Acceleration, Uniformity, Velocity

Galileo's determination that Gravity is constant means not only that its effects on distinct objects are the same, but that its effects on a single object in the course of a single event is uniform.  So, insofar as Acceleration is defined as 'increase in Velocity', uniform Acceleration means uniform change in Velocity.  On the other hand, Velocity is defined as 'change of Distance in a Time-interval'.  Hence, it is conceived as an average, and, hence, as uniform in an interval.  Therefore, the notion of Velocity is problematic, if not contradictory, in a gravitational event, as well as in any another in which Acceleration is uniform.  So, the infinitesimal analysis that reduces an interval to instantaneity concomitantly minimizes the discrepancy between Velocity qua uniformly changing, and Velocity qua constant.  In such cases, mathematical precision can also be evasive abstraction.