An algorithm that enhances the stability and traction of a road vehicle (which may be steering) during ‘acceleration’ (meaning either braking or accelerating) is presented. This algorithm has two domains: partial-effort acceleration and maximum-effort acceleration. During partial-effort acceleration, stability enhancement requires only proper distribution of longitudinal traction forces. During maximum-effort acceleration, stability enhancement requires distribution and reduction of longitudinal traction forces. The algorithm attempts to provide the desired levels of acceleration while it simultaneously constrains trajectory disturbance of the vehicle. The algorithm uses total information about the road surface characteristics, the driver's actions, and the vehicle's design and dynamic states. It fully accommodates non-linear vehicle dynamics and tyre force characteristics. The algorithm has the form of a linear program and its operation is traced in a series of graphs where the geometry of linear programming is used as a setting.