in this video I'll be talking about related velocity relative velocity is the velocity of one object with respect to another object as I strike down here so it is object so let's assume we have a car there so we have a car here and this car is moving with 75 miles per hour with respect to an observer which is sitting or standing here and now let's say you have another car which is also moving with 75 miles per hour in the same direction both moving in the same direction we call this object or this car a and we call this as a car B and this is an observer so just write down o always transport the observer then the velocity of car a should be a be the V a V that means the velocity of car a with respect to car B gotta be so what is the velocity of this car with respect to this car as both are moving with exactly the same speed in the same direction the relative velocity is equal to the zero and now if I take the velocity of car with respect to observer that means the velocity of this car with respect to this observer then this I will just write it down here this means the velocity of car a related to Dover oh and we know that this is 75 mile per hour similarly the velocity of car a velocity of car B with respect to observer o is again 75 mile per hour now let's assume this car is moving in the other direction if you have a car which is moving in the opposite direction let's say it's hard to okay let's say this car is now if moving if we're moving in the opposite direction then the the distance between a and B will be changing with respect to time there will be more separation between the two cars in the distance it if this car were moving in the opposite direction if car be we're moving in opposite direction then the velocity of car a with respect to B would be simply equal to 75 minus minus 75 this 75 is the 70s 75 mile-per-hour of this object or I can write it down this way in a better way or you can write down the velocity of B minus velocity of a or this can't for the better of the most appropriate way of writing this one a is the velocity of car a with respect to observer o- velocity of car B with respect to observer this one we say is 75 if we take this direction as a positive direction - as this car if this car were moving in the opposite direction then it will be negative 75 so it would be 150 mile per hour say if the two cars were moving in the opposite direction and the relative velocity of one car with respect to another car would be 151 forever now how do you let me give you a little bit more mathematic background here let's say you have two cars here this is a car this is the position so let's say this is called a and this is car V these and this is the x coordinate and this is the y coordinate and this is a origin and we call the position of the car a with respect to this origin which is denoted by r0 that we call the position vector the same way the position of this car be with respect to this observer or this reference point we call it as the position vector of car B and it is denoted by this and you have an arrow the arrow denotes the vector and Direction team and that here our goal is to find out the position or the how does the position of car a is changing with respect to the car B this is our a B vector or we simply call how do you write down our a B again if you have to write down already the way you just write down is first right number are a - power B and then write down oh you know that's how you write down here and it makes sense Rab if you need to write down our at B then you have to go this way and then this way so our vo is negative which makes sense so our B let's say you have a vector here our a B vector this arrow if you need to go from B to a the path is going this way so it'll be negative and then this way which is positive so we have our a off - our do so our AO vector is the position of God a with respect to observer Oh similarly rb/o in the position of car B with respect to observer ho now our goal is to find out our a B what are the our a B means what is the position of car a with respect to car B this gives you the position caught a beam so so now so I'm calculating our a B vector our a B vector again as I said if you want to write down this vector how do you write down first start with our a vector minus B vector the same order and then now you want to find out with respect to because this position our a is given with respect to observer oh she's just right down over here and oh here all right then this becomes our a B vector this is the position vector of call a with respect to B now I'm taking the time derivative time derivative the time derivative this is our a vector minus B over DT or the co vector this means this is the position of a car a with respect to B so this will give you the velocity of car a with respect to car B and this is the velocity of car a with respect to observer and this gives you the velocity of car B with respect to observer B so what do you see here if you need to find out the velocity of car a with respect to car B then unity then it's simply equal to the velocity of car a with respect to an observer and then a negative or the minus the velocity of car B with respect to the same observer that's how you find out the relative velocity so this is the formula for calculating the relative velocity of one object with respect to another object you see since this comes our simply the difference of the the velocity with respect to a fixed object all right thank you