People have purpose and goals but natural science excludes final causes. People plan and design but natural science excludes formal causes. In that case call the science of formal and final (be)causes “hypernatural science”. These higher causes are not against nature (unlike supernatural) but are not inherent to nature (and so hypernatural).
A physics for people includes formal and final causes. People engage in motion with a purpose, an origin, a route, and a destination. Such movement is usually from place to place over a route, so that the spatial characteristics are chosen first. People are travelers. People also send (ship) objects for travel; such objects are called freight and the people are called shippers.
Once the destination is chosen, what remains is the temporal aspect which depends on the means and conditions of movement. Timed movement, as for exercise, is motion without a destination, which is less common. Even much exercise and game-playing has a place or target as a goal. Racing has a place goal par excellence.
Direction with space-time is measured from an origin, whereas direction with time-space is measured toward a destination. Extent of motion with space-time is measured spatially given the length of time, whereas extent of movement with time-space is measured temporally given the length of space. The difference is between the people-oriented view of movement given routes and destinations vs. the object-oriented view of motion given time and capability.
Given an origin, a route, and a destination the rate of progress is the pace, the elapsed time per unit distance. A zero rate is instantaneous, which is impossible. An infinite rate is motionless, which is no movement. Actual rates are finite. The pace of light is apparently the minimum pace. The other variables of lenticity, relentation, and so on are defined from here.
As the physics of space-time works best for natural motion, so the physics of time-space works for hypernatural movement.