Path planning is discussed in this article for an autonomous vehicle given a route to follow. Route data is considered to be available for a distance ahead of the vehicle in a receding horizon manner. Linear approximation of the nonlinear equations for a vehicle following a path is obtained. Based on these equations, the optimization problem is formed in a convex optimization format and solved to find the optimal path. Optimality is a trade-off between comfort and travel time. Results are provided for some cases considering that the vehicle is traveling in the Suzuka circuit and the observable horizon ahead of the vehicle is a part of this track. Results are discussed for a few trade-off values and analyzed from the practical point of view, which shows that the method is capable of producing an optimal path to follow in an insignificant amount of time. Finally, an alternative approach for improving model accuracy is proposed and discussed. Finally, it has been concluded that the proposed method has a significant potential for motion planning/controlling applications for an autonomous vehicle using model predictive control.