 okay so this is the third question and it says which of the following is the position time graph for a body at rest so again as I have been telling you read the question which of the following is the position time position time so they're asking about position time graph for a body at rest so what is the identity of rest how do we define rest so what happens in rest so this is what is the definition of rest rest meaning position doesn't change position doesn't change right position doesn't change of what of the particle of which we are analyzing the motion so position doesn't change very good can there be any other definition or characterization for rest yes velocity is 0 but this velocity is 0 not momentarily not for a moment velocity is 0 continuously okay for a long period of time continuously what is the difference so when you throw something up against gravity it also when it reaches the highest point then also its velocity is 0 but that velocity 0 is for only a moment right but in the very next moment it starts falling down and its velocity increases is it so that's momentary velocity is 0 but if the velocity of something is 0 continuously for a long duration of time then we say the body is at rest and again since rest and motion are relative so this is all dependent on the frame of reference okay frame of reference so we all are let's say in right now when you are watching this video so let's say you're watching it on a laptop and you are not moving with the laptop laptop is you know or the desktop or the computer is lying on these on the table so that laptop is at rest with respect to the table but if you go to let's say sun or outer space you'll see earth moving around the sun so then the laptop is also moving with the table so with respect to outer space it's not at rest so again rest and motion is again dependent on from which frame of reference you are evaluating them so keep that in mind so nothing is at absolute rest nothing is at absolute motion okay so now coming back to the question position time graph right of a body which is at rest so again position doesn't change that means if you draw curve or graph like this okay so here is where I am measuring time and here is my position position time graph is measured as or called as s t curve this is my zero t equals to zero s equals to zero line point now position doesn't change with time so hence if you this is time t1 this is time t2 this is time t3 okay different different times are there at 12 o'clock full 30 1 o'clock 1 30 1 2 o'clock wherever you're coming you're observing with one particular reference frame let's say on earth or with respect to you the body is not changing its position so if it is located at this this point I said this point this is not the plane at which it is located it means that if you draw this line so whatever is this distance so this distance is let's say s1 so the body is at s1 distance away from the origin in a straight line something like that okay physically so this is not the physical position of the body many people think that this is a physical location no physical location is something like this so let's say the body was moving in a straight line like this okay and this is t is equal to 0 so if at t equals to 0 how far it is from origin let's say this is origin so s is equal to 0 so at t equals to t1 so as time becomes t1 the guy is at s1 location at t equals to t2 the guy or the body is at s2 location right so hence now I am plotting these two t and s on a graph paper so t1 this is the time time axis this is my position axis so at t1 the body was as s1 so hence corresponding to this t1 you get this s1 here then corresponding to this t2 you get this s2 let's say s2 okay so you can imagine if you're drawing the time axis like this this is the time axis okay the body is moving in this direction oh let's say y in this direction the body is moving and but you have to measure the time also so you're measuring time like this so this is t1 and you're saying when the time moves here the body is at s1 when the time moves to t2 the body is at s2 right that doesn't mean the body is moving in this direction so many people think that body is moving like this no this is the graph of the motion but the actual movement physical movement is happening in this direction we're just measuring or you know just it's a way of visualization so hence it appears like that so at t3 it is that let's say s3 something like that so if you join now this is the curve or the graph of st okay st right so here if you see the positions are changing with time but in our case the position was not changing is it position time graph is rest so rest is what position doesn't change so let's see so now you know what's happening so the body is where it was at initial time let's say at t1 the body was at s1 so at t2 also it will be at s2 at t3 also the body is in the same location okay so hence if you join all these you will see this is a straight line is it so this is what is position time graph or something which is at rest so hence the option a is correct what is this guys then what is this one so if you see the slope is constant positive slope isn't it this is delta s change in position divided by change in time so positive slope so this is uniform uniform motion right so this is uniform motion uniform motion or constant speed okay this one this is also uniform motion uniform motion constant speed or constant velocity but then how are they too different how are they different so clearly here the body is moving away from origin see the body is away moving away from origin but here body is coming towards the origin that's the difference so it is coming towards the origin it is going away from the origin so hence its displacement is reducing here the displacement is increasing that's the difference and what about this this is a curve like that what is this this is accelerated motion acceleration is happening and why do I know and how do I know basically so you can see if you just divide it into equal interval of time equal interval of time let's say one second each let's say one second each okay and then find out corresponding change in displacement so clearly if you see the specimens are increasing for every second the change in position is increasing so if you take the next one second maybe here so it is very high isn't it so corresponding to that the displacement will come somewhere here this location so again very very high so displacement is changing with time every second in every interval of one second you have higher values of displacement so hence this is acceleration so the body is not covering same amount of displacement every unit time so hence it is accelerated motion I hope you understood this