 Hi, so in this question we have to find out the slope of a velocity time graph and Find out whether it gives the distance the displacement the acceleration or the speed. So let's start so we are having a velocity Time graph. So this is x axis is time in let's say seconds and velocity in meters per second Okay, so slope of velocity time graph. Okay, now What is slope of velocity time graph? So first of all, we'll have to have a Slope of a graph. So let's say this is the graph So this represents a Velocity time graph and we have to find out what does the slope depict now. Let's take two points on this graph Let's say this is point a Let's say this is point a And this is point B. How do I find out the slope? You have to first drop the perpendicular To the time axis and then to the velocity axis Okay, now complete this right and Okay, let's let's call this point as C Okay, now slope is let's say, okay. First of all, let's say this is T2 This was T1 This is V2 and this is V1 that is this point. This point is V1 This point is V2. This point is T1 and this point is T2. Now, how do we define the slope? slope is given by slope is given by This distance divided by this distance On this length divided by this length now, this is nothing but change in V from V2 to V1 to V2 So delta V we can say And this is delta T and This is equal to T2 minus T1 so slope of slope of VT graph is nothing but Delta V upon Okay, so why is this called slope because it's like, okay, let's say you are ascending a hill sending a hill and How to define the steepness of this hill? So you will say that if I get displaced by let's say X meters in the horizontal direction This leads to a displacement of Y meters in my meters in Vertical direction so my slope slope or inclination of this hill was nothing but Y upon X So for every meter moved in X direction, how much do I rise up in Y direction? Let's say how do I know whether it is steep or not? So let's say if there is a steeper Hill, so let's say this is the hill and you are ascending this hill now Again, so let's let's say this distance is Y dash so what's the slope in the second case? Let's say this was case one or a and this is case B So this was the case a now in case B the slope will be slope will be Y dash upon X right for X meters moved in X X direction or horizontal direction you rise up by Y dash meter So hence slope of slope In case of B is greater than slope in case of a or inclination case of B is greater than inclination in case of a So clearly Y dash by X is greater than Y by X Why because Y dash is greater than Y? Right, so this is how the slope is measured So in this case also if I imagine if I'm measuring the slope of this line So I have to find out If I move horizontally horizontally by delta T how much Delta V change do I get in vertical direction so hence slope is delta V by delta T now by definition by definition by definition acceleration acceleration is given by Delta V by Delta T or this is nothing but rate of of change of Velocity with respect to time So this is rate of change of velocity and that's acceleration. So if you see Delta V by Delta T is acceleration is acceleration. So hence the slope here in a velocity time graph will give me Acceleration right so this is nothing but Acceleration right so slope in a velocity time will give you Acceleration right now if it was let's say Think about this question. What will the slope of a distance time graph give you? So let's say distance or displacement time graph, right? So this is displacement S and this is time So again, there is a displacement time graph. So slope of displacement time graph will give you what this is a question to ponder think about it the Solution or the answer is one of them one of these four options So the for the for this question slope of a velocity time graph the answer is Acceleration for this question the slope of the slope of displacement time graph Find out or distance time graph find out the answer. The answer is One of these four. Thank you