This paper investigates the data accumulation velocity of 12 Altmetric.com data sources. DOI created date recorded by Crossref and altmetric event posted date tracked by Altmetric.com are combined to reflect the altmetric data accumulation patterns over time and to compare the data accumulation velocity of various data sources through three proposed indicators, including Velocity Index, altmetric half-life, and altmetric time delay. Results show that altmetric data sources exhibit different data accumulation velocity. Some altmetric data sources have data accumulated very fast within the first few days after publication, such as Reddit, Twitter, News, Facebook, Google+, and Blogs. On the opposite spectrum, research outputs are at relatively slow pace in accruing data on some data sources, like Policy documents, Peer review, Q&A, Wikipedia, Video, and F1000Prime. Most altmetric data sources' velocity degree also changes by document types, subject fields, and research topics. The type Review is slower in receiving altmetric mentions than Article, while Editorial Material and Letter are typically faster. In general, most altmetric data sources show higher velocity values in the fields of Physical Sciences and Engineering and Life and Earth Sciences. Within each field, there also exist some research topics that attract social attention faster than others.