hey guys welcome to another video we're going to be going through the topic of motion which is the second part of general physics so this is just a quick summary of the points that we'll hope to cover today and uh we'll take a look at the first section here which is to do with speed and velocity so you've probably heard and you are familiar with the idea of speed which is just how quick you are or how fast you're going and so if you were to put it into mathematical terms speed is simply just the change in distance per second a fast object just happens to cover more distance per time unit than a slower object right so therefore the the the formula for speed is the total distance divided by the total time so so that should make fairly good sense for example if you did a 100 meter race and you finished in 10 seconds your speed would be 100 meters divided by 10 seconds which would give you 10 meters per second meters per second is the unit for speed and velocity so speaking of velocity then what is velocity well velocity is actually the change in displacement per second and the concept between speed and velocity is very similar but also very very important to distinguish now the question then becomes well what is distance and what is displacement and what's the difference between the two so the main key difference here is that displacement actually takes into account not only just the pure amount of distance but also the direction of travel as well so what seems to be a very good example here is if you imagine point a down below there and you imagine point b the difference between point a and point b is say 500 meters and let's just say that your starting point is a right so you start at a and then you walk to b and from b you walk back to a so the total distance that you've covered would be 1000 meters right because walking to b takes 500 meters and walking back to a is another 500 meters so the total distance is 1000 meters so according to the formula of speed 1000 meters divided by imagine you took 200 seconds i sorry 2 000 seconds to get that trip done imagine then the speed would be 1 000 meters divided by 2000 seconds which would give you 0.5 meters per second okay so that makes sense now displacement is actually a little bit more different because as i said before displacement actually takes into account the direction of your travel as well so from going from a to b is 500 meters okay so that's in a certain direction right you're traveling let's just imagine um a compass and so you're traveling east okay 500 meters now when you travel from b back to a what it means is that you're traveling in the complete opposite direction that you came from so essentially what what uh what it means is that um we're going to take the initial um initial distance of 500 meters and we're going to call that positive 500 and when you go back the other direction because it's going in the opposite direction we're going to call that we're going to put a negative sign on top of that so essentially what it means is 500 meters positive going to the right and minus 500 going to the left and when you get that it sort of cancels out and you get an overall displacement of zero another way of thinking about it is well ignore the total journey the total journey doesn't matter what's really important really in terms of displacement is how far off you are from your original starting point so if you started at a and you end up back at a your overall displacement the amount of change from starting point to end point is zero you haven't actually moved anywhere if you consider starting from a and so therefore that's another way of thinking about the fact that if you go from a to b and b to a the total displacement would be zero so therefore since velocity is displacement divided by time what you get is actually zero divided by two thousand seconds so despite the fact that your entire journey was two thousand seconds you actually have had no displacement or you have had no velocity uh as a result of that okay so i hope that makes sense so acceleration is um a term that you would use to ch to define the change in velocity per second okay so for example if something is speeding up okay going from 100 meters per second to 200 meters per second to 300 meters per second you can gradually see that it is speeding up and that speed up is what we uh call acceleration and how quickly something speeds up is essentially what the term defines so acceleration in mathematical terms is change in velocity divided by the time taken for that change to occur now positive acceleration is when an object increases in velocity over time which is for example you have a car at the starting line and then it you know starts to accelerate that is what we know as positive acceleration but uh an object can also decrease in sort of in its speed as well it can go from 100 meters per second all the way down to zero when it comes to a stop now that is sort of a negative form of acceleration which is of course when the object decreases in speed over time or decreases in velocity over time and we call that in other words deceleration so these are very very important terms we've covered so far we've covered the idea of speed we've covered velocity and we've covered acceleration just to sum it up speed is just distance over time velocity is displacement over time and acceleration is the amount of how quickly velocity is changing over time in other words change in velocity divided by the time taken for that to occur so as we know now that acceleration is the amount of change in velocity per time unit let's think of something an object to say falling um just on on on earth um as a result of free fall so like imagine you throw something off a cliff and obviously that object is going to fall down and you know just from looking at it you'd find that the object gradually increases in speed gets it drops quicker and quicker and quicker as it