I was wondering how much playing time and injuries effect the speed at which players develop.

The red bar approaching blue happens during practices and is drives by the coaching hierarchy above the player (position-coordinator-head); playing time does not impact the skill development. Position experience and conditioning improve a small amount during practice but really require playing time to see significant improvements. Injuries only effect this in the sense that they are playing less; of course, better conditioning = less chance of injury, so there's that catch-22 that you have to decide how to solve for your team (normally the standard preseason schedule of starters pulled after the first quarter in game 1, the second quarter in game 2, the third quarter in game 3, and the first quarter in game 4 will get your starters well-conditioned without risking too much injury. This is in the Misc. Gameplan settings.)