 so here is another question guys the question says what does area under a velocity time graph give okay so whether does it give distance acceleration displacement or another so let's first find out what does it mean right so area under a velocity time graph again just to remind this is velocity time graph so in motion chapter you would have come across at least two varieties of such graphs one is position time graph displacement time graph or you know position time graph or displacement time graph or velocity time these are the things right so what does velocity time graph give okay so let us first draw the graph this is x and y coordinate axis so this x is nothing but our t so this is t and this is velocity t isn't it this is what our velocity time graph looks like and let us say the graph is something like this okay what are these values so here it is t is equal to t1 and at t equals to t1 the body was moving with velocity v1 and let me say this is t is equal to t2 okay this is t is equal to t2 and corresponding to this t2 the body had velocity v2 i'm writing it here so what does the area under the curve first of all understand what is area under the curve so if i have to just let me take another color for better understanding so if i take yeah so area under the curve is nothing but area bound between the given graph the time axis and the two perpendicular line corresponding to two time x two time values so between these two time okay this is what is area so we have to basically calculate this area we don't need to calculate we need to understand what exactly this means so for that what we're going to do is let us take let me take another color for how do we find out what exactly does it give okay so let me take this one now if you take any time t right any time t and corresponding to that time t let us say this is my v okay and let's take some some time after t but at a very small time gap okay so i'm saying this time gap is or this time is actually t plus delta t delta t small delta t is there so and then again draw a vertical line so you find out its corresponding velocity value let's say this value is v plus delta v now understand once again at time t the velocity was v okay no doubt at time t the velocity of the object is v which is given by this point so this is at this location at this time this is the velocity and at t plus delta t so this gap if you see if you this see this gap this gap is nothing but delta t gap so in a duration delta t so i'm writing delta t here so in delta t time gap the velocity increases by some value delta v right so hence this location now this point is v plus delta v okay now don't you think the this this particular diagram here so let's let me name it so let's say this point here is a this b this is c and this point is d so abcd looks like a trapezium abcd is a trapezium is a trapezium is it it now what is the rough cut area of roughly what is the rough area of this trapezium so if delta t is too small so this trapezium is almost like a rectangle right so this is anyways 90 degree this is anyways 90 degree so only this slant line is there but if delta t is too small you can say that this is almost like a rectangle so hence nearly this abcd has an area what ad into assuming it to be closer to the rectangle so ad into ab almost like a rectangle yes it's not exact but somewhat what is ad if you see ad ad is nothing but the v check this ad here is same as this v in this axis and what about this ab ab is nothing but delta t if you check isn't it so now it is as we are saying that for delta t amount of time the velocity was v and hence this particular quantity is nothing but distance traveled or displacement travel in this case velocity is given so displacement traveled in delta t time right at a velocity at a velocity how much v is it so hence this small area if i shared it using the screen so this area is displacement covered in delta t time so don't you think if i add all these small small trapeziums though you know if you somehow find out the exact trapezium area then don't you think this will give you the displacement cover between t1 and t2 so if in in abcd you can see in delta t time the displacement cover is given so from t equals to t1 to t equals to t2 if you add all such small small small trapezium areas you will get what displacement covered so hence area area under vt graph gives what gives displacement again remember it gives you displacement area under vt graph gives displacement if it is speed time graph it will give you distance simple so yeah so hence distance will be from speed time graph speed time right so hence right answer is c in this case but where do how do i get acceleration from vt so how do i get acceleration from vt graph so if you see if you have a vt graph so acceleration is nothing but the slope of the line okay so slope of this curve okay so let's say this is delta t and this is delta v what is delta v change of velocity from v1 to v2 okay and delta t is change of time from t1 to t2 so my dear friend this is delta t isn't it okay so hence acceleration a is given by delta v by delta t which is v2 minus v1 change in velocity divided by time taken to affect that change right in how much time that change was happening so hence this is acceleration so acceleration is nothing but how do i find out acceleration so what is it actually so what did we calculate if you remember the concept of slope so we calculated slope so slope of vt graph gives acceleration isn't it right so this is what is our learning so distance is given by area under speed time graph acceleration is given by slope of velocity time graph and displacement is given by area under velocity time graph i hope you understood this part