hey everyone today we're going to be looking at three different types of motion graphs physician velocity and acceleration all Against Time we set up these two graphs we'll find some interesting relationships between them we know from our formula that velocity is change in position or displacement over time position is on our y-axis so a change in this position is how far up or down that axis we move and a change in time is the change on our x-axis this sounds a lot like rise of a run or our slope that makes the slope of a position versus time graph our velocity we can use the same logic to see that the slope above velocity versus time graph gives us our acceleration now let's discuss the difference between average and instantaneous velocity we know that average velocity is displacement over time since displacement only cares about initial and final position as we've talked about before we can just draw a straight line between two points and the slope of that line becomes our average velocity see that here from T1 to T2 and T2 to T3 instantaneous velocity is a bit different we want to know the velocity at a given instant to do this we draw a line that is tangent to the curve of the graph like right here this means that it only touch the graph once at the instant that we want to know our velocity which here would be at our T3 the slope of this line right here will be the instantaneous velocity at the x or the time value of our graph and as before acceleration velocity will have the same relationship as velocity does with position so you can see here the tangent line for instantaneous acceleration in our average acceleration going from initial to final Point here now we're going to look at some diagrams specifically for these four types of motion zero speed constant speed acceleration and deceleration for zero speed it's quite self-explanatory think about it when an object is at rest both the velocity and acceleration are at a constant zero that's the position time graph will be a horizontal line with the Y position value unchanging the slope of a horizontal line is zero so our velocity time graph stays at zero on the y-axis and the slope of that graph which represents our acceleration is you guessed it also zero for constant velocity we have this animation to help out the car is driving along the x-axis at a constant speed for each second of motion the car moves the same distance so the position time graph has a straight but diagonal line slope of this line is our velocity and we can see in this graph and in the animation respectively that neither the slope nor the velocity are changing thus our velocity time graph has a horizontal line notice that it still has a non-zero y value we take the slope of this and we'll get zero so once again our acceleration is going to be a horizontal line at our T equals zero let's work backwards to look at constant acceleration we can see here that our car is moving faster and faster in our graphs show a constant acceleration with this horizontal line above zero right here to achieve this the velocity time graph will have to have a constant non-zero slope which we do see here is true it increases the same amount every second so it is a straight diagonal line starting at the origin because this car started from rest this then means the slope of a position time graph is changing since velocity is increasing the slope of our position time that's also increase we start with a low slope close to zero and it slowly becomes more and more steep now let's look at constant deceleration or are Vehicles slowing down to a halt deceleration means a negative acceleration it is still a constant so still a horizontal line but it would be below the x-axis to indicate that it's negative since we didn't start from rest our velocity graph will start higher up on the y-axis since the acceleration is negative we have a constant negative slope and the graph stops when it hits the x-axis as that's when our velocity is zero the position graph will once again be curved because there is a change in velocity but this time we're starting with a large velocity a large slope and it slowly shallows out over time until is a perfect horizontal indicating that the car is at rest now these graphs don't have to be just for cars or driving they apply to any situation with the motion described for example the graphs for a constant acceleration car would or are constantly accelerating car would look exactly the same as this block would sliding down a ramp this is constant acceleration so is the block slide down our graphs will look exactly the same thank you guys