[Music] in this video we're going to be taking a look at kinematics and we're going to do a full overview of six main areas that cover uh terms calculations strategies ideas in order for you to have a good foundational understanding of kinematics that will be really helpful for AP Physics 1 but also for any High School course or even introductory college courses as well okay so let's get started um we're going to start off with taking a look at some different terms um and ideas some basic stuff about um terminology and how to understand different words that are going to make a significant change in what you solve for and how to interpret graphs and other ideas later on we're going to start off with constant motion after that we're going to take a look at some main Concepts calculations and take a look at some motion graphs and then take it a step up from there and take a look at acceleration same thing Concepts calculations and graphs and embedded in that we're going to take a look at some problem-solving strategies and how to isolate variables and then the last portion we're going to start taking a look at two different things where it's going to be taking a look at free fall motion objects only affected by the influence of gravity its main Concepts and important values and then our most complicated part of our kinematics overview is likely going to be our projectile motion which we're going to talk about Concepts problem solving how to set up everything take a look at everything that's going on to develop a good problem-solving approach to those different sorts of questions and different calculations all right so let's go ahead and get into the first topic which is the terms um scalar versus vector and ideas so the first thing we're going to start off with is taking a look at something called a scalar and something called a vector and we're taking a look at these two things um each of the values we're going to be looking at throughout this overview is either going to be a scalar or a vector so a scalar is anything that has just a magnitude which basically just means how large the value is which is basically just represented by a number in most cases especially in physics and then with a vector it is something that has a magnitude and a direction and the direction is going to be a big piece in it because the direction is going to often determine whether something is positive or negative so these are things that are a little bit more descriptive that we're going to be using a little bit more often in physics and they will have positive and negative signs which will tell us the direction so common scalars would be things such as time speed and a distance so these things are just purely a number value to tell you how much of something you have the amount of time that's elapsed how fast you're moving and then the actual length that you've traveled that's time speed and distance all of these must be positive because they are scalar values when you're taking a look at speed speed is actually distance over time and since you're taking two scalar values that are just positive number values of the total length you traveled divided by the total time elapsed the speed is just going to tell you how fast you're going but it won't give you any descriptors about which direction you're facing now with time it is going to be in seconds speed is in meters per second and then distance is in meters so if you're not in one of those basic metric units then you definitely want to do a little conversion to get there four vectors ones that we're going to commonly use would be ones like velocity displacement and acceleration okay those ones are all more descriptive values and those can all be positive or negative which are just going to tell you a little something about its direction so is it going to the right or is it going to the left is it going up or is it going down is it speeding up is it slowing down and then the formula for velocity is displacement which is shown as a Delta X the change in position over time and then because displacement can be a positive or negative value that means that velocity can also be a positive or negative value which means it'll tell you which direction that the object is going for these ones these ones have some of the same units velocities in meters per second displacement is similar to distance which is in meters displacement is just telling you your final position minus your initial position which you would either call x i or X naught but that change in position depending on where you make your origin could be positive or negative and then acceleration is in meters per second squared it's how many meters per second you're changing per second all right so those are going to be six terms that are going to be very very common you want to make sure you understand what each of those mean um in order to solve questions accurately and effectively all right so now let's start at taking a look at constant motion now for constant motion or constant velocity that basically means that you're traveling and along the way you have the same displacement per time or per second so maybe if your constant velocity is 2 meters per second that means you're traveling exactly two meters on the DOT every second that you travel and then with constant velocity you're mainly just using one formula so if you take a look at the standard AP Physics 1 formula sheet it'll give you a formula that looks like this and it says final position equals initial position X naught Plus V naught the initial velocity times time plus one half a t squared okay that's a little bit over complicated for constant motion um what you all really need is just a condensed version of that so for something that's going a constant velocity that means your acceleration is always zero which means that you're not adding or subtracting any amount of velocity to the object or person per second your change is always zero which means