This is inspired by a project I undertook for my Physics class last year; I'd like to apply it in the future.
Background: For the project, I and a few classmates were required to build a small car powered by any of a number of sources; we opted for a mousetrap that turned two rear wheels on a four-wheel car as it was released. Our group's goal was to make the car go as far as possible.
One problem was that the power source was not constant. The lever arm of the trap lifted in an arc for about five seconds, then returned to its resting position. During this time, it propelled the car. The car then coasted for the rest of the way.
In the powered stage, we wanted to increase traction. The wheels were CDs (because we had a $5.00 budget), which have a tendency to spin out. So we attached pieces of cloth to them to get better traction. On the second stage, however, we found that this cloth slowed down the car quite a bit because it dramatically increased friction (as we found out after several hours of testing different combinations).
Other groups used duct tape to cover the wheels, and some used records, which seemed to do slightly better than CDs (though that violated the size restrictions). Cloth seemed to have the best traction, though - we didn't have many spinouts. The tests were done on a typical classroom floor (I'm not sure what it's made of - linoleum? - but it's the same as in almost every school, at least in America).
In a wheeled vehicle in general - obviously not just a small car powered by a mousetrap - how can I substantially improve traction on the wheels while the power source is on yet reduce friction while it coasts? Is it as simple as choosing certain tires, or is there a bigger and better engineering solution?
As a final wrap-up: My thought would be to have a shifting center of mass for the vehicle, where the powered wheels have a lesser tendency to slip and the front wheels are nearly frictionless. During the powered stage, the center of mass would be near the back, while in the coasting stage, it would be near the front. This could help reduce the normal force on certain wheels and thereby produce or avoid extra friction.