falls down the cliff right and that is the acceleration of the object due to the gravitational pull of the earth's gravity so any object that's falling in the presence of the earth's surface will be pulled specifically by a constant acceleration of 9.8 meters per second per second okay so that's a constant value no matter what you throw off a cliff it will fall and an acceleration rate of 9.8 now over time what tends to happen is that the acceleration starts to drop and the object starts to fall at a constant speed right the reason for that is because the air resistance starts to oppose the acceleration that the gravity causes so eventually the downward force of the gravity gets cancelled out by the force of air resistance which pushes it upwards so eventually the object will start to stop accelerating and it will start to fall at a constant velocity and we call that terminal velocity it might be easier to take a look at it on this white board let's just imagine a big cliff here and you throw a ball off the cliff what will eventually happen is that the ball will start to accelerate downwards and as i said before it accelerates at 9.8 meters per second squared so the ball will start to accelerate downwards as a result of the gravitational force of gravity but what tends to happen is that the acceleration starts to slow down over time and in a perfect world with no resistance it'll just accelerate at a constant rate of 9.8 forever pretty much until it hits the ground but the reality is not like that where we have air and what happens is that as the object starts to gain speed from acceleration what also increases is the resistance going upwards which is air resistance so air resistance is the force that pushes it upwards and the force that's sort of accelerating the ball downwards is going to be as i said the gravitational force so as the object accelerates more and more and more speeds up more and more sorry as the uh ball starts to increase in speed as a result of the acceleration the air resistance starts to increase and eventually what happens is the gravitational force gets cancelled out by air resistance right the force is equal and as you'll learn when it comes to the nature of forces later just because the forces cancel out doesn't mean the ball just suddenly stops what it does mean is the ball stops accelerating the ball is still falling but it's falling at a constant rate it's not actually speeding up anymore and when that happens the ball will just drop at a constant rate without speeding up as it falls and that is what we call the terminal velocity so i hope that makes sense now as we as we take a look at the idea of displacement and uh velocity and all that we come across these various graphs the very first graph we'll be looking at is the displacement time graph which is simply a graph to show the displacement per time unit and so here if we take a look at this particular displacement time graph you need to be able to interpret what's going on here so if you take a look at the first part right over here you can see that the displacement goes up and up and up and up up until this sort of six second mark here what that means is that over the time of six seconds you're getting a change in the displacement of this object so remember the displacement over time gives you the value of velocity which in this particular graph you can figure it out by measuring the gradient of the particular region you're looking at and the gradient is simply what you would you know calculate as the change in y axis divided by the change in x-axis so for this particular time frame from 0 to 6 as the displacement goes up from 0 to 10 if you wanted to calculate the speed of the object in this particular region you would just need to look at the gradient which is the change in y-axis so the change in y-axis is 10 because it went from 0 to 10 divided by the change in x-axis which went from 0 to 6. so if you were to do those calculations you would find that you get 10 over 6 which will give you 1.67 meters per second which happens to be the velocity of this object in this given region now between the region of 6 seconds to around 11 seconds you can see that the displacement is just a straight line what does that mean it means that there's no displacement which means that the object is stationary it's not moving at all it's just sitting there and as you make your way over to this right hand side part of the graph you can see that the displacement starts to go downwards what that means is the uh the object is sort of going back to its original um original position remember because displacement uh starts to go downwards as you go closer to your original starting point so you can see that the object is returning to where it had already started from and you can see that the line isn't a straight line the what that means is the velocity is not constant right because the gradient of each particular region of this wiggly line is going to be different because again it's not a straight line so when you see that the line is not straight you can tell that the object is not moving at a constant pace so i hope that makes sense key points if it's a straight line it's moving at a constant pace if uh if it's a straight horizontal line like this middle area there it means it's not moving at all if you see a line that is wavy that means that the object is moving at a certain speed that seems to be changing over time okay the other graph that we need to look at is the speed time graph a speed time graph pretty much plots the speed on the y-axis and the time on the x-axis so here there's various things that you can take note of now if you have a speed and time graph you can actually calculate the distance that is traveled in a particular region by calculating the area underneath the graph so if you take a look at this particular graph down below here you can see that there is a you know certain change in