you could be going fast or slow as long as your velocity isn't changing now for acceleration to zero we don't need this entire part because it's going to go down to zero and if you subtract the final position minus the initial position that just gives us Delta X so we'll say Delta x equals and then V naught means initial velocity but if the velocity isn't changing you could just basically say it's V for velocity so Delta x equals V times t or often times it's written as Delta X over t equals V and all of those things we just mentioned earlier which are displacement which could be positive or negative we have our time which is always positive and then we have our velocity which is in meters per second now when you solve for stuff you're basically getting two out of the three variables and then you're solving for the third and in this case if all of the forces are balanced then you're going at a constant velocity which would either be zero or some non-zero number all right now let's go ahead and take a look at the graphs for constant velocity we have position versus time graphs we have velocity versus time graphs and we have acceleration versus time graphs for the first one position versus time if you are not moving at all that means you have a completely flat line that completely flat line could be anywhere because if you have a constant position over time that means you're just standing there and you're at rest now if you take the change in position per time which is the slope that slope tells you the velocity because the velocity is the change in position per time if you take a look at this slope that is a zero slope that means you have zero velocity because you're at rest anyways so it's zero right at that x-axis and then four constant velocity as I said earlier that means all of your accelerations are zero so we are for sure going to have no change in velocity which means the acceleration is zero and the change in velocity per time is acceleration so again moving down you would take a look at the slope so this has a zero slope which indicates that this one is zero this one has a zero slope that indicates this one is zero now there's not too many combinations for constant velocity if you're moving forward at a constant velocity you're going to have something that looks like this and the steepness of that slope is going to tell you how fast you're going so if it's more upright so if it was slanted a little bit more upright like this that tells you that the rate of its position changing per time is greater which means it's going faster okay I'm not going to add that on there though because I don't want my graph to get too cluttered but if it was a flatter or less steep slope something that looked like this right under the green line that means that its rate of change is less which means that it's slower okay now this one does have a constant positive slope so it has a constant positive velocity and then again there's no slope here so we're going to have no acceleration there okay and then finally if you're going backwards or just back towards the origin then you're going to have a negative slope something that looks like this so if you're going backwards or towards origin you're going to have a negative slope something that looks like this and again that steepness of the slope is going to tell you how fast you're going so if it's more upright that means you're moving faster now since we have a constant negative slope that means we have a constant negative velocity and again there is no slope there so we have no acceleration okay so for the acceleration versus time graphs they are the worst descriptors of what's happening because all of them are going to be zero okay when you're taking a look at the position versus time graphs it's basically are you not moving moving away from the origin like the green one in the four direction or you're moving towards the origin or backwards like the purple one since it's constant velocity all of your lines on the velocity versus time graph are going to be constant which means they are going to be flat now moving to acceleration um acceleration is definitely one step up from constant velocity and acceleration is the rate that the velocity is changing per time and that is measured in meters per second per second and when you're changing how many meters per second or changing per second it is very commonly expressed as meters per second squared but just conceptually it's telling you how many meters per second you're adding or subtracting per second to the object okay now keep in mind that has nothing to do with how fast an object is actually moving it's just a rate that which is changing so is it slowing down really quickly or speeding up really quickly now there are three ways to accelerate you can either speed up which is obviously increasing your velocity you can slow down which is decreasing your velocity or you can change direction or turn now for this one there are various graphs just like we saw with constant velocity there's definitely a lot more going on with these but there is a position versus time graph velocity versus time graph and then acceleration versus time graph now for this one if you have something that's accelerating it won't have a constant rate of change it will have something that is curving something that has a changing slope okay as we said before when you take the slope of a position time graph that gives you the velocity versus time graph and you take the slope of a velocity versus time graph that gives you the acceleration versus time graph so same rule applies now if you're taking a look at this slope it starts out flat which it's like almost zero and then it gets progressively steeper in the positive direction so that means it is speeding up so something that is speeding up in the positive direction is going to move away from zero and be above the x-axis if it was speeding up in the negative Direction it would still get