 चृका व Kathleen च्टेनाक नों भी अदे थाऍए यहाज़ा वाउम तो प्लाइ क Rosen अंद़ त bare now व नोज पंघर हमबो रही milestone उसे Kombat वुस क्ग्णे त बलाई money चाए दे थे व ال मिजे।豆ु�ög। भॉर ओर सट unserer चलिद बहॉंसि Austा życie ऑना ढ�ana now let me explain i think all of you understand all this u is initial velocity or speed whatever you want to say v is final speed after time t seconds or as whichever unit we are using a is acceleration so the first question is that we have an object which is having a velocity initial velocity of 4 meter per second and acceleration is 1.2 meter per second square and time which is given to you is 5 seconds so what you have to find you have to find final speed and you have to find distance traveled in the given time period so which two formulas we will use here for finding out the final speed we will use v is equal to u plus a t so what is u u has been given as 4 a has been given as 1.2 and t has been given as 5 so what i do 4 plus 1.2 into 5 is how much 6 so 4 plus 6 is how much 10 meter per second to find out d or s look at here this is ut so u is 4 t is 5 plus half a a is 1.2 and t square which is how much 5 in 5 square is how much 25 so this is 4 into 5 20 plus i divide 1 by 2 by 2 so you get 0.6 0.6 into 25 will give you 15 so how much distance 35 one thing that that generally people do is and i have seen while checking the paper they write the number and they don't write the unit please don't miss the unit this is very important otherwise you can lose half marks or one marks here and there which is not a good thing when you have solved all everything correctly so d is equal to 35 meter v is equal to 10 meter per second now let me go to other question so second question is a person is traveling at a speed of 43.2 kilometer per hour now he's applying break so when a break would be applied some kind of deceleration would be working so what is that value given deceleration value has been given as 6 meter per second square now guys try to understand whatever formula i have written suppose v is equal to u plus a t so here plus sign has been used in front of a why because it has been assumed that a denotes acceleration when you use a as deceleration you have to change the sign so this will not remain positive this will become negative because what is being used as data deceleration is used as data so here a becomes how much minus six i'm not saying i'm using this formula in this question so what you have to find out you have to find out distance after which it stops so if you want some 10 15 second 30 seconds time to solve it you can solve it i just want to know which formula you will apply here so till now you could have written the formula see in this question only speed deceleration and distance is being talked about there is no time so when i write all three formula there is only one formula which is v square is equal to u square plus 2 a s where i talk about two speeds initial and final speed and then i talk about acceleration and distance in this particular formula no time has been used so here i'll use this formula now what is u so u has been given to you as 43.2 kilometer per hour now how do you convert it into meter per second because why i need to convert it into because the deceleration has been given in meter per second so i need so try to understand here the formula is one kilometer per hour is equal to thousand divided by 3600 if you do it you will get five by this is meter and this is second one kilometer is thousand meters one hour is 3600 seconds five by 18 meter per second so multiply it with five by 18 how much you get you get 2.4 here so 2.4 into five is 12 meter per second so u comes out to be 12 meter per second now when the vehicle will stop it means that speed becomes zero or velocity becomes zero so final speed v is zero so i'm putting in this formula v is equal to u square as it is deceleration i am putting a negative sign minus 2 s so from here u square would be equal to 2 as or s would be equal to u square by 2 a u is how much 12 so this is 12 into 12 divided by 2 a what is the value of a value of a has been used as 6 so this is gone this is gone how many meters it is coming out to be it is coming out to be 12 meter that's simple so this is how you have to solve these kind of questions now i'm moving to another question another question is another question is try to understand so this question is a bullet is traveling with the velocity of 16 meter per second penetrates a tea trunk and comes to rest in 0.4 meter find the time taken during the retardation so what happens you have been given that speed of bullet u b is equal to 16 meter per second and there is a tree trunk over here the bullet comes and penetrates it and after going how many meters after going suppose this distance s is equal to 0.4 meter it stops so speed is 16 meter per second and after traveling inside this tea trunk for 0.4 meter it is getting stopped it means that some kind of retardation is working so minus a is working so the question is what would be the time taken for the bullet to stop so i don't have to find this retardation i have to find the time taken in which the bullet will stop so