For kinematics and dynamics, one can begin with a body – something that takes space – and apply a motion to it. Or one can begin with a motion – something that takes time – and apply it to a body. In either case the result is a body and a motion – either a body with a motion or a motion with a body.
That, in a nutshell, is the difference between the spatiocosm and the tempocosm, that is, 3D space with 1D time and 3D time with 1D space. They are two ways of saying the same thing with a different emphasis.
Yes, a motion can be a “thing” – an entity of its own – the motion around a race track, for example. Applied to different contestants such a motion produces different timings. That is what the race is all about.
A body applies to different motions, too – a body such as a projectile, for example. When launched in different ways such a body travels different lengths, as in a contest for the longest length.
Compare the von Neumann computer architecture in which instructions and data share the same address space. Whether an address represents data or instructions depends only on the interpretation.
Different situations call for different perspectives. A race against time calls for a tempocosmic vew. A contest for distance calls for a spatiocosmic view.
Is there a combined perspective? Yes, in a relativistic sense, but it collapses to one or the other perspective as soon as a measurement is taken. If spatial position is measured, it’s a spatiocosmic view. If time and direction are measured, it’s a tempocosmic view.