 Welcome friends to this problem solving session on physics. The topic we have taken is motion and The question says that a person moves along the boundary of a square plot of side 10 meter in 40 seconds What will be the magnitude of? Displacement of the person at the end of two minutes 20 seconds. This is the question. So there's a square field. Let's say the square field is a bcd and The person is going like that, right? He's going like that. I'm coming back to a and finally, you know, whatever time it takes He is going around at this periphery. Okay. The question is find the displacement after the end of two minutes 20 seconds so let's try and understand how to solve this problem and You have to take care that it is displacement and not distance. So what is the displacement guys? displacement is all of you know displacement is defined as final position final position minus initial position initial position, right? So it's a vector quantity and It's primarily or basically what is it final position minus initial position? That means let's say if you have a xy coordinate system The reference frame and a particle or a person moves from point a to point b In any of the path like that. So the displacement is the shortest distance between the a And the b point ready. That is initial and the final point. This is The displacement, isn't it? That is what we have learned in our theory displacement Okay, so in this case We need to find out the initial position and the final position and find the shortest distance between them. That is the That is the problem. So hence, let's say it starts with let's say he starts at a so starting point starting point Is let's say a Okay, now he is moving uh 40 seconds in uh So he's he's covering in 40 seconds full full Perimeter. So hence his speed Or velocity in this case speed because the direction of the you know speed is changing. So hence we'll use the term speed and not velocity Because the velocity is changing because of the change in direction. So speed is Not changing but speed is constant. So what is the speed guys? So speed is nothing but distance now distance not displacement distance traveled Divide by time taken isn't it? So if you see he is traveling how much distance in 40 seconds 10 plus 10 plus 10 Plus 10 total Full perimeter in 40 seconds That means his speed is 40 divided by 40 That is one meter per second. Okay. So distance traveled Distance traveled by him by him in two minute And 40 seconds, right? This is the time given two minutes and oh, sorry not for not 40 second 20 seconds So be careful the time given is two minutes 20 seconds now two minutes 20 second has to be converted into Seconds only so two into 60 seconds plus 20 That means it is 140 seconds correct So distance traveled by him in 140 second will be how much speed times Time speed into time is different distance in this case. There is no acceleration. There is no variation speed Speed is constant. So speed into time, which is nothing but one meter per second into 160 seconds Oh, sorry not 160. My bad. It is 140 seconds Right, which is nothing but 140 meters So he travels 140 meter as a distance traveled. This is a distance traveled. So how much is the displacement? So he is going around the The perimeter so hence displacement will be how many, you know, a full Perimeters he covers. So hence displacement will be Displacement will be how much? So he is covering Right, so how do you calculate displacement? So 40 meters is One full round, right? So he comes comes back to the same point a in 40 meters. Isn't it if you see 10 plus 10 Plus 10 plus 10 he comes back to the same a right So in how so in 140 meters, that means in next 40 meters He would cover two full rounds Right two full rounds. So total is 80 meters now In next 40 meters, he will cover the third full round Isn't it that means now 120 meters covered. So in 120 meters, he'll be back to You know point a so hence after that he is covering how much is left? 20 meters. So if you see he would have After 120 meters, he has come back to the same Same location. Let me draw it little Clearly. So let's say Let's say he has Come back To the same location So he is now at a d c And d right so hence after 120 meters. He is again at a he has covered three full rounds now. So next 10 meters. So he's now covered 130 meters here In total and now he moves. Let's say from b to c So he's again now total distance traveled is 140 meters. That means the final position is c I hope you understood this so he had traveled in total 140 meters distance In 120 meters. He is back to a So next 10 meters till 130 meter. He is at b And then from b again another 10 meters at c and now he has covered total of 140 meters distance. So final position is c And what was displacement guys Displacement is Sorry final position minus or the shortest distance between Final and initial. So this is our required Displacement So let's calculate this value very easy. So hence it is 10. This is 90 degree So this displacement will be nothing but by Pythagoras theorem 10 square plus 10 square under root, right? So hence displacement Displacement Displacement will be equal to Under root 10 square plus 10 square, which is nothing but 10 root 2 meters Okay, this is the final displacement in this case. I hope you understood the problem