For navigating vehicles, new two dimensional curves are proposed using kinematical principles. The vehicle is subject to a normal acceleration which is constant during motion. The minimal time paths with the restriction of constant normal acceleration are found using the principles of variational calculus. The minimization process leads to a nonlinear ordinary differential equation with third order. The path equation is transformed into a dimensionless form first. In this form, the equation contains a path parameter which is non-dimensional. The differential equation system is solved numerically by applying a fourth order Runge-Kutta algorithm. By adjusting the path parameter within the differential equation, the final destination point can be reached from the given initial conditions for the system. A shooting like algorithm is necessary to determine the exact value of the specific path parameter to reach a given final location. The velocity functions corresponding to the specific paths are also calculated. The curves enable smooth transitions from a straight path to a curved path for land, aerial and marine vehicles moving in two dimensional horizontal or vertical motions.