Viscosity field evolution of the constant-traction model (CTM) and the variable-traction model (VTM) at 9, 10, and 10.8 Ma with isotherms at 773, 1273, and 1613 K. Only CTM reached continental breakup.The complex evolution of continental rift systems results from the intricate interplay of external driving forces and the rift system’s responses. For this reason, allowing plate kinematics to emerge from the force balance can provide deeper insights than imposing prescribed velocity boundary conditions. This study investigates the influence of temporally varying driving forces, possibly resulting from changes in slab dynamics, on rift evolution using numerical and semi-analytical models. Our results show that a continental rift can accelerate towards breakup even when it is currently extending slowly due to a reduced driving force that can arise from many different situations.