A new transition curve-3 (NTC-3), joining two straight lines by providing second-degree contact related to the properties of vehicle-road system without the necessity of a circular arc, is presented. The NTC-3 is offered by curvature and superelevation functions and is compared with the new generation transition curves-1 and -2 (NTC-1, NTC-2) and spiral curves. The properties of vehicle-road system, represented by function of lateral change of acceleration (LCA), are examined for these curves. Three criteria are taken into account to compare the curves. The NTC-3 and NTC-1 are compared in five-different motion models: model with constant velocity, model with positive acceleration, model with negative acceleration, model with negative acceleration - positive acceleration, and model with positive acceleration - negative acceleration. Examination of three criteria shows that NTC-3 is superior to the other curves on the basis of vehicle-road system.