 Hello friends, welcome again to problem solving on mechanics motion chapter in physics So we have been given with another good very interesting problem So what does this problem say? It says a body travels first half distance with a uniform speed you, right? Mark these words uniform speed you and next half distance Travels with uniform speed again and this time we find its average speed So you have to find out this is the demand of the question. So mark it again thrice average speed We have to find out So it's a very good practice to read the question thoroughly at least a couple of times so that there is no Ambiguity in your understanding, right? So a body travels first half distance with a uniform speed you Next half distance travels with the uniform speed V find its average speed in such question guys What you need to do is first draw our representative diagram. It gives a lot of clarity to your mind while Solving problems is very very good practice, right? So let me say this is the a and this point is B and let's say this is a half distance, right? So this point to be let's say C. Correct. So what is being said? So he moves like that with a uniform speed you okay? It's a case of uniform speed very clearly. It's a straight line motion and from here to here C to B It moves with the uniform velocity V and I have to find out what average speed, okay? So let's go one by one. So what is average speed basically? Let's start from the demand of the question itself. So let me write solution how to find the solution right what is average Average speed if you go by the Definition of average speed in physics. We say average speed is nothing but Total distance since it is speed. So it's right total distance covered by the body or we also say traversed traversed by the object object divided by divided by what? time taken time taken to cover the same Distance time taken to cover Cover that distance. So don't take any other time the only time which it takes to cover that distance. That's important Okay, so total distance traveled divided by total time taken clearly Here the total distance traveled is the length of AB, right? So let's say the total distance in this case was D No problem. Let's say assuming D even you know Many people get scared of the fact that no information is given how to find that No worries. Let me let us, you know, assume it to be D. What will happen at max? You will not be able to find the value of D. So big deal. Let's try So D is that and clearly C is the midpoint. No doubt about it. C is the midpoint So half the distance, right? So C is the midpoint is all of us No, so the moment it is midpoint So Euclid says and you would have studied that in maths as well So AC will be clearly D by 2. I Hope there is no ambiguity in this understanding D by 2, right? right guys and Okay, so D by 2 so Total distance traveled. I know in terms of D, but total time how to go about the time So we don't know anything about the time are the two times same I don't think so why because the velocities are same and they are covering the same distance So time need not be same. So can I just assume that in the first? First part it takes t1 time and in the second part second half that is it takes t2 time, right? So I don't know what t1 and t2 are so no problem We will see you know if we can find the value nothing like it Otherwise, we'll see how to go about it. So t1 and t2 becomes the time taken for the first half and the second half Now what do we know know from the physics point of view? So in physics, we can say that speed or uniform speed is what uniform speed? This is the underlying physics Concept, what is uniform speed if the body is undergoing a straight line motion again uniform speed always happens in straight line Motion no, sorry it is only for uniform velocity. It happens in straight line motion But uniform speed can happen also in non straight line motion because we are not talking about the direction We are only concerned about the magnitude, right? So uniform speed if you see it's nothing, but in this case the first half Let's say the first let's take the case one first half. Can I not write I is equal to you In this case you is equal to D by 2 upon t1, right? D by 2 upon t1, right? So you is equal to D by 2 upon t1, right? So hence what will be t1 guys t1 can be written as D by 2 you D by 2 you right? I hope this is understood. So this is speed upon time uniform speed Whatever is the speed? What is the formula of speed speed is equal to? Distance upon time. So the time taken was t1 Distance was D by 2. So hence t1 is D by 2 you let's come to the second part of the journey. What is happening here here the velocity or the speed uniform speed is V and The distance was D by 2 again and the time was t2, right? So from here, can I not say that t2 is equal to? D by D by 2 V t2 is equal to D by 2 V So let's go back to our average speed formula. Average speed is total distance traverse by the object Divide by time taken to cover that distance. So hence can I not say that average speed which is which can be written as U or V Anything and a bar over it. So this bar represents average, right? Or many many literature or many books will say U average will be nothing but total distance. How much is the total distance guys? D by 2 plus D by 2 first half and the second half Divide by total time. So t1 plus t2. This is a total time So hence it is D upon what was T1 guys D upon 2 U check T1 Plus D2 or T2 T2 is D upon 2 V Correct. So now only mathematics is left. I hope you understood total distance is D T1 is this one T2 is this one and you don't need to simplify it. So how is it? So if you see this can be written as D upon and D common in the denominator D by 2 rather and 1 by U plus 1 by V. I hope the mathematics part is clear to you So this D and this D will go. So what will happen? This 2 will just go up in the numerator So hence it becomes 2 divided by 1 by U plus 1 by V see automatically all the variables Which we didn't know D and T1 and T2 are eliminated So no problems U and V was already given. So if you simplify this you will get 2 and common denominator thing You have to take so this becomes U plus V, isn't it and hence finally the last step will be this part will now go up in the numerator, so it becomes 2 U V divided by U plus V Okay, so this can be remembered as a result also Let's say if half the distance is traveled with a uniform speed U and half with uniform speed V So the average velocity will not be U plus V by 2 many people make this mistake and they write U plus V by 2 So please be very very careful, right? So the distance are traveled and as in half the distance is traveled with you and half the distance with V So the average velocity will be 2 U V by U plus V that is the result. Okay. I hope you understood this problem