Rayleigh-Taylor instability (RTI) is of critical important in a broad range of natural and industrial processes and is an intellectual challenge for theoretical studies. In this work, we analyze the scale-dependent linear and nonlinear Rayleigh{Taylor (RT) dynamics within the group theory approach. We link the governing equations, through an associated dynamical system based on space groups, to a momentum model based on scaling transformations. In doing so, we precisely derive expressions for the buoyancy and drag parameters of the momentum model, exactly integrate the model equations and determine solutions for bubbles and for spikes in both early-time and late-time regimes. In particular, we focus on the general situation in which the instability is driven by an acceleration having power-law time dependence. Our analysis provides extensive benchmarks for future research.