It is suggested that the salient features of the velocity structure underlying the broad absorption lines of some quasars (BAL QSOs) are produced in a time-variable, freely expanding wind. The observed span in velocities of absorbing elements is produced by time variations in the ejection speed of the gas and not by acceleration of the gas in the absorption region, as must be the case in steady state models. We characterize such a wind by time-dependent mass injection and energy injection rates M^dot^_0_ and E^dot^_0_, respectively, producing a characteristic ejection velocity u_0_ = (2E^dot^_0_/M^dot^_0_)^1/2^. The observed width of the broad absorption troughs thus reflects the amplitude of the variations of u_0_. Connected, detached, and multiple troughs are readily produced. The shortest time scale, τ, over which the injection varies appreciably affects the total mass column density, N, in the high-velocity region: N ~ E^dot^/u^4^_0tau. The typical radius of high-velocity region is R ~ u_0tau. Time variations of smaller amplitudes and shorter time scales produce finer structure superposed on the wide troughs.