In physics, the choice between using average velocity and instantaneous velocity depends on the specific context and the nature of the problem you're trying to solve.
Average velocity is typically used when you want to describe the overall displacement of an object over a certain time interval. It is calculated by dividing the total displacement by the total time taken. This is useful when you're interested in the average behavior of an object over a given period, such as determining the average speed of a car during a road trip or finding the average velocity of a projectile over a specific time interval.
On the other hand, instantaneous velocity is used when you want to describe the velocity of an object at a specific instant in time. It represents the velocity of an object at an infinitesimally small time interval, essentially capturing its velocity at a particular moment. Instantaneous velocity is often derived from the concept of derivatives in calculus, and it can provide more detailed information about an object's motion at a particular point in time. It is commonly used when analyzing the motion of objects undergoing acceleration or when studying the behavior of objects at specific points in time.
In summary, average velocity is employed when considering the overall motion over a given time interval, while instantaneous velocity is used for examining the behavior of an object at a specific instant or when studying the changes in velocity over infinitesimally small time intervals.