1999 Mercury Villager Car Sputters after driving for 10 min

When I drive the car after it has been sitting over night, it starts up fine. I was driving on a highway going 55 mph for about 10 minutes and the car started to hesitate, car would sporadically accelerate when I hit the gas pedal. I took it to a mechanic and he noticed the distributor was breaking apart when it looked at it (said he saw pieces). He wasn't sure if this was causing it or not.

This has happened twice so far and both times it happened after I was driving the car for about 10 minutes.

Any suggestions would be appreciated.
Jeff Norberg, Orange, VA