Third order
If the Pythagoras(570-495 BC) picture above would not change under velocity, then we can differentiate x = R cos( a ) and y = R sin( a ) and then square them and add them up. This results in the first order space by time relation. Assuming that this picture is not changing under acceleration, results in the second order space by time relation. See the picture below. Assuming that this picture is not changing with any higher order movement results in a higher order space by time relation. See below. Coriolis (1792-1843) created the second order space by time relation.
Third order
Third order
Third order
Third order
 
Some pictures out of my reasoning
Third order
Third order Third order Third order
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