The time evolution of the radiation pressure forces due to the action of laser light on matter in the form of neutral molecules, atoms, and ions is considered when the frequency of the light is comparable to a dipole-allowed transition frequency. We find that the transient regime, applicable from the instant the laser is switched on, is important for the gross motion, provided that the upper-state lifetime ??1 is relatively long, while the steady-state regime, formally such that t???1, is appropriate for the evaluation of the forces and the dynamics for large ?. With a focus on the orbital-angular-momentum-endowed laser light, the light-induced time-dependent forces and torques are determined and their full time dependence utilized to determine trajectories. Marked differences are found in both translational and rotational features in comparison with the results emerging when the steady-state forces are assumed from the outset. Intricate and detailed atom trajectories are plotted for Laguerre-Gaussian light at near resonance for a transition of Eu3+ that has a particularly small ?. The implications of the results for trapping and manipulating atoms and ions using laser light are pointed out and discussed.