What is the relative velocity equation?

Answer 1

If an object A moves with velocity #vecv""_A# and object B with #vecv""_B#, Then velocity of A with respect to B (As observed by observer B) is,

#vecv""_(AB)# = #vecv""_A - vecv""_B#.

To keep things simple, let's use linear motion as an example and assume that what we observe in one dimension also applies in two and three dimensions (which is a happy result of using vector notation).

Two cars A and B moving with velocities #v""_A# and #v""_B#.

Then, naturally, the velocity of A as perceived by a passenger in car B is

#v""_(AB) = v""_A - v""_B#

if #v""_A# is greater than #v""_B#.

The observer sees the car A going away (ahead) from it with speed #v""_(AB)#.

If the opposite is the case, #v""_(AB)# is negative.

The car B goes ahead of A with the speed #v""_(AB)#.

It is very easy to extend what we have seen here to three dimensions; all that needs to change are vector notations. All other details stay the same.

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Answer 2

Adrian Ayala

The relative velocity equation is given by:

[ \text{Relative Velocity} = \text{Velocity of Object A} - \text{Velocity of Object B} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.