 Hi So in this question we have been given four distance time graph of four different cars And we have to find out which car is moving With fastest speed highest speed and which car is moving with slowest speed So basically we'll have to arrange these four cars in order of their speeds So from a distance time graph, how do we figure out? What's the velocity? What is the indication of velocity or what is the method to find out velocity from a distance time graph? Now it's distance time graph given so In a distance time graph we can find out the speed and not the velocity for velocity time graph We have to have displacement time graph. So let's see So this is why distance time graph So here is distance in meters and here is time In seconds, so if there is a straight line straight line Okay, so the How do I find out the Velocity so velocity of velocity Velocity or As the velocity will be wrong term to use here by because it's a speed time graph. Sorry a distance time graph. So speed is given by is given by speed in In a distance distance time distance time graph distance time graph is given by the slope slope of the graph So what is meant by slope? So let's say the slope of this line Our graph in this case will be nothing but You take any two points on the On the graph. Let's say this is point a This is point B. So what you do is you drop perpendicular to both the axis from these two points Okay, so these are the let's say these are the perpendicular sign Okay, so so slope of slope of The curve is given by this length vertical length of the triangle. Let's say this is y and this Horizontal length x so slow Change the color slope Slope is given by Delta s upon Delta t in this case Delta s. This is Delta s. Why is Delta s? Why because this is s 2 if this is s 2 and This is s 1 so Delta s is nothing but s 2 minus s 1 divided by t 2 minus T 1 it's a slope now this slope is also equal to average speed Now in in case of a uniform speed motion Average speed is equal to instantaneous speed. So throughout the motion the average other speed speed is same as the average speed. So this is a uniform Motion now so basically Now the slope when the slope gives speed higher the slope Higher the slope of s t graph higher Would be higher would be the speed So clearly in this case if you see Slope of c is highest. So in this case slope slope of we can clearly see that slope of Of c is greater than slope of D which is greater than slope of a which is greater than slope of B By slope of c greater than slope of D Where because the inclination if you see C's C's graph is steeper than that of D's Again D's graph is steeper than that of A's and A's graph is steeper than that of B So hence C will be having the highest slope. So highest slope means highest speed So the speed will be also speeds of all these four cars will be on in the order c greater than D greater than a B this is the order of speeds of these four cars So clearly car a is faster than D is ruled out. Why because D is faster than a Car B is the slowest. Yes Car D is faster than car C. No, why because D is having Lesser slope than that of C and car C is the slowest is wrong Because C is moving at the fastest speed. So answer B is correct