first i'll do what i'll see i have to use this formula v is equal to u plus at now if v is equal to u plus at or suppose you can use this formula s is u equal to ut minus or plus half at square everywhere in whichever formula there is a there is a t available a is also available there or wherever t is present a is also present so first i need to find out a by which formula i will find out a i'll find out a with this formula v square is equal to u square minus 2s why i'm writing minus because the retardation is there if it is stop stops final velocity it's 0 so again like previous question s would be equal to u square divided by sorry a would be equal to u square divided by 2s so this is 16 meter per second so i'm writing 16 into 16 divided by 2 into what is the value of s s has been given as 0.4 so this is nothing but i can write it 16 into 160 divided by 2 into 4 see this decimal is there so i'm multiplying numerator denominator everything so this is 8 and this will give me 20 20 into 16 is nothing but 320 meter per second square if it is like this then you look at here in this formula also v will be 0 so t would be equal to so i can write this formula as i can write this formula as v is equal to u minus at because retardation is working and if v is 0 so i'll write t is equal to u divided by a and what is the value of u 16 what is the value of a 320 so how many times it goes it goes 20 times so 1 by 20 which is equal to 0.05 seconds that is your answer so i hope you all are understanding whatever i'm teaching now let me move to some other question so i'll take one or two difficult questions and then i'll move to newton's law of motion okay i'm writing one question and i expect all of you to find this answer i'll give you two minutes to solve this question i'm writing a question i want all of you to solve the question a driver takes 0.2 seconds to apply brake after he sees a need for it find this is called reaction time if he's driving at a speed of 54 kilometer per hour deceleration is equal to minus 6 meter per second square find the distance covered look at this question this is very very good question find the distance covered traveled by car after he sees the need to put on the brake after he sees the need to put on the brake assume that after the brake is put on assume that after the brake is put on the speed becomes zero so final speed you have to assume here to be zero solve it for one minute how many of you have solved it can you give me the answer please okay so let me solve this question so what has been given it has been given that okay gurman it's saying 2.88 meters guys just give me one minute i'll post a few questions here only so that you can solve it it's somebody saying 2.88 meters okay let me just check so now look at here so what happens in this question is for this reaction time till the time brake is getting applied what happens is till the time brake is getting applied the car will keep on moving with what speed 54 kilometer per hour first i need to change this 54 kilometer per hour into meter per second so how much it is 15 meter per second now once reaction time is over so till reaction time what would be the distance covered distance covered would be 15 into 0.2 how many because for 0.2 seconds during reaction time there would be no brake applies i mean no brake would be applied during reaction time why no brake would be applied because in the question it has been told that it takes 0.2 seconds for the driver to apply the brake so what happens for those 0.2 seconds for those 0.2 seconds non-retarded motion or motion without any acceleration deceleration will happen so distance covered for first 0.2 seconds which is reaction time is 15 into 0.2 which is 3 meters after this what happens after this you use this formula v square is equal to u square minus 2 a s i told v has to be assumed to be 0 so s comes out to be equal to u square divided by 2 a so u square would be how much 15 into 15 divided by 2 into 6 so how much it is so look at here this becomes both 5 times this was 2 times so this comes out to be 75 divided by 4 how much it is 18.75 so what should be the total answer total answer should be how much total answer should be first you add these 3 meters and then you add this 18.75 meters so how much it will be 21.75 meters that simple is that so in this case what need needed to be understood is that in this case what needed to be understood is that if reaction time is there and during that time brake is getting applied so for 0.2 seconds the motion would be non-retarded if the motion is non-retarded so it will keep on moving in the same direction without any acceleration or deceleration so that's why i have done d is equal to v into i mean u is into t which is equal to 15 into 0.2 which is 3 meters and then it comes out to be any doubt guys any doubt murmur man did you understand two people who have given me answer three people who have given me answer did you guys understand what was the problem okay so answer could have never been two point because see when 55 54 kilometer per hour is there you convert it into meter per second that comes out to be 15 meter per second and then you have 