mysql fulltext query is very slow
Usually FULLTEXT searches need more than a single letter, there is actually a setting that prevents them from being used if less than X number of characters are used.


  ft_min_word_length: The minimum length of the word to be included in a
  FULLTEXT index. Note: FULLTEXT indexes must be rebuilt after changing
  this variable


My guess is that you are not using your index when you search for a single character like that.