Imagine competing in a 42-kilometer-long marathon. You and your other friend who is participating in the marathon are running with the same velocity from the beginning of the race. Consider you both started at the same time. Then at every position, you both are at the same distance. If you observe the surroundings, you will notice you are in motion. But, when you observe your friend, you will notice that you are stationary, meaning, you are at rest. With this intuition from basic education that rest and motion are relative terms, we will rise further and dive deeper into relative velocity.
Consider there are spectators at some part of the journey. You already know that you are at rest with respect to your friend. But, any stationary observer who is watching you running will observe that you are travelling with a certain velocity. Therefore, the velocity of any object is a relative term.
While the instantaneous velocity solely depends upon the rate of change of displacement during that particular time, the velocity observed by an observer will depend upon the frame of reference. More specifically, we will only talk about the inertial frame of reference.
Relative Velocity
The velocity of an object observed by an observer through their frame of reference is called relative velocity.
Consider two objects A and B moving with velocity $\rm{\vec{v_a}}$ and $\rm{\vec{v_b}}$, respectively. Let the relative velocity of object A with respect to object B be denoted by $\rm{\vec{v_{ab}}}$ and defined as
$$\rm{\vec{v_{ab}} \ = \ \vec{v_a} \ - \ \vec{v_b}}$$
CASE I: Both objects are moving in the same direction
$$\rm{\vec{v_{ab}} \ = \ \vec{v_a} \ - \ \vec{v_b}}$$
CASE II: Both objects are moving in the opposite direction
$$\rm{\vec{v_{ab}} \ = \ \vec{v_a} \ - \ (- \vec{v_b})}$$
$$\rm{\vec{v_{ab}} \ = \ \vec{v_a} \ + \ \vec{v_b}}$$
By definition, the relative velocity of object B with respect to object A is defined as:
$$\rm{\vec{v_{ba}} \ = \ \vec{v_b} \ - \ \vec{v_a}}$$
$$\rm{\vec{v_{ba}} \ = \ - ( \vec{v_a} \ - \ \vec{v_b})}$$
$$\rm{\vec{v_{ba}} \ = \ - \vec{v_{ab}}}$$