Many of the advances in rapid solidification processing of metallic alloys exploit the trapping of solute which occurs at high solidification velocities. The difficulty of performing experiments which measure such high solidification velocities in metals has until now prevented accurate measurements of solute trapping in these systems. We have observed the transition from near-equilibrium solute partitioning to solute trapping during solidification at m/s velocities in aluminum alloys, and have compared the predictions of various solute trapping models. Aluminum thin films deposited on insulators were ion-implanted with Sn, Cu, Ge, and In, and were pulsed-laser melted; plane-front solidification was achieved, and regrowth velocities of 0.6 m/s to 5 m/s were measured with the transient conductance technique. Of the existing solute trapping models, the Continuous Growth Model of Aziz was found to fit the observed dependence of the partition coefficient on solidification velocity more closely than any other single-parameter model. The diffusive speed, which locates the transition from solute partitioning to solute trapping, was found to vary from 6 m/s to 38 m/s for various solutes in aluminum. We have examined correlations between the diffusive speed in the Continuous Growth Model and known alloy properties in order to allow better estimates of the diffusive speed to be made for alloy systems in which it has not been measured; the relation between the diffusive speed and the equilibrium partition coefficient will be discussed.