The game essentially packages a character's maximum velocity, acceleration potential, and agility into a commodity called "speed". This makes sense because these attributes are impossible to meaningfully compare across a variety of creatures of different sizes, strengths, body configurations, etc.
The Mobile feat (PHB, p. 168) essentially adds 10 "speed points" to a character's movement budget to reflect an increase in all movement abilities.
Thus a fighter with a pre-feat budget of 30 "speed points" must spend 15 (50%) of those to stand from prone. The question is: does it still cost him 15 "speed points" to stand post-feat? Or must he now spend 20 "speed points" (5 more) to do the exact same thing (more slowly) when, post-feat, he is presumed faster and more agile?