This paper proposes a new approach to the boundary value problem of finding a vehicle path from an initial state, defined by a position and velocity vector, to a target position. The presented method explicitly considers magnitude constraints on both the velocity and the acceleration of the vehicle when determining the path. A semi-analytic and computationally efficient algorithm is employed, applicable for real-time and embedded environments. The generated trajectories aim to minimize the time to target, using parabolic arcs and straight lines. Solutions to both the 2D and 3D problem are introduced. Additionally, a comparison with proven time-optimal path planning approaches, namely Dubins curves, demonstrates the contribution of the presented algorithm.