0.2 seconds of reaction time you multiply 0.2 which comes out to be 3 meters so it can never be 2.88 meters okay now give me a moment i'll give you two three questions let me just download it for you so i'm giving you two three questions so that i'm trying not to write any question and i want you to solve a few graph questions so i will tell you the question number and you will have to solve that so one second guys solve question number 13 can you all see question number 13 is it visible solve question number 13 guys and let me know the answers i want all of you all those all eight people who are watching this i want answers from all of you whether you are getting right answer or wrong answer solve question 13 so you have to ask in this particular question a car is starting from rest has a speed of 30 kilometer per hour at one instance two seconds later its speed is 36 kilometer per hour again two seconds later its speed is 42 kilometers per hour so first of all what you have been given change in speed is always six kilometer per hour in what in how much time what time span in two seconds but first six kilometer per hour that change in speed has to be converted into meter per second so guys please whenever you are solving the question please look at the units very properly it should not happen that at one point of time it has been given kilometer per hour and at the second point of time it has been i mean or the second data has been given as seconds and you are using both the data simultaneously without converting any one of them so either you convert seconds into hours which is preferably which is preferably not done so here we will convert kilometer per hour into meter per second so the change in speed which is six kilometer per hour has to be anura your answer is wrong it is not three meter per second convert look at here all of you it is going from 32 36 and this is kilometer per hour in how many seconds two seconds and it is again going 36 kilometer per hour to 42 kilometer per hour in how many seconds two seconds what is acceleration acceleration is change in speed v2 minus v1 divided by t2 minus t1 so this time span has been given given to you as two seconds now what is the change in speed either it is 30 to 36 which is again six kilometer per hour in two seconds and or 36 to 42 kilometer per hour which is again six kilometer per hour in two seconds so how do you do it so try to understand it can be done like this so v2 minus v1 so 42 minus 36 but as it is in kilometer per hour i will multiply a converter which is 5 into 18 meter per second divided by 2 so this is 6 into 5 by 18 into 2 and how much it would be so this was three times so that comes out to be 5 by 6 meter per second square okay so how many of you are getting d as a answer a lot of you are getting d as a answer so answer is actually d now let me move to some other question so now let me move to motion under gravity so how many of you can solve first solve first question i have not told i have not specified this kind of question but let me tell you only three only three you can tell me the you can tell me the answers a b c d no no need to write it you just you can just see options which options now guys try to understand i am telling you to solve question number 15 you will solve as many questions as possible what is your answer for question number 15 can anyone tell me the answer what is the answer for question number 15 okay let me solve this question for you anyone who has got the answer nobody has given me the answer okay look at here what happens so i am reading the question for you a stone is thrown vertically upward with an initial velocity of 14 meter per second a maximum height reached and the time of accent is so look at here so what is the speed speed is 14 meter per second by which it is thrown up so time of accent we have to find out and maximum height we have to find out now if you look at the concept of acceleration and deceleration properly if acceleration means whichever direction the speed is if speed is in this direction and we are pushing the object only in this direction its speed will automatically increase retardation means if a speed is in this direction and we are pulling it back in the other direction the speed will start decreasing so deceleration is nothing but acceleration in opposite direction so what happens in case of gravitational question if we throw an object with certain speed upward we should know that there is an pulling back force which is gravitational force which is acting towards the earth so this gravitation force pulls back the object towards the earth and in what format we utilize it in physics so we apply a gravitational acceleration or retardation which is in this case retardation and what is the value of that i am taking 9.8 meter per second square few times we use 10 meter per second square we also use more exact value is 9.81 per meter second square so what happens accent time till what time it will go up it will go up till the time speed becomes zero so i utilize this formula v is equal to u minus at or minus gt why i am writing minus g because u is in direction above the earth g is towards the