Controlling the flow of electrons by manipulation of their spin is a key to the development of spin-based electronics. While recent demonstrations of electrical-gate control in spin-transistor configurations show great promise, operation at room temperature remains elusive. Further progress requires a deeper understanding of the propagation of spin polarization, particularly in the high mobility semiconductors used for devices. Here we report the application of Doppler velocimetry to resolve the motion of spin-polarized electrons in GaAs quantum wells driven by a drifting Fermi sea. We find that the spin mobility tracks the high electron mobility precisely as a function of T.However, we also observe that the coherent precession of spins driven by spin-orbit interaction, which is essential for the operation of a broad class of spin logic devices, breaks down at temperatures above 150 K for reasons that are not understood theoretically.The transistor, the iconic invention of 20 th century science, is a semiconductor device in which the flow of electrons is modulated by voltages applied via electrodes known appropriately as gates. In a conventional transistor the gate electrode controls the number of mobile electrons in the current carrying pathway, or "channel." In pursuit of transistors with faster response and lower rates of energy dissipation, there has been intense investigation aimed at modulating current through manipulation of spin by applied electric fields [1,2], a coupling that occurs because of the spin-orbit (SO) interaction. Recently, gate-controlled modulation of current via SO coupling has been demonstrated in prototype device structures that operate below room temperature [3,4].Further progress towards spintronic logic requires a deeper understanding of the basic physical principles upon which such devices are based. Essentially the question is this: how far, and how fast, can spin polarization propagate in a current-carrying electron gas? This question was first addressed in pioneering work that used magneto-optic imaging to follow the drift of spin polarization packets in real space [5]. These experiments were enabled by the enhanced spin lifetimes (in excess of 10 ns) that arise near the metal-insulator transition of a doped semiconductor at the expense of electron mobility, . However, the high electron gas needed for fast devices is in a very different dynamical regime, where spin lifetimes are ~ 10-100 ps, during which time spin may propagate only 10-100 nm (depending on the temperature, T, and