At a small time interval, the average velocity is approximately equal to the instantaneous velocity. However, the values of the average velocity and the instantaneous velocity approach each other , as the length of the time interval is decreased more and more.
When there is no acceleration or when there is constant acceleration. When either of these cases is present, the graph of velocity versus time will be linear. When there is linear velocity, the average velocity will equal the instantaneous velocity at any point on the graph.
The tangent at a point on the position-time graph represents the instantaneous velocity. 1. The tangent is the instantaneous slope. 2. Rather than "average" velocity, the slope gives you "instantaneous" velocity. The average of the instantaneous gives you average velocity.