Low-mode drive asymmetries are known as significant performance degradation factors in indirect-drive inertial confinement fusion (ICF) implosions. We propose a two-dimensional (2D) dynamic model to explore the impact of time-dependent low-mode drive asymmetries on the shell asymmetries in acceleration phases of implosions. Since during acceleration, the shell areal density () asymmetries are relatively small, we can treat the shell as thin shell pieces with finite mass and infinitesimally small thicknesses, neglecting the angular flows between these pieces. The radial motion of each shell piece is dominated by Newton's law. Through this model, the evolution of the shell radial velocity and the shell radius asymmetries of degree n can be characterized in terms of the drive temperature, time-dependent drive asymmetry of degree n and the average , , obtained from one-dimensional (1D) simulations. The acceleration phases of typical gas-fill capsule and layered DT capsule implosions with P2 or P4 drive asymmetries are explored using this model and validated using both 2D radiation hydrodynamic simulations and available backlit shell distortion measurements. This model gives a useful tool for ICF design, with an advantage of simplicity and speed.