# Relative motion between two particles

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

• 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. – G. Smith Jul 28 '19 at 4:42
• @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? – Atharav Karhad Jul 28 '19 at 4:46
• And also does the observer always considers himself/herself stationary with respect to his/her frame of reference? – Atharav Karhad Jul 28 '19 at 4:48
• What would your reference frame mean, if not a reference frame in which you are at rest? – G. Smith Jul 28 '19 at 4:56
• In reality, it is fine to decouple the concepts of “reference frame” and “observer”. You can have one without the other. – G. Smith Jul 28 '19 at 4:57