steeper which means it goes more and more upright okay now people will get confused because they'll see a line going down here but as you can see it's getting steeper and steeper right because it starts flat over here and then it has a little bit of a slant and then it's a little bit steeper here that's just going faster and faster in the negative Direction so this one would move away from zero but be under the x-axis to show it's going in the negative Direction okay again when you go from the velocity versus time graph to the position versus time graph you just look at the slope this is a constant positive slope and then the red one is a constant negative slope now the opposite of speeding up would be slowing down and when you're slowing down you have something that would maybe be going forward but not get steeper but it's going to get flatter so it's going to rise in the graph and then become more and more flat so that one's going in the positive direction because it's rising but it's getting more flat which means it's slowing down okay so because it's going in the positive direction we're going to be in the positive region over here but we're going to make it slow down by starting up here and then moving towards zero and then on the opposite and if something is slowing down and going in the negative direction that means it's getting lower on the graph but it's also getting flatter so the rule is if it's getting steeper or more upright that means it's speeding up in some way and then if it's getting more flat that means it's slowing down you know it's going in the positive direction if it's rising on the graph and you know it's going in the negative direction if it's going lower on the graph so my orange one is coming down and it's getting flatter so it's going down so that means it's in the negative region over here and because it's getting more and more flat it is going to head towards zero to show that it's becoming progressively slower and then our green one is a constant negative slope so it's going to be down here and then my orange one is a constant positive slope so it's going to be up here now let's take a look at the different formulas from the AP Physics 1 formula sheet we have velocity equals V naught plus a t Okay V is basically the final velocity so that's sometimes known as v f um and then we have a second formula which I did write earlier which is final position equals the initial position X naught sometimes written as x i Plus V naught T initial velocity times time plus one half a t squared and then for our final formula we have um final velocity squared equals initial velocity squared plus two a Delta X which is x minus X naught now with all these different formulas you have four different variables in each one which means if you were to solve for something and there's four different variables then you want to make sure you have three known variables so that you can algebraically find for your one unknown variable okay so for example your red one you have your final velocity your V your initial velocity your V naught your a your acceleration your T your time all them are the same thing as in like they have four different ones this one has your final velocity your initial velocity your acceleration and then your Delta X so for any of them if you have three out of your four then you can algebraically solve for the fourth if you are missing something else then you might have to use a series of formulas or an a substitution now the strategy I would recommend is one make sure you label your known and unknown variables number two I would highly recommend drawing a picture with the variables on your picture with arrows and then possibly including positive or negative values along with your picture and then number three you are going to isolate your unknown variable and then do a little bit of algebra to solve for your unknown variable all right so let me show you what this might look like so say for example you have an object that starts at five meters per second at a position of zero meters and then it travels 20 meters and then reaches a final velocity of 15 meters per second so then we know our Delta X is 20 and then we might be solving for acceleration okay so what I did is I labeled my known variables where they happened in the situation as in like the V naught happened right at the beginning my initial position is right here in the beginning um I did the same thing with my final velocity my final position and then I'm solving for my acceleration okay it turns out in this scenario I don't need any positives or negatives possibly if this started up high and then went down low I might have something like a negative displacement um so I drew my picture I added in the variables um I can put some arrows here there's not too much going on directionally but adding some arrows never hurts and then I see um if I need to add any positives or negatives doesn't look like I need to so then I can isolate and then solve for my variable okay so one thing you want to be comfortable with is you want to be comfortable with isolating a variable without the numbers so you may need to solve for things in variable form so let me just go ahead and solve for this a in variable form and if you want to add in the numbers later you definitely could so if I'm looking at my different formulas I know for sure I'm going to use the orange one the reason I know that is through experience and a process of elimination I see that I have V naught I have V and I have Delta X so if I have everything except my unknown variable then I'm good because I have three known variables and then one unknown variable now if I were to solve for that what I could do is I could go ahead and clear myself a little bit of room and what I would do is I would subtract V naught squared from both sides and then I have V minus V squared excuse me minus V naught squared equals 2 a and then I'll condense the x minus X naught to