With recent advancements in the research and application of robotics, sensory devices, and Intelligent Transport Systems, autonomous vehicles are expected to become an integral part of the future transportation system. This paper focuses on developing a Car-Following(C-F) algorithm for a platoon of Connected Autonomous Vehicles (CAV) in freeway traffic. The platoon C-F algorithm is modeled to achieve stability and safety making use of the Vehicle to Vehicle (V2V) and Vehicle to Infrastructure (V2I) communications technology available. CAVs can travel at very short gaps between two consecutive vehicles with the Cooperative Adaptive Cruise Control (CACC) technology readily available/implemented. In this context, platooning stands out as a collaborative driving management strategy with great potential. From the existing literature, it is understood that there is limited research on platoon stability and safety in a CAV platooning environment. In this paper, we develop a microscopic modeling approach for the platooning of CAVs. The performance and stability of the platoon are analyzed, showing that the C-F algorithm ensures stability with transient and asymptotic dynamic performance. Sensitivity and safety analyses are also done, proving that the resulting platoon of CAVs is safe in the most demanding traffic conditions.