earth so that's why this negative sign because speed and acceleration is working in different direction which is a case of deceleration so it will keep on going up till the time this is zero so how much time t will be equal to u divided by g so you can write 14 divided by 9.8 for that matter for simplification i am writing 14 divided by 10 which is equal to for 1.4 seconds it will go up or what is the value given so one point so here it they have taken 9.8 so value would be 1.429 so t comes out to be 1.429 429 seconds now till what height it will go it will go so i will use this formula i will not use time formula v square u square minus 2 gh till what height it will go the maximum my height is where this final velocity becomes zero because it will keep on moving like this till what height it will go here the velocity becomes zero now acceleration is in this direction so from this particular point it will start free falling towards the earth so for at maximum height always remember at maximum height this v is equal to zero so h comes out to be u square divided by 2 g so u square is how much 14 into 14 divided by 2 into 9.8 so how much it is 14 into 14 is 196 divided by 9.19.6 9.8 into 2 that comes out to be 10 meters so here the answer would be 10 meters and 1.429 seconds option a how many of you got this answer i am getting few anurag it's saying c is not an answer two people ishani and one more people have given right answer now let me move to few questions which are best on graphs so let me solve those kind of question so how many of you can solve question number 26 i will solve two three questions best on graph and then i'll move ahead so i'll move to motion and then i'll move to if i'll have time i'll move to other things also okay gopika your answer is right ishani your answer is right question 26 okay have you done this kind of question in the class guys okay take one minute otherwise i'll explain it's a very good question don't don't do it like this b or c or something like that so few people are saying see ishani is saying it is b try to understand what happens in this kind of graph so you look at here what happens is you have to find out maximum speed of a particle will be maximum after time so after which time speed of the particle would be maximum so what kind of graph is this the graph is like this so it is starting like this then it is going like this then it is going like this and then it is going like this so what is this this is a t graph so a on y axis and t on x axis this is 10 meter per second square this is minus 10 meter per second square this is how many seconds two seconds and this is how many seconds four seconds so see guys what happens what do you mean by 10 meter per second square and minus 10 meter per second square see the magnitude of acceleration is same but the sign is different what does sign signifies here what does sign says sign of sign of acceleration so see assume that if i am assuming that this a is equal to 10 meter per second square is in east direction if for this value the object is getting accelerated in east direction this negative sign is telling me that object will get accelerated in exactly opposite direction of east because i am assuming east to be positive so negative would be which direction negative would be west direction so what happens over here try to understand u is equal to zero so if i apply formula v is equal to u plus at which remains at so for two seconds see here it is going in west direction i am assuming that positive is east direction so negative would be west direction so two into how many seconds ten seconds so that comes out to be 20 meter per second so at this value the speed is 20 meter per second in which direction in west direction so that's why i'm making this direction now what happens suppose this particle is moving in this direction at 20 meter per second at what time t is equal to two seconds exactly at t is equal to two seconds acceleration becomes in opposite direction so acceleration becomes 10 meter per second square in east direction don't you think it's a case of retardation i think it's a case of retardation and i'll explain why because speed at two second is in the direction of west and at two seconds the acceleration becomes in the direction of east so acceleration is in the opposite direction of speed which is a case of deceleration so at four seconds which is a time span from here to here is how much two seconds so v would be equal to at two seconds u is how much 20 meter per second and as for complete duration the acceleration is in opposite direction so i write 10 into 2 which equals to 0 so see here at two seconds speed is 20 meter per second in west direction after two seconds speed is in west direction and acceleration is in east direction so that would be a case of retardation hence the speed will start reducing from here and at four seconds speed will again become zero so answer would be b now let me give you one more question so one more question of this type solve question 27 and 28 both the questions are there on the sheet give me the answer i give you two three minutes to solve this question both the questions then