Final answer:
The average velocity and instantaneous velocity vectors are identical when an object is moving with a constant velocity, implying no changes in direction or speed. This occurs typically when a car travels at a constant speed on a highway without turning.
Step-by-step explanation:
A situation in which the average velocity and the instantaneous velocity vectors are identical is when an object is moving with constant velocity. This implies there is no acceleration (= 0), and the velocity remains the same over the duration of the time interval considered. As such, the average velocity, which is the total displacement divided by the time taken, will match the instantaneous velocity at every point in time.
In practical terms, this could be observed if a car is cruising on a highway at a constant speed without changing direction. Since there is no change in speed or direction, the instantaneous velocity at any given point is the same as the average velocity over the entire trip.
Significance: The average velocity can be equal to the instantaneous velocity when the motion of an object is uniform, meaning its path doesn't involve any acceleration or deceleration, and there are no changes in direction. If, for example, a train moves from point A to point B at a constant speed and then returns back to point A at that same speed, the average velocity would be zero because the starting and ending points are the same (