Relative velocity is the velocity of one object as observed from another moving object's frame of reference. It is a vector quantity that indicates how fast and in what direction one object is moving relative to another. The concept is crucial for analyzing motion when multiple objects are in motion and helps to understand their behavior from different perspectives. Mathematically, if object A has velocity v⃗A\vec{v}_AvA​ and object B has velocity v⃗B\vec{v}_BvB​ relative to a common reference (like the ground), the relative velocity of A with respect to B is given by:

v⃗AB=v⃗A−v⃗B\vec{v}_{AB}=\vec{v}_A-\vec{v}_BvAB​=vA​−vB​

Similarly, the relative velocity of B with respect to A is:

v⃗BA=v⃗B−v⃗A\vec{v}_{BA}=\vec{v}_B-\vec{v}_AvBA​=vB​−vA​

This means the relative velocity tells how fast one object appears to move as seen from the other. For example, two cars traveling in the same direction have a relative velocity equal to the difference of their speeds, while two cars traveling in opposite directions have a relative velocity equal to the sum of their speeds. The relative velocity helps determine how quickly two objects move towards or away from each other.