i'll go to motion sorry i'll go to newton's law so what is the answer guys okay enough time how many of you are getting the answer you are saying question a b c all the answers are coming we have started playing k b c okay so first of all try to understand always remember this thing in a vt graph in in question number 27 do we have vt graph yes we have a vt graph what would be the distance traveled always remember i'm not talking about displacement let me again repeat my concept i'm not talking about displacement i'm just saying in case of vt graph the distance traveled would be equal to area under the vt graph so let me make it for you you see here you see here after these two questions i'll move to force and motion and and conservation of motion and all those things so look at here the graph was something like this so it is starting from here it is becoming like this and it is going like this what was the 40 20 2345 so this is 40 this is what 20 this is 2 this is 3 this is 4 and this is 5 so this is v in meter per second and this is t in seconds i think so meter per second and yes meter per second so what i have to find out distance traveled it work so find out area under the graph so i have this one triangle plus this one rectangle so this is triangle 1 this is a rectangle 1 this is a rectangle 2 now this is triangle 3 and this is triangle 4 and i'll add all the area so triangle 1 area would be 1 by 2 base is how much from 0 to 2 base is 2 multiplied by height height is from 20 to 40 so which is 20 area of rectangle is length into width so 20 from 0 to 20 is 20 and and this is 2 so 20 into 2 again this height is 20 but this is only 2 to 3 so this is 20 into 1 area of this t 3 is 1 by 2 height is 20 and time span is only 1 and area of this is minus 20 so this is 1 by 2 and this is minus 20 it means that height here also is 20 so even if it is minus 20 i am assuming it to be positive because distance travel does not depend on direction of the travel it is path characteristics not the direction characteristics so 1 by 2 into 1 so how much it is coming this is nothing but 20 plus 40 plus 20 and this is how much 10 here and 10 here so 10 plus 10 so 20 plus 40 60 20 80 80 plus 20 is 100 so answer will be which answer answer would be 100 meter now 28th question answer is or let me i think you can solve this question i'll give you the answer just by looking at it you have to find out displacement displacement would be zero no displacement no what what you have to find out displacement in average no it's not zero try to understand how to do it look at here so in a vt graph how to find displacement i'm teaching you now look at here let me first draw the draw it four meter per second 246 so it is something like this four meter per second this is two two to four the velocity is zero then what happens so this is four and this is six this is how much four meter per second this is how much minus two meter per second is it fine now what happens what is the difference between this four meter per second and minus two meter per second it's exactly the same thing and it's exactly the same thing it means that change in direction so i'm assuming that four meter per second positive is in east east is positive and this is west west is negative so what happens for how many seconds it is running this is v this is t it is running for two seconds so try to understand it is it starts at two seconds and and speed is is is uniform so distance travel would be equal to v into t and which direction as the as the velocity is in east direction displacement will always be in east direction so four into two that comes out to be how much eight meter so it goes eight meter in east direction now what happens from two seconds to four seconds here there is no speed if there is no speed suppose the object has started from o and it has reached a after two seconds it will remain at a for two to four seconds because the speed is zero so that is the condition of stability now what happens the direction of the speed of this particular object changes so for next two seconds it will move from a in the west direction which direction west direction so how much it will go d is equal to away into t time is two and speed is two so how much it is four meter per second sorry four meters is not per second so from here it comes back four meter so what is the distance remaining from here distance remaining from here displacement is always a straight line joining the initial point and the final point so this is initial point and this is final point how much it would be it would be four meters so displacement would be how much four meter and average velocity after 10 seconds so try to understand after 10 seconds what happens so suppose one second after here suppose this is 10 seconds so look at here what happens at six second again speed becomes zero now what is average velocity average velocity is equal to total displacement divided by total time now what is total displacement so see after six seconds again the speed is zero so this particular object will remain at b which is four meter east from o so total displacement is how much four total time is how much 10 seconds