In treating the motion of solitonic exitations in polyacetylene Newton's equation is used to approximate the lattice dynamics. The force field is obtained from the deviation of the π-electron densities in the bonds from their equilibrium densities. The π-electron density distributions are evaluated with the step-potential model. This model of a nearly free π-electron coupled to the elastic lattice of σ-bonded hydrocarbon ions is the conceptually simplest approach and has no free parameters. The electron-phonon coupling constant is scaled to butadiene and benzene. It is shown that a neutral kink moves frictionless for velocities up to three times the velocity of sound and shakes off phonons at higher velocities. This is in contrast to the results of the SSH-model, where the maximum velocity of the neutral kink is expected to be in a considerable range (0.6-4.0 times velocity of sound) depending on adjustable parameters.