Sounds to me like you VO2 max isn't high enough for the level you are riding at and when you stop, you don't have near enough oxygen getting to your brain. It also sounds slightly like dehydration. A newbie in my club passed out the other day because he did 20 miles at about 20 mph with out taking a drink. We were riding along and I noticed he was looking dazed and having a tough time keep ing up, so I asked when the last time he drank was, he said, "right beofre we started". When we stopped he stood up for maybe 5 mintues, then his eyes rolled back in his head and my buddy noticed he was falling soon enough for me to run over and catch him.
Take a few weeks and build up and aerobic base, then do intervals to work on your V02 max. And make sure you are hydrated. Starting a ride dehydrated is a really bad idea, don't just hydrate on the bike, hydrate all day so that when you start riding you are already ahead of the game.