In this paper, the problem to find the minimum control efforts trajectory of constant speed vehicle is reduced by non-dimensionalization and is formulated as a two point boundary value problem (TPBVP). Optimal input is given as a function of states and unknown parameters; the parameters are determined by solving the TPBVP using shooting method. The method for providing the initial guess of the shooting method is also proposed. The number of iterations in shooting method shows the validity of our method for initial guess.