Equations for Speed, Time and Distance for Vehicles Under Maximum Acceleration

The acceleration achieved by a road vehicle falls off as it is taken up through the gears, due largely to the higher gear ratios employed at the higher speeds. The formulae of constant acceleration, which give a reasonable approximation when the vehicle is accelerating within a given gear, are greatly in error when the vehicle is accelerating up through the gears. Alternative formulae are presented, based upon the gear ratio changing to be always suitable for the speed of the vehicle. It is shown that these alternative formulae closely predict the results of road tests.