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I already know the relation of relative velocity as : Vab=Va-Vb So is there any derivation for this relation or is just how it is defined?

Relating to this i am finding some hard time to imagine why why velocities of two particles is added when they move in opposite direction and subtracted when they move in same direction?

Although i should not have asked two questions at a time but still i would be grateful if i get both answers at the same time. Thanks

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  • $\begingroup$ If we are both walking at 3 km per hour in the same direction, what is our relative velocity? Since the answer is zero, you obviously have to subtract, not add. $\endgroup$ – G. Smith Jul 28 at 4:42
  • $\begingroup$ @G.Smith it will be zero. I am actually struggling to imagine how velocities get added in opposite motion like if i am in a car moving with 5m/s and another car is moving towards me with 3m/s so i will feel that the car infront of me is moving with 8m/s and i will be at rest? $\endgroup$ – Atharav Karhad Jul 28 at 4:46
  • $\begingroup$ And also does the observer always considers himself/herself stationary with respect to his/her frame of reference? $\endgroup$ – Atharav Karhad Jul 28 at 4:48
  • $\begingroup$ What would your reference frame mean, if not a reference frame in which you are at rest? $\endgroup$ – G. Smith Jul 28 at 4:56
  • $\begingroup$ In reality, it is fine to decouple the concepts of “reference frame” and “observer”. You can have one without the other. $\endgroup$ – G. Smith Jul 28 at 4:57
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That relative motion expression for your question was non relativistic motion.

When consider non relativistic motion, people take it from the usual experience. The additive property was assumed. i.e. the so called "if you are traveling at 20 km/h, you add an extra 30 km/h in the same direction, your speed would be at 50 km/h". With velocity, it's the same ideal of speed with vectorization.

Some mathematicians though, define such relation directly on vector space by some type of transformation, of which in consist with the daily observation.

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