four divided by 10 is point four meter per second in which direction this direction so you can do like this point four meter per second and or it is asking guys it is asking displacement after three seconds so look at here displacement after here i am calculating displacement after six seconds that's why my answer was not matching this answer is correct displacements after three seconds see after two seconds it is at eight meter from two to four seconds it is not moving so displacement after three seconds would be eight meter why because from from zero to two seconds it has moved to eight meters but from two to four seconds speed is zero so it will remain at eight meter so here answer would be eight meters and point four seconds which is option b anurag this is a question this is this is not a question of slope this is a question of uniform speed so you cannot assume if if there would be a slope it cannot happen that the speed would be why you are getting undefined acceleration because on a slope the motion will never be of uniform speed the motion if if motion has to be uniform speed then you cannot take the condition of slope there and for for this particular graph at least so that's why you are getting undefined acceleration now guys let me move to another chapter and i am giving you another question so let me make some space for you i'll teach you for half an hour more okay so my next question to you is like this my next question is write down guys two objects i have two objects and this is conservation of momentum question of conservation of momentum two objects masses are m one is equal to hundred gram m two is equal to 200 gram and they are moving along the same line so they are moving along the same line like this the first speed v one is v one is equal to two meter per second and v two is equal to one meter per second after they collide what happens they collide here a collision happens here and after collision this first object starts moving with the speed of 1.67 meter per second you have to find out what would be the speed of second object after collision i am asking after collision so how do you solve this kind of question so always remember i am solving this question for you always remember so this is a collision where momentum is conserved what is momentum momentum p is given by m v if two objects are there momentum is given by total momentum is given by p one plus p two which is m one v one plus m two v two now this momentum initial momentum would also be equal to final momentum which is m one v three plus m three sorry m two v four so i have been given values what are my values first one is what do you do hundred gram first of all don't write hundred gram or can you write hundred gram here can you write hundred gram here see m one m two m three m four so what happens is you write point one into two even if you write hundred gram does not matter because both the side it is grams so gram gram will get cancelled out so point one into two plus point two into one how much it is so this initial would be equal to so point two plus point two so it comes out to be how much point four so that comes out to be point four and now this point four should be equal to m one which is point one into v one guys i am writing one point six seven is nothing but five by three so i am writing this five by three meter per second plus m two is how much m two is point two into v four so how much i have to get see i am removing all the decimals multiply both the sides with ten so you get four is equal to five by three and that is equal to plus two into v four so two into v four comes out to be equal to four minus five by three which is equal to eight minus five by three how much it comes sorry twelve minus five by three i am sorry so that comes out to be seven by three so v four is equal to seven by three multiplied by two how much it is seven divided by six so that is your answer seven divided by six can be written as one point one six five meter per second so how many of you got this got this question okay good few of you are giving me the answer nice let me solve another question for you you guys so this question is like this so let me write down that question for you the question tells that a truck starts from the rest and rolls down a hill with a constant acceleration so what happens there is a hill so suppose i am making this hill and there is a truck and suppose this is touching it it is not in the air so it rolls down the hill at a constant acceleration so what has been given to me that a is constant now what it has been given it travels a distance of so the truck is equal to 400 meters in what time time is equal to 20 seconds find the force acting on it if its mass is seven metric tons so you look at here you have to find out force acting on it you have to find out force what is the mass given mass is given as seven metric ton now if you don't know what is metric ton i tell you one metric ton is equal to how many kgs thousand kgs thousand kgs so how do you do it distance has been given time has been given d is equal to ut plus half 80 square u is zero so i am just writing half 80 square so look at here d is 400 half