How do I change culture on team as an athlete?

[sick of being mediocre]

I am a college cross country and track athlete. My team is highly talented but has failed to be successful. As the least naturally talented member, I have risen to the top of our team. However, despite modeling excellence and trying to encourage my teammates to follow me in that they are stuck in mediocrity. Everyone on the team has paid lip service to doing what it takes to win and are upset when we under-perform, so that's a start. I am frustrated because a lot can be blamed on my coach, and I am struggling to lead up the chain of command. I have been named a captain going into the upcoming season and have the best opportunity yet to lead my team to victory. Do any of you have any advice for making dramatic culture changes to turn a losing team into a winning team. Thank you in advance. 

[mynewunit]

There are lot of variables to get a hold of. First is the deficiencies of the athletes. Learn what needs to be done to improve that.
Second is why are they not performing better. Do they want to win?

If you want some actual things to work on. Speed is a product of maximal strength. Getting some team members to learn to Deadlift would be a huge help. Look into Mark Rippetoe and starting strength.
Another thing is to do some non-ideal condition training. This does 2 things. Number 1 is it builds the team. Doing hard things together increases cortisol, which deepens relationships. That will help you guys succeed together. The other thing is it removes the problem. I didn't do well because I fell, it rained, my side hurt, or whatever. Try this start a day of training by having a water balloon, squirt gun fight. Then shoes off, roll around on the ground, get dirty and sandy, shoes back on and run 2 miles. This is a way to inoculate you to the stress of something going wrong.
Your leadership will say neither of these things are helpful. They will say it will cause injuries. Confirmation bias will have them believe they are correct once someone gets injured lifting or rolling on the ground.
Understand that before you start and you should be okay.