# What is the relative velocity equation?

Jul 26, 2015

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) = $\vec{v} {\text{_A - vecv}}_{B}$.

#### Explanation:

As an example, let us consider linear motion for simplicity and assume that our observations in one dimension holds for two and three dimensions. (By using vector notation, this happily turns out to be the case.)

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

Velocity of A as observed by a person sitting in car B is then naturally,

$v {\text{_(AB) = v""_A - v}}_{B}$

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).

Extending what we observed here to three dimensions is trivial.
We just have to use vector notations for that. Other details remain unchanged.