 miles hour I'm being thrown back well you're being thrown back because of air resistance not because you're accelerating and that's why I didn't want to go with that example why the airplane's a much better calmer example as as long as you're at cruising velocity and it's constant there's no acceleration and it's a very calm ride but right as you take off and you're thrown back in your seat that's when you have acceleration so hopefully you see that difference all right so we want to deal with three situations analogous to what we saw with velocity but now instead of plotting position versus time we're going to plot velocity on the y-axis time on the x-axis and so in this case in this graph here notice this is no longer about position and so my question for on this first one is are you moving are you moving and that's tricky don't answer so quickly because if we were doing position versus time if this was position well then this would mean your position's constantly the same value and not changing and so you know you're not moving but that's not the case here here it's your velocity that is not changing but it's not zero if your velocity was zero down here that means you're not moving but here you've got a positive velocity it's somewhere up the y- AIS you're moving but your slope is zero and your velocity is not changing so we might call this constant velocity so keep in mind here that we've got velocity on the y-axis time on the x- axis and again slope is equal to rise over run and rise over run in this case is equal to the change in velocity over the change in time the change in velocity over the change in time the slope on this graph is now equal to acceleration whereas again that slope on the position versus time graph was equal to Velocity this is where students start to get confused again we're going to have a whole lesson on these motion diagrams to make sure you really understand the difference so but in this case the slope on the velocity versus time that is the definition of acceleration and so if your slope is zero that means your acceleration equals zero as well okay let's go on to the next one here so here we've got again velocity versus time you've still got a constant slope here but now you can see your velocity is not the same the whole time your velocity is not constant your velocity on the y- axis is going up and up and up and up and up as time progresses and so now you've got a velocity that is going up over time you now are not at constant velocity you actually have an acceleration and we might call this uniform acceleration or constant acceleration because again on a velocity versus time graph the slope is equal to the acceleration well because this is a straight line it means you have a constant slope constant slope means constant acceleration I.E which means more more commonly is going to be called uniform acceleration you can call it constant acceleration there's nothing wrong with that but you're going to hear this word uniform used pretty commonly and then finally in this last one here now it's not a straight line it's a curve and so in this case your slope is changing all the time and if your slope is equal to your acceleration then your acceleration is changing every time and here we're going to have a varying acceleration now here's the deal you are going to deal with problems in kinematics over the next couple of chapters that deal with this situation where there's no acceleration I.E constant velocity you're going to deal with mathematical problems calculations where you have a uniform acceleration a nonzero but constant acceleration but mathematically you're probably never going to deal with any kind of calculations dealing with a variant acceleration you might deal with it graphically and have to identify it graphically or something like this but you're probably not going to do any calculations with it throughout the entirety of this course FYI it would be a horrendous pain in the butt to treat okay so that is acceleration so now we've got displacement velocity acceleration and let's do our first actual physics calculations so now we're going to do our first actual physics calculations and if you're taking this as part of my master course uh then you've got the study guide and the questions are right on the study guide with plenty of room for you to work out the answers and take notes and all that stuff so if you don't I will make sure the the the questions actually end up on the screen here but the first question here says a man makes one complete revolution around a 400 met circumference circular track what is the magnitude of his displacement so we're going to go one full time and that circumference is 400 m the question is what is the displacement well again displacement only cares about where you start and where you finish and you kind of think of it as the straight line distance between those two and so in this case the displacement would be zilch now the distance traveled would not be zero the distance traveled would be 400 m of circumference here right so but the displacement is indeed zero so definitely just showing this example to make sure you realize the distinction between displacement and distance all right next question related to the first one it says a man makes 1/ half of a revolution around a 400.0 meter circumference circular track what is the magnitude of his displacement we'll find out that 400.0 part was all about uh sigfigs uh so it would make this kind of a little bit trivial uh