 Welcome my dear friends and we are going to take up another problem on motion and Try to solve it with whatever learning we have. Okay, so let's let's first read out the question thoroughly two times so on a 120 kilometer track a train travels the first 30 kilometer first 30 kilometer with a uniform speed my friends uniform uniform speed of 30 kilometers per hour. Okay, this is what I got to understand that there's a 120 kilometer track A train is traveling the first 30 kilometers Out of those 120 kilometers this traveling with the uniform speed of 30 kilometers per hour How fast must the train travel the next 90 kilometers? So as to average 60 kilometers per hour for the entire trip Once again, so there's a 120 kilometer track train travels the first 30 kilometer with the uniform speed of 30 kilometers per hour How fast must the train travel the next 90 kilometers? So as to average 60 kilometers per hour for the entire trip so clearly You know the only first look of it. It appears to be a problem related to average speed Okay, so let's try and you know what should be the first step What should be the approach so average speed? Problem, but for any problem in physics, I normally recommend that you first have a representative diagram to Give a clarity to the mind about whatever you are Analyzing so let's say this is the 120 kilometer track Okay, so let's say this point is a this point is B endpoint and for the you know Convenience sake we have taken a linear or a straight line. It could be any Curve linear path also Doesn't matter because we are talking about speed. We are not going to take up You know the direction because velocity is not talked about it's only speed So immaterial it is whether you take a straight line or a curved path Okay, now they say that this is 120 meter 120 kilometer. Sorry, so please also be very very careful about the Unit so this is 120 kilometer guys. No problem Then the first 30 so let's say this is the first point P AP right and let's say this distance is 30 kilometers 30 Kilometers and this one automatically becomes 90 kilometers Isn't it so the diagram gives gives a lot of clarity now, let's say the Time taken as a what do you think do you think the time taken will be same or do we even need time taken but there's no problem in Taking some value or some variable as time. So let's say this is T1 and This journey takes T2 hours will be talking out talking in only in kilometers and ours Okay, so T1 ours and T2 ours So now the question is how to find out average speed so average speed guys if you recall your Knowledge average speed from physics classes. You would have learned average speed of any body is nothing but total Distance traveled mind the word distance. I'm not talking about displacement. It is total Distance traveled. Okay. So if it was displacement Then we have to just take the final and the initial points and the length of the path would become immaterial So total distance traveled Since we are talking distance here, we have to take the total length of the path and total time Taken So let's write physics first and then the problem is reduced only to do mathematics with it So this is what we have to find out average speed. So if you see We can write this as v average Right is total distance. So what is total distance traveled guys? So 120 kilometers no doubt about it Hmm and divided by P1 plus T2 is the total time in ours Isn't it? So somehow if I find out T1 and T2 my job is done So can I find T1 and T2? Yes, I can how So it's given. What is given it's given that the first 30 kilometers it travels with a uniform speed of 30 kilometers per hour. So here let's say I'm writing v1 as 30 kmph Kilometers per hour And in the second trip the velocity is not known. That is what we have to find out That is what we have to find out. We do not sorry not average speed. We have to find out v2. Isn't it? So v2 has to be found out never mind What else data is there? 60 kilometers per hour is average speed. So we are aware of this quantity So we can write here v average Is equal to 60 kilometers per hour right Now so if I find out somehow You know an expression which is involving v2 then our job is done So let's try to analyze what these T1 and T2 are. What is this T1 and what is T2? What is T1? T1 is time taken to complete ap. So let's write ap journey in this journey A to P journey What happens? We have v1 is equal to 30 upon T1. Isn't it? 30 kilometers is the distance traveled and T1 is the time taken so I can tell you T1 is 30 upon v1 And what was v1 my dear friend 30? So 30 is the kilometers divided by 30 kilometers per hour. So this is kilometers and kilometers per hour So this is simply one hour. So we got to know T1 value is now known So what is T2 guys? Let's take T2 now. So what is T2? If you see T2 similarly, so this is PB journey in PB journey P to B journey that is What happens T2 again can be written as 90 is the distance divided by The speed v2. Isn't it time is distance by speed always remember Let me write it here over here time is distance upon speed Okay, because speed was distance upon time Now if that is so can I you know, that's what we have to find out v2, right? So let it be like this Right now go to equation number one. Let us say this is equation number one Okay, so in one if you see what is we average guys 60 Given right and on the right hand side. So we average is 60. How here is the value? Here is the value so 60 is 120 upon T1 T1 We just found out it is one see T1 is one and T2 cannot write T2 as 90 upon v2 and we were supposed to find out v2 So we have got a relationship. We'll be able to find it So if you see you take this entity whole to this side And take 60 to this side. What will happen? You will get Just simple cross multiplication will lead to one plus 90 by v2 And this is equal to 120 by 60 Right, just simple manipulation of mathematics. We are not doing physics anymore. It's only about maths now. So this is two Okay, so what do I get from here 90 upon v2 Is equal to two and then this one if you transpose on the left right hand side, it will become two minus one Right, so this will become 90 is equal to 90 by v2 is equal to one So from there we can say v2 is equal to 90 and do not forget to mention the units since everything goes into kilometers and hours So v2 will be 90 kilometers per hour So with this speed if the train runs on the track for the next 90 kilometers after covering First 30 kilometers at a speed of 30 kilometers per hour Then the average would be 60 kilometers hour per hour average speed will be 60 kilometers per hour. So I hope You've got the Solution so what is the learning learning is draw the diagram read the question carefully find the demand of the question Go to the basics what you have learned So the concept here was the concept of average speed which was total distance by total time And then whenever the speed is constant you can always write Speed is equal to distance upon time these two things we employed here and We got the solution. Okay, so that's how you should approach these problems