As microblogging services like Twitter are becoming more and more influential in today's globalised world, its facets like sentiment analysis are being extensively studied. We are no longer constrained by our own opinion. Others opinions and sentiments play a huge role in shaping our perspective. In this paper, we build on previous works on Twitter sentiment analysis using Distant Supervision. The existing approach requires huge computation resource for analysing large number of tweets. In this paper, we propose techniques to speed up the computation process for sentiment analysis. We use tweet subjectivity to select the right training samples. We also introduce the concept of EFWS (Effective Word Score) of a tweet that is derived from polarity scores of frequently used words, which is an additional heuristic that can be used to speed up the sentiment classification with standard machine learning algorithms. We performed our experiments using 1.6 million tweets. Experimental evaluations show that our proposed technique is more efficient and has higher accuracy compared to previously proposed methods. We achieve overall accuracies of around 80% (EFWS heuristic gives an accuracy around 85%) on a training dataset of 100K tweets, which is half the size of the dataset used for the baseline model. The accuracy of our proposed model is 2-3% higher than the baseline model, and the model effectively trains at twice the speed of the baseline model.