This has existed for decades. A small two stroke gasoline motor attaches to the wheel, and kicks in on command. You pedal as much as you can or like, and switch it on for hills, etc. Same thing for motorized scooters.

Obviously a fine idea.

Would you settle for 20mph and no engine emissions? Thisbike uses the wavecrest motor.

There are a remarkable number of choices here. A great place to look is electric-bikes.com where you'll find 1-person electric cars, electric trikes, recumbant electric bikes, regular ones, even Lee Iacocca's entry. The wavecrest motor referenced above was way cool.

Look up moped or motorised bicycle in Wiki. Don't they have these where you come from?

These things already exist and are increasing in popularity everyday with gas prices hitting all-time highs. A good idea might be to manufacture something simple that would be low-cost and pre-made and mass marketed to the states as a way to save on fuel. Take a look at our Motorized Bicycle Forum - I am sure you could get a lot of support there.

Lithium-ion batteries would make this form of transport more attractive (fairly fast recharge, greater charge per unit of weight), although there'd be a high cost of purchase.