In recent years, the rapid increase in online video content has underscored the limitations of static Video Question Answering (VideoQA) models trained on fixed datasets, as they struggle to adapt to new questions or tasks posed by newly available content. In this paper, we explore the novel challenge of VideoQA within a continual learning framework, and empirically identify a critical issue: fine-tuning a large language model (LLM) for a sequence of tasks often results in catastrophic forgetting. To address this, we propose Collaborative Prompting (ColPro), which integrates specific question constraint prompting, knowledge acquisition prompting, and visual temporal awareness prompting. These prompts aim to capture textual question context, visual content, and video temporal dynamics in VideoQA, a perspective underexplored in prior research. Experimental results on the NExT-QA and DramaQA datasets show that ColPro achieves superior performance compared to existing approaches, achieving 55.14% accuracy on NExT-QA and 71.24% accuracy on DramaQA, highlighting its practical relevance and effectiveness.