Delta X and then what I can do is divide both sides by 2 and divide both sides by Delta X which is basically dividing this by two Delta X okay and then my a would equal V squared minus V naught squared divided by 2 Delta X okay so you want to be very comfortable with moving variables around even if you don't have the numbers and doing something like that so you might need to report your answer in variable form if you needed to plug in the numbers and you go ahead and plug those in and press enter in your calculator and then get yourself an answer that way all right now going to Free Fall motion that means something that's un only under the influence of gravity so something that only has the force of gravity acting on it and no other Force so the term fall would make it sound like that something is maybe moving downward doesn't necessarily mean that anything that is moving um through the air without the effect of air resistance on it and only the force of gravity pulling on it would be considered something in free fall so something in free fall has a couple rules that it follows a bunch of rules that it follows if it is rising and it only has a force of gravity acting down on it then it would definitely be slowing down so if something is moving upwards and it has a positive velocity and then it has a downward negative force acting on it then it's definitely slowing down now the acceleration due to gravity is negative 9.8 meters per second squared that it's sometimes rounded off to negative 10 meters per second squared so if you have a positive number let's say that that initial velocity is 50 meters per second and something is tossed up in the air and you keep on adding negative 9.8 meters per second every second then eventually it's going to take that 50 and it's going to decrease and decrease and continue to slow it down until at its very Peak it has an instantaneous velocity of zero meters per second so at its peak it has an instantaneous velocity of zero okay so that's at the peak the very top of its flight now when it's going down it follows a similar set of rules but when it's coming down and it has that same force of gravity that keeps on tugging it downwards we now have a negative velocity so if we have a negative velocity and we are subtracting 9.8 meters per second every second it is going to become increasingly larger negative number which means that it's going to be speeding up because the direction of the velocity and the direction of the force are working together in this case and it's becoming faster and faster in the negative Direction just so happens that if it reaches ground level again so if it gets popped up at 50 meters per second and then reaches ground level again then your final velocity would be negative 50 meters per second same number and different sign so the rule is if you're Rising you're definitely slowing down at the rate of negative 9.8 meters per second squared at the peak you're going to reach an instantaneous velocity of zero after you tap zero and you come down and you're moving down in the Direction with the force of gravity and you're working together you're speeding up and you're still subtracting negative 9.8 or excuse me you're still subtracting 9.8 meters per second per second creating a progressively greater negative number showing that it's speeding up in the negative Direction hey that's basically straight vertical Free Fall motion now when you add a second dimension to that now you are going into projectile motion which is the first time we're taking a look at two-dimensional motion okay now we still have a lot of those same rules we still have the force of gravity acting on it we still have an acceleration of negative 9.8 meters per second squared um the way it's going to look is a little bit more complicated a little bit different so if we have some kind of initial velocity we're gonna what we're going to want to do is we're going to want to break it up in to a component which we can call V naught X and then we also have a vertical component which is called V naught Y and then we're probably given some kind of angle Theta right here so as something is moving in this two-dimensional motion it only has a force of gravity pulling on it downwards so projectile motion does something interesting to where it's moving sideways but it's horizontal velocity stays completely constant so whatever velocity that is to begin with say it's like moving two meters per second sideways it'll remain at two meters per second the entire time because there's no forces going in the horizontal Direction which means nothing going directly left and right we know that force of gravity is going downward so that is definitely the vertical Direction so our Vertical Velocity is going to start out great and then it's become smaller smaller non-existent at the very very top because it's not rising or falling for an instant and then as it falls down it's going to go faster and faster towards the ground as we spoke about before now that's everything in the vertical Direction so this one has the force of gravity in the vertical Direction which is going to greatly change the way that it acts so before we talked about constant motion and constant velocity that's how this horizontal portion works as it's moving from left to right and then we talked about accelerated motion How Stuff speeds up slows down and changes Direction which our red arrow our vertical one shows as it's rising it's going progressively slower it does change direction come down and go progressively faster because of that FG acting on it now when you're solving one of these problems lots of things to consider first of all you definitely for sure want to make a and X and Y columns so X meaning anything that's going left and right or horizontal and y column anything that's going up and down in the vertical Direction now the first thing you're going to want to do is if you have that initial velocity you want to go