This paper develops a new principled framework for exploiting time-sensitive information to improve the truth discovery accuracy in social sensing applications. This work is motivated by the emergence of social sensing as a new paradigm of collecting observations about the physical environment from humans or devices on their behalf. These observations maybe true or false, and hence are viewed as binary claims. A fundamental problem in social sensing applications lies in ascertaining the correctness of claims and the reliability of data sources. We refer to this problem as truth discovery. Time is a critical dimension that needs to be carefully exploited in the truth discovery solutions. In this paper, we develop a new time-sensitive truth discovery scheme that explicitly incorporates the source responsiveness and the claim lifespan into a rigorous analytical framework. The new truth discovery scheme solves a maximum likelihood estimation problem to determine both the claim correctness and the source reliability. We compare our time-sensitive scheme with the state-of-the-art baselines through an extensive simulation study and a real world case study. The evaluation results showed that our new scheme outperforms all compared baselines and significantly improves the truth discovery accuracy in social sensing applications.