  Spin transport was studied in a two-dimensional electron gas hosted in a wide
GaAs quantum well occupying two subbands. Using space and time Kerr rotation
microscopy to image drifting spin packets under an in-plane accelerating
electric field, optical injection and detection of spin polarization were
achieved in a pump-probe configuration. The experimental data exhibited high
spin mobility and long spin lifetimes allowing to obtain the spin-orbit fields
as a function of the spin velocities. Surprisingly, above moderate electric
fields of 0.4V/cm with velocities higher than 2$\mu$m/ns, we observed a
dependence of both bulk and structure-related spin-orbit interactions on the
velocity magnitude. A remarkable feature is the increase of the cubic
Dresselhaus term to approximately half of the linear coupling when the velocity
is raised to 10$\mu$m/ns. In contrast, the Rashba coupling for both subbands
decreases to about half of its value in the same range. These results yield new
information for the application of drift models in spin-orbit fields and about
limitations for the operation of spin transistors.