speed over this time frame right um and what you can do is the shaded area here that is the area underneath the region of the graph that you're trying to calculate the distance for and so remember the the area underneath a triangle is just going to be half the base times the height um so if you were to use that calculation you'd be able to figure out the amount of area that's present underneath the region you're looking at and that will actually give you the amount of distance that the object traveled in the particular region that you are looking at and the acceleration can actually be calculated by calculating the gradient of the region so again uh the gradient is the change in y-axis divided by the change in x-axis and you know if you were to calculate the gradient of a particular part of a speed time graph the result of that calculation is going to give you the acceleration of the object in that time frame so those two important uh those two things are very important for you to know because in an exam they might give you a graph and they they might get you to calculate these things and so you need to know how to do that um here we're just going to take a look at various speed time graphs and sort of interpret what's happening so here is an example of a car that's accelerating until it reaches its maximum speed so as you can see initially there is a fairly steep gradient right what that means is remember gradient is acceleration it means that the star the the car starts with its greatest acceleration meaning a steepest gradient at the start of the graph here and eventually you'll find that the line sort of plateaus horizontally and if it's a horizontal flat line what does that mean it means the speed is not changing it doesn't mean that the speed is zero because again it's still high up on the y-axis here it just means that the speed isn't changing what that means is that the speed is constant and that also defines the acceleration as being 0. no change of speed means there's no acceleration okay so it means that the car reaches its maximum speed and stays there for a certain period of time which also means that the car is not accelerating okay and a runner who accelerates with a constant acceleration gets to maximum speed and steadily decreases to a complete stop this is what this graph suggests so let's take a look at how that is the case now at the start here you can see that it the speed increases steadily we know that it increases steadily at a constant rate because it's a straight line right so it's a straight line going upwards meaning that there is a constant level of acceleration happening there now eventually the line results in a horizontal sort of plateau in this middle section here which means again speed is not changing it's constant meaning acceleration is zero so the runner has reached their maximum speed um and is not going up any longer and it's and is simply maintaining their maximum speed for a certain period of time and eventually you start to find that the speed starts to go downwards meaning that the runner is essentially losing speed and therefore they are decelerating uh eventually coming to a complete stop which is when the speed hits zero right at the end there now last one is an example of a skydiver from the time that she jumps until the time she reaches the ground including the point at which she opens a parachute so initially you can see that there is a very steep level of acceleration happening now is the acceleration constant no the reason for that is because clearly you can see that the segment where the speed starts to go up is not a straight line it's curved and when it's curved it means that there is no the speed is not constantly going up at the same rate which also means that acceleration is not constant and is changing and the reason why the acceleration is changing is something that we talked about before because when the jumper jumps off the plane initially they are going to be pulled by the surface of the earth by gravity and they will start to accelerate at 9.8 meters per second per second or 9.8 meters per second squared uh what that means is they start to fall at that level and they increase in speed by 9.8 every second but eventually this uh the the air resistance will start to uh push them upwards and they will start to lose their speed um or they will start to lose the acceleration so and as i said before therefore the acceleration seems to be not be so constant eventually and it starts to sort of decrease a little bit as a result of air resistance and then at some point the the parachute will open up and there's that sudden amount of huge deceleration that occurs when you suddenly open the parachute and so again when they open the parachute the deceleration isn't constant because you have that curvature of the graph occurring in that middle section and eventually as they fall below uh with the parachute open uh the speed eventually levels out and the speed eventually levels out as a result of what we call terminal velocity when the gravitational pull uh becomes pretty much uh equal to the air resistance the force that pushes it upwards and so the speed at which you're going down or free falling seems to stay constant which is signified by this flat line here and the speed um remains constant during this period so that's uh an important concept to understand so um i hope that was helpful that was uh quite a lot to go through any questions feel free to just comment down below and i'll try to help you out for those of you guys that are interested feel free to have a look at my patreon channel where i'm just adding various resources here and there once i finish the entire physics syllabus here on youtube i'll probably go through past papers i have already done so for a lot of the biology and chemistry so for those of you that are taking that you might want to check that out otherwise i will see you in the next video