Relative velocity refers to the velocity of an object or observer with respect to another object or observer. It is the velocity of one object as measured from the perspective of another object, taking into account their relative motion. In other words, it describes how fast one object appears to be moving with respect to another object.
On the other hand, the velocity of separation or approach specifically refers to the rate at which two objects are moving away from or towards each other, respectively. It is a measure of the change in distance between the two objects over time.
To understand the difference more clearly, let's consider an example:
Suppose there are two cars, A and B, traveling on a straight road. Car A is moving at a speed of 60 km/h towards the east, and car B is moving at a speed of 40 km/h towards the west. In this scenario:
The relative velocity of car B with respect to car A is the sum of their individual velocities. So, the relative velocity would be 60 km/h (velocity of A) + (-40 km/h) (velocity of B) = 20 km/h towards the east. This means that car B appears to be moving towards the east with a speed of 20 km/h when observed from the frame of reference of car A.
The velocity of separation between car A and car B is the difference between their individual velocities. In this case, the velocity of separation would be 60 km/h (velocity of A) - (-40 km/h) (velocity of B) = 100 km/h towards the east. This indicates that the distance between the two cars is increasing at a rate of 100 km/h.
In summary, relative velocity describes the velocity of one object with respect to another, taking into account their relative motion, while the velocity of separation or approach specifically refers to the rate at which two objects are moving away from or towards each other.