A one-dimensional fluid model was developed and used to investigate the spatiotemporal dynamics of a pulsed-power inductively coupled argon plasma at 10 mTorr. Particular attention was devoted to extraction and acceleration of positive ions by a radio frequency (rf) bias applied in the afterglow stage of the discharge. For bias frequencies in the range omega/2 pi=100 kHz-10 MHz the rf sheath is resistive in nature. Significant oscillations of the ion flux at the driven electrode observed at omega tau approximate to 1 are related to the finite ion transit time tau through the sheath. The latter depends on the sheath thickness which is a complicated function of time in the pulsed plasma. For a constant time-average power, the time-average ion energy flux bombarding the wafer has a minimum with respect to the pulse period. This has implications for the wafer thermal budget.