So the first thing that we're going to be looking at is the distinction between distance versus displacement it's a slide distinction but it is definitely important to know so displacement is that final minus the initial point and its path independent versus distance which is the total amount traveled and its path dependent .
Um and so we'll take a look at an example without definitely make it a lot simpler so say we have um this path that we took right um and I started from this point and I went a B C and then to D and then back to a so this is my initial this my final point so what would the displacement be if I if I asked what the displacement is so and let's just assume .
All these are one meter well the displacement is the final minus initial so zero meters the distance however is just how much I travel so the total amount that I traveled which is 4 meters so we can see that distance and displacement although for the most part is not going to make a difference but in certain cases especially when you make .
The same changes back it will make a huge difference and we see that with velocity and speed so speed is distance over time not just displacement and velocity is the speed including some type of direction so you know if I'm going say north at 10 meters per second versus south at 10 meters per second all right my speed may be the same my speed .
Is both 10 meters per second my velocity is very different my velocity is 10 meters per second north and 10 meters per second south ok so the speed with direction that's where velocity is different in these cases so here's an example I travel five meters north in five seconds what is my velocity and what is my speed .
So let's just see so velocity equals the amount we traveled over the time so five meters over five seconds one meters per second so is that the velocity or is that the speed so this by itself would be speed and if we were to look at the velocity we would just have to have the speed plus the direction so 1 m/s and .
Then we need a direction well it's said in the question that is going north so now I'm going to look at acceleration so acceleration is the velocity per unit time so it's the change in velocity actually and so an example of this would be I'm on a train going 50 meters per second and I slow to a complete stop in 10 seconds what is my acceleration and .
One thing to note about all these is that there is a difference between that positive velocity and a negative velocity as well as a positive acceleration and a negative acceleration and we'll see that here so the first thing we do is we say that our initial speed is 50 right and our final speed is zero right because we went to a complete .
Stop so our equation is Delta velocity over time so does velocity is always the final minus initial sorry and then this is over our time in our time we took this 10 so we see that it's negative 5 and then our units would be meters per second over second or meters per second squared .
All right so that's pretty much it is negative 5 meters per second squared is our acceleration so the next thing we're going to look at is pretty important it's being able to read a graph and interpreting that into you know velocity and acceleration and this is something that the MCAT loves the test because it doesn't so much test you on numbers or .
Manipulating numbers they're just manipulating graphs and seeing if you can interpret them so in this question it gives you a graph distance versus time and it says in each of the areas so in each of these you know locations or segments of time is the velocity negative positive or is it zero and also the acceleration um so I guess the .
Easiest way to figure this out is well what is the relationship between velocity air and distance so velocity is the derivative of the displacement over time right and all that means is that it's the same thing as the slope so velocity is the slope of the distance versus the time graph right .
Same thing with acceleration is the slope of the velocity versus time right so that's one thing to keep track of is noting that no for the MCAT you don't actually need to know derivatives you don't need to know anything like that but this is the only thing that is somewhat calculus related is we need to know slopes so velocity is the slope of .
The graph of distance versus time and acceleration is the slope of velocity versus time all right so let's think about that right here so we have this graph right there in this location if we were just to look at velocity the slope remember is the rise over run so let's write that against the slope for if we forgot the equals rise over run y2 minus .
Y1 over x2 minus x1 so something like this would have a positive slope something like this would have a negative slope and something like this would have a zero slope right so we'll see that right here so in this first case would you say that a has a positive negative or zero slope we would say that for sure it has a positive slope and and .
B we would say that this has a zero slope see this one's a little tricky but it's still going in the positive direction it just may not be going as straight as we would have liked so it's still positive and D would be negative all right so those are for the velocity so that's for the velocity but a good way to think about this since we're .
Going only to acceleration is let's graph a velocity versus time plot all right and this will help us when we have to make acceleration because it's hard to find it the is gonna be positive negative or zero just from the distance versus time so let's do that so it's not important that we know the .
Exact numbers it's important to know whether that's negative positive or zero and if it's flat or if it's going in a line so we'll see that right here um so this right here has a positive slope and if we note here if we broke these up into little segments we would know that the slope is exactly the same at every single point in time so we know it has .
To be a straight line like that right and if we got B we know it zero and we know it's all easy oh if we broke this up into little segments of time it would always be the same this one's a little bit trickier the way we know that it's positive we know that it has a positive slope but you don't know really what it is but we do know at this point it has a .
Zero slope right because it's about to go to zero so this is zero so we know it time three it has to be zero and at this point it's fairly positive it has a slope like that right and this slowly goes down and down and down so we know that this graph has to look something like that right and then deep has a negative slope so we know that it has to .
Be flat like that right so that's how we got between the velocity versus time versus the distance versus time that's how we got that graph and so the next thing that we want to know is how do we get the acceleration from this crap well we do the same thing we say that what's the acceleration at each specific point well we know this one's a flat so it has .
To be zero this one's also flat so it has to be zero this one though is negative right because we had a negative slope going down but this final one zero as well so there to ask us what is the velocity acceleration is a negative positive or zero well here we know it's positive zero positive and negative here we know it's zero acceleration now zero .
Negative and zero right and sofie's we see back here it shouldn't make sense it's hard to just go straight from distance versus time all the way to accelerate but it's something that we have to be comfortable doing and the only way to really do that is if we saw this distance versus time – velocity versus .
Time if we don't know calculus that is