all right a little bit different than the first question here so in this case we're starting at a certain point and we're only going to go halfway around the track now again we know the circumference of the whole track is 400 m and the question is what's his displacement now well it's not zero and it's not zero because the point where he started and the port where he ended up are not the same point so but again we don't want the distance and again if you think well a full circle is 400 MERS so a half circle would mean he's traveled 200 M well that's true the distance distance he's traveled is 200 M but again that's not the question the question is what is the displacement and in this case that is the straight line distance between the point you start at and the point you finish at which is definitely going to be less than the path we took less than 200 met but how do we figure out what that is well it's going to require you to remember just a little bit of geometry from back in the day you might recall that the circumference of a circle is equal to 2 pi r and so we can use the the circumference given of 400 m to figure out the radius then use the radius to to figure out the diameter because this would be the diameter of that Circle the other thing you might realize is that 2 * the radius is the diameter and so sometimes you'll see the circum circumference simply written as Pi times diameter and we can use that so but again whether you use the first one and solve for the radius and then double it or just solve for the diameter directly take your pick I'm going to solve for it directly it looks a little bit easier and so in this case we're going to have 400.0 M = < * the diameter and we'll just divide through by pi and the diameter is going to equal 400.0 m all over Pi now here you're going to see why I made it 400.0 MERS not just 400 truth be told that was a recent edit uh cuz I didn't want only one Sig fig so now the it ends in a zero right at the decimal that zero is significant that four is definitely significant and so these zeros are now in between significant figures and their significant so now we've got four significant figures if it was just 400 without the 0 at the end that would only be one significant figure and I definitely didn't want only one sign all right but we're definitely going to let our calculator do the work for us here when dividing by pi and so we're going to do 400 divided by pi we're going to get7 and some change and the change here I want to go at least five five digits if I want to end up with four sig figs uh and so it's going to be 3 2 and again my four sig figs here there's your first there's your second there's your third there's your fourth and the reason I included the fifth digit is just so I know if I need to leave that and round down or to change it and round up well in this case with a two following we're just going to round down and leave it alone so we'll just get rid of that two and there is your diameter of that Circle which in this case again is the magnet itude of the displacement and no said just asked for the magnitude because it'd be hard to ask for the direction you know based on what was given here and stuff like that obviously the way I drew it you could say well straight down chat across the track but technically if you were at a track you wouldn't be traveling straight down you'd be traveling across the track and that would be in certain direction but that's why I only asked for the magnitude and not the associated Direction all right the next question here says that a car travels 300 miles due north in 5 hours what is its average velocity during this journey all right so in this case just the definition of velocity and it's displacement over time here all right in this case both of those are given so it travels a displacement of 300 miles du North in a time of I believe that was 5 hours yeah 5 hours and so in this case 300 divid 5 we can see this out to 60 MPH so it's not SI units but the question ask us to give SI units but we're not done so because the question says what is the velocity not simply what is the magnitude of the Velocity so but again the velocity here is just going to point in the same direction as uh uh uh the displacement in this case and so it's going to be North cool next oh by the way sigfigs we had one SigFig provided in both our numbers and so our answer has to show up with one Sig SigFig well 60 fortunately has one SigFig all right next question a car accelerates uniformly from 0 to 60 mph in 6 seconds what is the magnitude of its acceleration during this time all right we look at that definition of acceleration we've been provided with and acceleration is just equal to the change in velocity over the change in time and again this didn't actually ask for SI units and I'm not expecting you to convert this to SI units but I want you to especially for those who in the US to use units you're familiar with and come comtable with before we go full on metric system here so in this case that's going to be final velocity minus initial velocity and one thing to note a lot of people and a lot of textbooks write initial velocity as V not you probably see me using these interchangeably I will try to be consistent but I probably will fail on occasion so but it's like V at Time Zero is what that means so whether it's V initial with a little I or V not either way but often V final is used in either case all right so change in velocity final minus initial all over the the change in