 next question is what is the slope of the vt graph of body when it moves with uniform velocity so let me take another color for this okay so orange and what do you think light green so let's use light green okay so what is the slope of vt graph of a body when it moves with uniform velocity okay before jumping on to the conclusions let's first understand what is the meaning of the keyword slope what is a slope guys so slope so you would have encountered this word when let's say you are going for a trekking right so let's say this is a mountain mountain and you are going for a trek okay so hence this is let's say this is one slope and this one is more arduous slope right so we say that the slope of the second mountain is more and we slope of the first mountain is lesser so second mountain is more steeper so how do we in in mathematics how do we quantify this so it's very easy so let's say you are now I'm further you know simplicity say I'm taking a very smooth inclined plane so we define slope like this so if you move delta x distance in one direction right in this direction so how much you move in the perpendicular direction right so if you see delta x towards right will give you delta y towards up so the same delta x will give you this this also let's say the slope was like this so this is one and two so which one has is having more slope line one is having more slope why because for the same delta x delta y is more for one than for two so hence we say one is having higher slope right so this is how we define slope how do we define slope once again change in y divide by change in x now what is x and y nothing but whatever quantities you are taking in x direction and y direction so that is how you'll define a slope so slope of a vt graph so what is x and y in a vt graph so let's see that so let's say this is a vt graph so mark the order since it is said vt graph so v will be in the y axis and t in seconds let's say of whichever other unit is in x axis v is measured in meter per second okay now how do I measure the slope so let's say at t is equal to t1 okay the object or the particle is is moving with v1 like that so this is at t1 v1 okay and at t is equal to t2 the object or the particle is moving with velocity v2 okay this is the scenario so t1 is the start time start time as in what was the time by your watch at start and t2 is what at you know end so let's say it was 12 o'clock and you reached like 12 30 something like that so how much time did you take 30 minutes okay and when I when you start in at t1 let's say you were moving with at 12 o'clock let's say the train was moving with some speed and 12 30 it is moving with some other speed right or you know velocity in this case so hence just how do I measure slope or let's say if you join these two points okay so you can measure the slope like this now so how do I measure slope so this vertical change is called delta v and you can clearly see delta v is nothing but v2 minus v1 and what about this thing this is delta t change in time t right so clearly you can write delta t is equal to t2 minus t1 now this don't get you know confused by this sign symbol here the symbol delta means or the stands for change change and the quantity which is written next so change in that quantity so delta t means change in time delta v means change in velocity delta p means change in pressure let's say delta you know so any anything if you attach with delta we will mean very small change or very you know any change not not necessarily small so when I write delta p let's say so it is nothing but change in temperature right the change in temperature from day and night so you can write like that right so we understood the terminology okay so hence the slope here if you see slope of this line as we defined slope what will be slope delta v so vertical movement divided by horizontal delta t right so this slope here delta v by delta t actually represents what change in velocity per unit time if you see change in velocity divided by change in time you already know is called acceleration my friend so this is acceleration now you're saying what is the slope of the vt graph of body when it moves with uniform velocity and we all know that uniform velocity uniform velocity meaning zero acceleration zero acceleration I'm just using the short form uniform velocity zero acceleration there is no acceleration since velocity is not changing hence it is uniform isn't it uniform meaning not changing so hence velocity is not changing so if you see if you see here what does it mean delta v is zero right so here clearly delta v by delta t is nothing but zero by delta p hence slope is zero slope zero meaning there is no rise in vertical direction as you move in horizontal direction isn't it that was how we defined slope delta in general case there is no rise in vertical direction so slope zero meaning it's a plane like this isn't it same uniform plane so hence if you draw this as x and y let's say this is t time and this is my velocity so this will be zero slope line so this will then be uniform motion or uniform velocity constant velocity uniform motion why because it is moving with constant velocity so hence in the same direction same speed so uniform motion or it is also called constant velocity right so what did we learn a vt graph mind you vt graph not s t graph that is position time graph no we are talking about vt graph of a body and it moves with uniform velocity will have zero slope so hence your answer is zero right what will be this case positive case just let's look at this as well what will be positive slope so positive velocity or positive slope will be it is an accelerated motion isn't it no more zero slope meaning no more uniform motion so hence let's say this is the curve this is t so I use curve and graph interchangeably so later on you will talk about curves so line is also typical or particular type of curve so hence I am calling it curve vt curve or vt graph both are same so when I say vt graph and this is having some non zero slope let me see there is non zero slope some theta angle is there so this is delta v change in velocity this is delta t change in time so delta v upon delta t is not zero is not equal to zero so this is what this is actually and and if you see this slope is constant everywhere since this is a line so slope is constant so delta v by delta t is not equal to zero but also a constant and this is a case of uniformly accelerated motion uniformly accelerated so acceleration is constant velocity is not constant but acceleration is constant accelerated sorry accelerated motion okay and it is with positive slope why because delta v in this case change in velocity is greater than zero you can have a negative slope as well so let me draw here with some space left so let's say this is this okay so this is a case of negative slope guys just change in velocity as time is progressing is decreasing or change is reducing right our final velocity is lesser than the initial velocity so delta v is less than zero so velocity is reducing meaning what it is decelerating is it so this case is deceleration okay so remember these graphs okay so this is what is the learning from this question let's go to the next one