Physics Related with Co-moving Coordinate System

We derive the metric of an expanding universe with zero accelerations by pure kinematic method. By doing so we expatiate physics related with co-moving coordinate system in details. The most important discovery or our study is, in an expanding universe with zero accelerations, the red-shift of photons from distance galaxies is determined by the co-moving coordinate of the source galaxy instead of the scale factor's time dependence. Our discovery is consistent with the current observed super-novaes's luminosity-distance v.s. red-shift relations.