time and so in this case we're going from 0 to 60 M hour so that's going to be 60 miles hour minus 0 all over the course and I believe it was 6 seconds so this going to have a little bit of funky units here so but 60 - 0 is 60 divid 6 is 10 and it's going to be 10 miles per hour per second what this means is that its velocity is speeding up 10 miles hour every second and so initially it's going zero 1 second later it' be have a velocity now or a magnitude of velocity of 10 mil per hour another second later it'd be up to 20 mil per hour another second later it'd be up to 30 miles hour it's getting faster and faster and faster and the rate at which that's happening is 10 miles hour faster every second okay now this is not your normal unit notice if we wrote this out a little bit differently we could write 10 miles per hour per second and this actually looks worse not better so and again these are not the normal units we're going to see and definitely not SI units but again this is going to be why I want you to think about uh the SI unit of meters per second squared as me/ second per second just like we have miles per hour per second you can see like oh 10 miles per hour per second means it's getting faster 10 miles per hour every second same thing in the next problem we're going to see an acceleration of 10 m/s squared but I want you to think of that again as 10 meters per second per second but we're going to use the exact same set of numbers here but go metric system instead with different units so now a car accelerates uniformly from 0 to 60 m/s in 6 seconds what is the magnitude of its acceleration during this time the process is exactly the same and so change in velocity over change in time which is again is V final minus V initial all over that change in time which now is 60 m/ second- 0 all over 6 seconds and now again my preference would be for you to look at this as being 60 m/ second I'm sorry 10 m/ second per second but the way you're going to formally write that is 10 m per second squared that's the unfortunate thing because the moment we make it 10 meters per second squared students don't think of it the same way they don't think oh when I see that that means it's getting faster and faster and faster 10 m/ second every second and that's why it's my strong preference that you look at the units for acceleration and divide it up as velocity over time meters per second per second and when you see this well it started at zero so 1 second later its velocity or the or its magnitude it's velocity at speed would be 10 meters per second faster so Time Zero it was at zero velocity at Time 1 second it's now got a velocity of 10 m/ second at time equals 2 seconds it's now got a velocity of 20 m/s at time equals 3 seconds it's now got a velocity of 30 m/ second it's getting faster and faster and faster now one thing to note especially with Motion in one dimension again direction is often defined when we're dealing with motion and direction is either forward or backward which means either positive or negative which usually refers to positive X Direction Negative X Direction so one thing to note in dealing with accelerations so in this case we saw that the acceleration came out positive because the final velocity was higher than the initial velocity but said this had been the opposite let's say instead this thing had been cruising down the road at 60 m/ second and hit the brakes and slowed down to zero over the course of 6 seconds and now of a sudden you would have had 0 - 60 m/ second over 6 seconds and you would have got -10 m/ second per second and it turns out the positive versus the negative that's actually considered a direction in this case like the positive X Direction the negative X Direction it's part of the direction when we're dealing with Motion in one dimension and so now of a sudden what does that actually mean well in this case what a positive acceleration versus a negative acceleration means is is it in the same direction as your velocity or opposite direction as your velocity so in the first case with a positive acceleration a positive acceleration is in you know is in the same direction as your velocity and your velocity is getting faster and faster and faster so but in the second case so it turns out your acceleration actually is in the opposite direction so our velocities were positive the whole time from 0 to 60 or in this case from 60 down to zero but they were in the positive the forward Direction the whole time so but the acceleration is in the negative Direction and so here's the deal when your acceleration and your velocity point in the same direction it means you're speeding up faster and faster and faster but when your acceleration and velocity point in opposite directions like when you put your brakes on on your car so now you're getting slower and slower and slower you're slowing down so big distinction to understand there between uh the signs on acceleration and velocity so that'll become important we start doing other kinds of problems and we'll find out that uh there are certain things we can do when your displacement your velocity your acceleration all point in the same direction so and turns out your sign is not going to be the most important thing in your calculations but if your displacement your velocity acceleration don't all point in the same direction you know keeping track of your signs becomes super important as we'll see in the next lesson now if you've liked this lesson then like the video Happy study