ahead and do a little bit of trig and you're going to end up doing V naught times cosine of the angle to equal your V naught X and then you're going to want to do V naught initial velocity times the sine of the angle to get your V naught y the reason why I use cosine is because you want the adjacent side matched up with the hypotenuse and then for the vertical side you want the opposite end of the angle matched up with the hypotenuse and then in the end you're basically doing something just like this to get your two different components okay now from there what you're going to do is let me just go ahead and make up some numbers and let's just call this 5 meters per second and then we can call this uh 10 meters per second so you're going to place your x value over here and I'm just going to call that V because on the X end it's moving at a constant velocity so there really isn't an initial and final velocity and then in the y direction this part is accelerating okay so if you are using the X side you're only going to use the one constant velocity formula which is basically um V equals Delta X over t and then on the Y side you're going to use the three acceleration formulas that we had on that previous page and what you're going to do is you're going to place your values in the columns that they belong to you're going to grab your x value and place it over here and you're going to grab your y value and then you're going to call it V naught 10 meters per second okay I dropped the Y because now it's in the Y column so now it's clear that it's a y value it's a vertical value now we can go ahead and do that in addition we know that's accelerating over here we discussed that it's a negative 9.8 meters per second squared because of the force of gravity and now some important values that you may add this all depends on the situation is if it comes back to ground level just like we said for the Free Fall motion then your final velocity will be negative 10 meters per second now that might be something valuable that you may use um again if something goes up it arcs like this just like this green Arc and comes back to the same ground level then your V naught and your VF are going to be the same values just different signs and then what you're going to do oftentimes is the thing that can be put into either of these columns is time because time does not have a Direction that's just the duration of time that it's in the air that applies to your vertical and horizontal components um other main things that you might use you might use a velocity a y velocity of zero meters per second because remember it reaches an instantaneous velocity of zero meters per second at the very Peak so if it says something about going halfway or to the top of your Arc you may use zero meters per second now there are a lot of variations for projectile motion problems so if you want to take a look at more of these variations or examples written out in a lot more detail then go ahead and click on the link up top okay other than that that's basically the foundation of how you'll set them up and everything from there just depends on the scenario you're looking at now let me go ahead and clear some of this space I can talk about one last idea okay that last idea is this um we have two different velocities that are operating in very different ways on the same thing what I'm talking about is your picture over here where you have a vertical velocity your right vector and then your horizontal velocity your blue one so they're both acting on the same time to show you how it's actually moving in reality which is this green Arc right here so if it's rising up and moving sideways to the right what it's actually doing is following this green Arc here so you're using both of those vectors separately now in different scenarios you might have to piece those back together and what you're going to use is a little bit of vector addition so if you want the final velocity of an object over here what you would do is you would use the tip to tail method that means that where one Arrow ends the next one starts so here's my horizontal component of 5 meters per second just kind of a number I made up off the top of my head for the X Direction and then at the tip of that Arrow um I'm going to start the tail of the next one which is this one this 10 meters per second okay so if I'm looking for the final velocity over here at the very end I have one vector to the right and one going downwards and then my answer is always going to be connecting the beginning of the first Vector to the end of my last one and that resultant Vector is going to tell me my actual final velocity so my actual final velocity isn't this negative 10 meters per second because that's only my vertical component it has to be combined with the horizontal one so if we went and used the Pythagorean theorem of a squared plus b squared equals c squared you would end up Square rooting the sum of the squares of each of the sides and then you would get the square root of 125 which is about 11.18 meters per second now the very last detail which is another one that make might come into play if you have to add some vectors together is possibly solving for some angles and if you need to solve for some kind of angle you can always use your inverse trig functions so in this case you would use an inverse tangent because tangent is opposite my opposite is my 10 and then my adjacent my adjacent is five so which is the inverse tangent of 2 because 10 over 5 is 2 and that would give me an angle of about 65.43 degrees all right so now that we've finished up the more complex details of two-dimensional projectile motion we are done with our kinematics review I hope that was helpful in being concise but also detail and giving you lots of good tips and strategies of how to do some problem solving as well as to understand a bunch of these physics ideas so thank you very much for watching and listening foreign