a i have to find out because acceleration has not been given t is 20 seconds 20 square is equal to 400 this 400 and 400 is 1 so you find a is equal to how much 2 meter per second square now what you do force is equal to mass into acceleration mass is 7 into thousand kgs and acceleration is 2 that comes out to be 14 000 newtons so that's your answer now next question which is a good question looks like a good question so look at here i am telling you that question and i'll give you some time question is i'll write down this question and i'll give you two minutes to solve this or eight metric ton and now i am not saying what is metric ton eight metric ton engine pulls five wagons of two metric ton each and where along or horizontal track now what happens engine is exerting a force of engine exerts a force of 4 40 000 newtons and track offers a friction force of 5000 newtons then calculate net acceleration force write down this question because i'll i'll i'll remove it while solving be acceleration of the train net net acceleration accelerating force b you have to write the acceleration of the train find this out then i'll give you third part with time permits do this question guys what's the answer gormand is saying 35 000 newtons or ishani is saying 35 000 newtons what is how are you getting your answer so 35 000 answer net accelerating force is exactly correct answer what happens engine is exerting a force of 40 000 newtons no need to solve this uh and and and and and frictional force is 5000 newton what do you mean by frictional force frictional force is applied opposite to the direction of the motion so exerting force the force of if engine would be pulling it towards east direction with 40 000 newton frictional force would be exactly direct exactly opposite direction of the motion which is in west direction and 55 000 is the magnitude of the friction force so total net force net force applied would be 40 000 minus 5000 which is equal to 35 000 newtons now what should be acceleration of the train so net force acceleration would be net force divided by mass now what is the mass so try to understand net force is how much let me write 35 000 newtons divided by what is the mass so mass would be mass of the engine plus mass of the wagons so mass of the engine is 8 000 kg mass of the wagons is 5 wagons 2000 kg each so 5 into 2000 is 10 000 kgs so total mass is how much 18 000 kgs so from here divide 18 000 kgs so how much it is 35 by 18 which is nearly 1.9 meter per second square now next question is let me solve another question let me guys did you understand this how many of you got the acceleration let me just check how many of you got the acceleration 1.9 anura got 1.9 great now let me move to another question this question is and this this would be probably the last question because we have done four kilometer of everything one question of gravitation also we have done so this would be probably last question so i'll wrap up the session after this the question is two objects each of mass one and a half kg are moving in same straight line so moving in opposite direction i'm just writing same straight line opposite direction opposite direction velocity of each one of them is 2 and a half meter per second before the collision so this is before the collision and after that after collision they stick together so what would be the resultant speed guys one mistake that i did in the previous question was in previous momentum question when i was doing it with 100 gram and 200 gram both the directions would be same and that is why i wrote m1 v1 plus m2 v2 no negative sign so this will go at two meter per second and this will go at one meter per second this two meter per second will go and collide with this so and here what happens if direction is opposite so if you are assuming this first object of 1.5 kg to be going in this direction with two and a half meter per second the other object will be in opposite direction which is also of 1.5 kg but its speed would be minus 2.5 meter per second why because if you are assuming this this velocity to be 2.5 meter per second this would be minus 2.5 meter per second so what happens m1 v1 plus m2 v2 now you look at here and that should be equal to because they they are sticking together so masses would be added m1 plus m2 multiplied by v resultant now look at here m for both of them are it same 1.5 into 2.5 minus 1.5 into 2.5 why minus because v2 is minus so this comes up to be how much 0 so that is equal to m1 plus m2 into vr now m1 and m2 cannot be 0 so from here vr comes out to be how much 0 so resultant velocity is how much 0 so that is how you have to solve these kind of question guys now so perhaps let me i think this this is sufficient enough for today so let me wrap up the session and if you have any doubt you can post it in the google sheet which has been spread on different groups so if if if there is any doubt regarding questions done in today's session you can post it on the chat box otherwise i'll wrap up the session thank you so much any doubt guys okay i'm not nobody is asking me any doubt so i'm wrapping up the session thank you so much for attending the class thank you