The V-model is the most appropriate lifecycle for developing a safety-critical application. This model integrates testing activities into each phase of the development lifecycle, starting from the requirements phase. For safety-critical systems, where failure can lead to catastrophic outcomes, this emphasis on early and continuous verification and validation is paramount. The V-model's rigid structure ensures that for every development phase (e.g., requirements specification, system design), there is a corresponding, pre-planned testing phase (e.g., acceptance testing, system testing). This provides the rigorous traceability, documentation, and systematic quality assurance mandated by safety standards like ISO 26262 or DO-178C.

B. Agile: Lacks the formal, upfront planning and comprehensive documentation typically required by certification bodies for safety-critical systems.

C. Rational Unified Process: While iterative and more structured than pure Agile, it is less explicitly focused on the strict verification-validation pairing inherent to the V-model.

D. Kanban: This is a method for managing workflow, not a full development lifecycle model, and it does not provide the necessary engineering rigor for safety assurance.

1. ISTQB Certified Tester Foundation Level Syllabus (2018, Version 3.1), Section 2.1.2, "Software Development Lifecycle Models in Context": The syllabus notes that the V-model is a sequential model where testing is planned and designed early. It states, "It is particularly well-suited for projects with stable requirements and high demands on quality and reliability, such as safety-critical systems."

2. Sommerville, I. (2016). Software Engineering (10th ed.). Pearson., Chapter 2, Section 2.1.3, "Process activities": The text describes the V-model as a representation of the relationships between development phases and testing activities. It highlights that this model explicitly shows validation and verification actions, which is a core principle in the development of critical systems where testing must be tied directly to specifications.

3. Storey, N. (1996). Safety-Critical Computer Systems. Addison-Wesley., Chapter 7, "The Development Process": This book discusses development processes for safety-critical systems, emphasizing the need for a structured lifecycle. The principles described align directly with the V-model's approach of linking verification and validation activities to each stage of specification and design to ensure all safety requirements are met and tested.