It is typically assumed that radiation pressure driven winds are accelerated to an asymptotic velocity of V ~ v_esc, where v_esc is the escape velocity from the central source. We note that this is not the case for dusty shells and clouds. Instead, i
f the shell or cloud is initially optically-thick to the UV emission from the source of luminosity L, then there is a significant boost in V that reflects the integral of the momentum absorbed as it is accelerated. For shells reaching a generalized Eddington limit, we show that V ~ (4R_UV L/M_sh c)^1/2, in both point-mass and isothermal-sphere potentials, where R_UV is the radius where the shell becomes optically-thin to UV photons, and M_sh is the mass of the shell. The asymptotic velocity significantly exceeds v_esc for typical parameters, and can explain the ~1000-2000km/s outflows observed from rapidly star-forming galaxies and active galactic nuclei if the surrounding halo has low gas density. Similarly fast outflows from massive stars can be accelerated on few - 10^3 yr timescales. These results carry over to clouds that subtend only a small fraction of the solid angle from the source of radiation and that expand as a consequence of their internal sound speed. We further consider the dynamics of shells that sweep up a dense circumstellar or circumgalactic medium. We calculate the momentum ratio Mdot v/(L/c) in the shell limit and show that it can only significantly exceed ~2 if the effective optical depth of the shell to re-radiated FIR photons is much larger than unity. We discuss simple prescriptions for the properties of galactic outflows for use in large-scale cosmological simulations. We also briefly discuss applications to the dusty ejection episodes of massive stars, the disruption of giant molecular clouds, and AGN.
