Multiple interrogation of spin density distributions by repeated application of narrow pulsed magnetic field gradients is introduced as a general approach to investigate the time behavior of a spin system undergoing macroscopic motion. The joint n-time probability densities obtained from this procedure can be treated directly in terms of the evolution of positions. Alternatively, appropriately designed pulse sequences allow the selective encoding of higher order parameters of motion such as velocity or acceleration. These quantities can be determined repeatedly within one gradient pulse sequence and can be statistically related to each other. Corresponding pulse sequences are presented and 2-dimensional propagators, correlation functions, and correlation coefficients are compared as different means of representing these correlations. The formalism is applied to numerical simulations of the following situations: rotation of an object at constant speed and laminar flow through a cylindrical pipe and a model porous system.