Joint sentiment/topic models are widely applied in detecting sentiment-aware topics on the lengthy review data and they are achieved with Latent Dirichlet Allocation (LDA) based model. Nowadays plenty of user-generated posts, e.g., tweets and E-commerce short reviews, are published on the social media and the posts imply the public's sentiments (i.e., positive and negative) towards various topics. However, the existing sentiment/topic models are not applicable to detect sentiment-aware topics on the posts, i.e., short texts, because applying the models to the short texts directly will suffer from the context sparsity problem. In this paper, we propose a Time-User Sentiment/Topic Latent Dirichlet Allocation (TUS-LDA) which aggregates posts in the same timeslice or user as a pseudo-document to alleviate the context sparsity problem. Moreover, we design approaches for parameter inference and incorporating prior knowledge into TUS-LDA. Experiments on the Sentiment140 and tweets of electronic products from Twitter7 show that TUS-LDA outperforms previous models in the tasks of sentiment classification and sentiment-aware topic extraction. Finally, we visualize the sentiment-aware topics discovered by TUS-LDA.