We present a study of the spatial distribution and kinematics of star-forming galaxies in 30 massive clusters at 0.15<z<0.30, combining wide-field Spitzer 24um and GALEX NUV imaging with highly-complete spectroscopy of cluster members. The fraction (f_SF) of star-forming cluster galaxies rises steadily with cluster-centric radius, increasing fivefold by 2r200, but remains well below field values even at 3r200. This suppression of star formation at large radii cannot be reproduced by models in which star formation is quenched in infalling field galaxies only once they pass within r200 of the cluster, but is consistent with some of them being first pre-processed within galaxy groups. Despite the increasing f_SF-radius trend, the surface density of star-forming galaxies actually declines steadily with radius, falling ~15x from the core to 2r200. This requires star-formation to survive within recently accreted spirals for 2--3Gyr to build up the apparent over-density of star-forming galaxies within clusters. The velocity dispersion profile of the star-forming galaxy population shows a sharp peak of 1.44-sigma_v at 0.3r500, and is 10--35% higher than that of the inactive cluster members at all cluster-centric radii, while their velocity distribution shows a flat, top-hat profile within r500. All of these results are consistent with star-forming cluster galaxies being an infalling population, but one that must also survive ~0.5--2Gyr beyond passing within r200. By comparing the observed distribution of star-forming galaxies in the stacked caustic diagram with predictions from the Millennium simulation, we obtain a best-fit model in which SFRs decline exponentially on quenching time-scales of 1.73pm0.25 Gyr upon accretion into the cluster.
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