The sliding of charged solitons in heavily doped trans-polyacetylene is investigated by undertaking a molecular dynamics simulation with a charged model molecule. The saturated soliton sliding speed is determined so that the period of the passing solitons achieves a constant value, i.e., 15 fs. A mechanism is proposed where coupling occurs between the passing solitons and the C-C stretching vibration. This coupling determines the saturated sliding speed. As the accumulated energy of the C-C stretching vibration is effectively used for the soliton lattice translation, the speed becomes stable. and coherent sliding occurs. A comparison of (CH), with (CD), shows that the C-D bending mode mixes easily with the C-C stretching mode in the sliding process. The soliton sliding speed of (CD)(x), is not as stable as that of (CH)(x). This implies that (CD)(x) cannot have a conductivity as high as that of (CH)(x).