What you want is apparently a light motorcycle or moped or vespa-like motorized scooter. You do not really power it by muscles, you need a really heavy and powerful battery, it will be much more expensive, you need a helmet, you need a license plate, you can't service it yourself, you really ought to wear heavy protective gear if you don't want to lose much of your skin in an accident or fall, you can't ride it in the winter because it is too cold, you need to use the road because you need far better overview at crossings. All these restrictions are written in blood.
Oh and on a 10 mile commute your speed advantage will be minimal in most cases.
The amazing thing about bicycles is that they hit a unique sweet spot of parameters and design constraints which simply is not accessible for motor vehicles. Mopeds have evolved multiple times from the (wrong) idea that you can have a fast bicycle by adding a motor, without changing fundamentally what it is.