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Connected and Automated Vehicles (CAVs) have the potential to significantly improve road safety, fuel efficiency, and traffic flow by forming platoons with short inter-vehicle gaps, enabled by vehicle-to-vehicle communications and onboard sensors. However, wireless connectivity for CAVs is subject to time-varying delays, which can significantly impact platoon safety during emergency braking. To this end, this paper evaluates the communication delays incurred by platoon vehicles during emergency braking under various data and traffic densities. Additionally, an emergency braking strategy named adaptive emergency braking is proposed and compared with five other strategies based on their ability to meet the functional requirements of collision avoidance and minimizing the stopping distance of the platoon lead vehicle, which are crucial for transitioning a platoon to a fail-safe state. Moreover, the emergency braking strategies are evaluated through rigorous simulations, considering non-functional criteria such as required inter-vehicle gaps, maximum allowable deceleration rates, and their robustness under time-varying communication delays.