The topic of definition of velocity in physics is a sporadically visited one.
However one has to be remined that it was one of the main issues at the begining of physics.
Definining velocity vectorially reduced the number of parameters needed to construct a theory to explain parabolic motion near earth surface. In this approach, the differing angles of projectile propulsion correspond to different velocities irrespective of the norm or average velocity of it.
This complemented the theory finely, explaining with the aid of inertia theorem and concept of acceleration the observed shape and temporal behavior.
However, it did not have to be. The fact that different angles give different shapes or spatial development (and thus temporal) could have been contained in a theory where a separate factor affecting motion, i.e. angle to gravity field, is taken into account with a non vectorial velocity and maybe some other principles that link the new factor in a theoretical framework that is able to produce results.
Such a theory has not been proposed- neither examined.
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