We present simulations of size-resolved cloud drop activation, condensational growth, and collision/coalescence performed with a cloud microphysics parcel model. The study investigates the efficiency of precipitation formation in a warm cumulus cloud with emphasis on the timescale of precipitation formation and on the amount of precipitation produced and examines the response of these parameters to modifications of aerosol size and chemical properties at different updraft velocities. Both parameters affect the lifetime of a cloud, but it depends on environmental conditions whether their responses have similar or opposite influences. In relatively clean clouds (with a cloud drop number concentration below ~200 cm-3) the growth rate of precipitation drops and the precipitation water content decrease with increasing aerosol abundance, whereas in more polluted clouds (~400 cm-3 and more) precipitation formation is delayed, but the amount of precipitation increases. Precipitation formation depends in a complex way on the updraft speed, especially in polluted clouds that are characterized by a relatively dispersed drop size distribution. In clouds with updraft speeds between 20 and 50 cm/s, an increase of the aerosol abundance causes a slight suppression of the growth of precipitation drops, but this effect is more pronounced in clouds with smaller or larger updraft speeds. The results suggest that global aerosol-climate models may simulate the second indirect effect more consistently when the dispersion of the drop size distribution is accounted for.