Adaptively Restrained Molecular dynamics (ARMD) allows users to perform more integration steps in wall-clock time by switching on and off positional degrees of freedoms. This article presents new, single-pass incremental force updates algorithms to efficiently simulate a system using ARMD. We assessed different algorithms for speedup measurements and implemented them in the LAMMPS MD package. We validated the single-pass incremental force update algorithm on four different benchmarks using diverse pair potentials. The proposed algorithm allows us to perform simulation of a system faster than traditional MD in both NVE and NVT ensembles. Moreover, ARMD using the new single-pass algorithm speeds up the convergence of observables in wall-clock time.