Calculations are presented from which the standard equations of motion of objects in expanding space, Hubble's law, are derived. Three independent approaches were used: the formalism of general relativity, Newtonian physics and equations based on the philosophy of dialectical materialism. All equations obtained in different approaches are consistent and do not contradict each other. Examples of using equations of motion to construct motion diagrams are given. Calculations are presented, from which the standard equations of motion of objects in expanding space, Hubble's law are derived. Three independent approaches are used: the formalism of the general theory of relativity, Newton's physics and equations based on the philosophy of dialectical materialism. All equations obtained in different approaches are consistent and do not contradict each other. Examples of using the equations of motion to construct motion diagrams are given.