let's call that as a x-axis that's what it means and it is changing with respect to the time okay and from this graph from this graph or from the position time graph we need to find out the average velocity between the different time intervals okay so what we are interested in calculating from this position time graph is what is the average velocity between this range what is the average velocity in this range so in each range or in each time here we have to find out the average the velocity so what is the average velocity is in order to find out the average velocity what we need to find out is the position the final position the initial position and the time difference so the way it is defined the average velocity is x f what is f stands for the final position and this is the initial position that's the final time and this is the initial time so we need to know the position okay so let's first calculate between 0 to 2 second or in this range here between 0 to 2 seconds here so at time 2 t equals to 2 second what is the position the position is 5 and at time t equals to 0 what is the position that is 0. so just plug in in this equation at time equals 2 second the position is 5 and at time goes to 0 second the position is 0. so you see now you click you can clearly see here from this graph so this is the final position at time t equals to 2 second and this one is 5 so just plug in 5 and time equals to 0 what is the position here this is 0 and this time is 2 minus it should be 0 here okay so i'm just making small correction here although mathematically it is correct so 5 over 2 is 2.5 meter per second so this quantity is positive what does it mean that means the particle is moving along the positive x direction okay so it is moving along a positive x-axis and with an average velocity of 2.5 meter per second and you can also see from this graph the slope the slope is positive whenever the slope slope is positive that means the particle or the object is moving in the positive direction okay and now let's find out what is the average velocity in this interval in this time interval and you can immediately see that the slope here is negative or it is downhill this is the upfield and this is the downhill the downhill means the slope is negative what does that mean that means the average velocity in this case has to be negative now let's calculate this one so again between two to three seconds so what do we have what we need to find out what is the position at this point that's the final position the final position is three second so that's the final position so i'm just plugging into this equation here the final position is three second and the initial position because we are interested in calculating in this interval so the initial position is 5 and the final position is 3 so that's all i'm plugging here 3 minus 5 and the time is 3 second and 2 second you see now we are interested in finding out this year so this is the final time this is the initial time 3 minus 2 second and if we solve it then it will be negative 2 divided by 1 which is negative 2 meter per second again minor correction here okay so what does this mean the negative sign tells you the particle or the object is moving in the opposite direction okay so it was first in this case it was going forward and now it is coming backward that's what it means now let's calculate from three to five second from here from this range here three to five second so what is the final position at this point at this point the particle the position of the particle is three and even at three times to three second the position is three second what does that mean the particle is not moving at all there is no change in position between three to five second the position is not changing so that means the particle or the object is at rest so i have calculated here so the final position is three and the initial position is three which is zero meter per second that means the particle is not moving at all so now we calculated in this range now let's calculate it in this range now and what you can immediately tell you from this one is there is a downhill more downhill okay downhill means there's the average velocity has to be negative so what is the final position at this point the final position at time equals to six second is zero and the and the initial position at time equals to five second is three so let's plug in this equation here between five to six seconds at time equals to six second the final position is zero at time equals to five second the position is three and this is the times six minus five what i guess is negative 3 meter per second the more the downhill is or the uphill is the higher the average velocity is so when you solve it what you get is negative 3 meter per second and the negative sign tells you the particle is moving in the negative x-axis and now i'm not going to solve this uh this year again the same way you can calculate from 6 to 7 second from seven to eight second let's do this one from seven to eight second seven to eight second between this time what is the position at this point the position at this point is zero what is the position of the particle at time equals to seven second this one is negative three so you have to write down the negative so once you do that now let's see here so at time cost to eight second this is the the particle is at zero position negative and at time equals to seven second the particle position is three so this negative and this negative will make it positive so this is three meter per second now okay so what does this mean that means in this case the particle is moving in the forward direction okay so because this is an upward slope that means the particle must be moving in the forward direction or the positive x-axis the same way now we can calculate from zero to five second so this is zero and this is a five second here so how did you calculate the average velocity between these two time again the information you need is the position so between zero to five seconds here i'm solving for this now so at time equals to five second the position is three so three let me write down here three and at time equals to zero second the position is zero divided by the time the time at this point is five minus zero so three divided by five if we solve it it will be zero point six meter per second that's what exactly i have solved here zero point six meter per second and it is still moving along the positive x-axis okay so that's how you find the average velocity from a given position time graph all right so if you want more interested let me draw a more a picture of this one so now let's say let's say how is the particle moving let's say i'm drawing here this is the x-axis and you were initially at this point so let's see how you moved so first you moved from 0 to five meter in time equals to two second so first what you did you move five meter you moved five meter so this is your first motion here okay this is the five meter five meter and then what you did you moved backward and how much you moved you moved from five meter to three meter in the backward direction so your second motion is five meter two you move this way okay and then for in this interval you were sitting you are just at rest so you're not moving this time interval and then you move from three to negative three meter in this portion here what does that mean that means you move from this point to this point this way negative 3 meter this is negative 3 meter and then again from this point you again moved back to the origin so what does this mean here you again started from this point and came back to the same location so this is how the particle was moving or you were moving let's say so first move five meter then turn back in and then again move in the negative direction and then again come back to the origin that's how is the motion of the particle okay so this is it from this position time graph and in the next video i will talk about how do you plot the velocity time graph from this position and time graph and i will also talk about how do you find out the acceleration time graph from the given velocity time graph stay tuned and again if you have any questions comment or concerns write down your questions in the comment section below and do not forget to like share and subscribe the channel thank you very much