Path planning algorithm integrated with a velocity profile generation-based navigation system is one of the most important aspects of an autonomous driving system. In this paper, a real-time path planning solution to obtain a feasible and collision-free trajectory is proposed for navigating an autonomous car on a virtual highway. This is achieved by designing the navigation algorithm to incorporate a path planner for finding the optimal path, and a velocity planning algorithm for ensuring a safe and comfortable motion along the obtained path. The navigation algorithm was validated on the Unity 3D Highway-Simulated Environment for practical driving while maintaining velocity and acceleration constraints. The autonomous vehicle drives at the maximum specified velocity until interrupted by vehicular traffic, whereas then, the path planner, based on the various constraints provided by the simulator using µWebSockets, decides to either decelerate the vehicle or shift to a more secure lane. Subsequently, a splinebased trajectory generation for this path results in continuous and smooth trajectories. The velocity planner employs an analytical method based on trapezoidal velocity profile to generate velocities for the vehicle traveling along the precomputed path. To provide smooth control, an s-like trapezoidal profile is considered that uses a cubic spline for generating velocities for the ramp-up and ramp-down portions of the curve. The acceleration and velocity constraints, which are derived from road limitations and physical systems, are explicitly considered. Depending upon these constraints and higher module requirements (e.g., maintaining velocity, and stopping), an appropriate segment of the velocity profile is deployed. The motion profiles for all the use-cases are generated and verified graphically.