"Bicycles" and "Electric Bicycles" are legally defined in the Texas Transportation Code Chapter 551., titled "Operation of Bicycles, Mopeds, and Play Vehicles" in Subchapter A, B, C, and D. The following definition of electric bicycle was passed by the Texas legislature in 2001. "Electric bicycle" means a bicycle that is designed to be propelled by an electric motor, exclusively or in combination with the application of human power, cannot attain a speed of more than 20 miles per hour without the application of human power; and does not exceed a weight of 100 pounds. The department or a local authority may not prohibit the use of an electric bicycle on a highway that is used primarily by motor vehicles. The department or a local authority may prohibit the use of an electric bicycle on a highway used primarily by pedestrians.
E-bikes are typically offered in 24V, 36V and 48V configurations. Higher voltage generally means higher top speed – but that may not always be the case. Since the efficiency of a motor and drive system can have an effect on power and speed, a 24V setup could have the same top speed as a 36V setup. Generally you can expect 15-18 mph on a 24v setup, 16-20 mph on a 36V setup and 24-28 mph on a 48V setup. Although it far exceeds Federal laws, some conversion kits can even be run at 72V for speeds of 35+ mph! However, this puts significant stress on bicycle components. Consider that even the fastest athletes only travel 17-18 mph on a conventional bicycle, so 20 mph feels very fast to most riders. Anything over this speed can be unsafe and exceeds law regulations.
The federal law will not prohibit a motor vehicle label and additional restrictions given by the state. States will typically define e-mopeds in the 1000W range (1.5 hp) and speeds attainable to 30mph, and include a few requirements such as a helmet, eye protection, and a driver’s license. States may also require title, registration, and insurance for mopeds.
Ebike definition in Colorado follows the HR 727 National Law: 20 mph (30 km/h) e-power and 750 W (1 hp) max, 2 or 3 wheels, pedals that work. Legal low-powered ebikes are allowed on roads and bike lanes, and prohibited from using their motors on bike and pedestrian paths, unless overridden by local ordinance. The city of Boulder is the first to have done so, banning ebikes over 400W from bike lanes. Bicycles and Ebikes are disallowed on certain high speed highways and all Interstates unless signed as "Allowed" in certain rural Interstate stretches where the Interstate is the ONLY means of travel.
It appears Tennessee has not passed any legislation that applies to electric bicycles. Some people think the laws pertaining to a Motorized Bicycle should be used for an electric bicycle. However, a Motorized bicycle would be a gasoline powered device per state law as it is defined as "means a vehicle with two (2) or three (3) wheels, an automatic transmission, and a motor with a cylinder capacity not exceeding fifty cubic centimeters (50cc) which produces no more than two (2) brake horsepower and is capable of propelling the vehicle at a maximum design speed of no more than thirty miles per hour (30 mph) on level ground." 
The second type of electric bike is a much smaller, often foldable unit designed for convenient urban (or suburban) commuting and for easy storage in minimal space. These compact electric bikes are perfect for trips of a few miles, and many are small and lightweight enough to be carried onto trains or buses, allowing their rider to make use of multiple types of transportation in a single trip, and to store their bike in a closet or even under a desk at work, at school, or at home.
The bicycle is also used for recreational purposes, such as bicycle touring, mountain biking, physical fitness, and play. Bicycle competition includes racing, BMX racing, track racing, criterium, roller racing, sportives and time trials. Major multi-stage professional events are the Giro d'Italia, the Tour de France, the Vuelta a España, the Tour de Pologne, and the Volta a Portugal.
An electric bike (also called e-bike, power-assist bike, pedelec…) is a fairly conventional bike combined with a battery and motor that helps out when you are pedaling to make it easier to get uphill or completely takes over driving and allows you to cruise along. Top quality electric bikes, along with electric scooters, are revolutionizing the bicycle industry. Not only is riding an e-bike simple and easy, but a rider can significantly extend their range with minimal cost or effort.
Electric powered bicycles slower than 20 km/h without pedaling are legally recognized as a non-mechanically operated vehicle in China. According to "TECHNOLOGY WATCH", this should help promote its widespread use. Electric bicycles were banned in some areas of Beijing from August 2002 to January 2006 due to concerns over environmental, safety and city image issues. Beijing has re-allowed use of approved electric bicycles as of January 4, 2006. Some cities in China still ban electric bikes.
Electric bicycles have two main methods of operation: pedal-assist and/or throttle-control. As the name implies, pedal-assist “assists” your pedaling and requires some input. With this method, a torque sensor picks up movement or stress to determine the power requirements of the rider. Everything is automated so there’s nothing to think about, just jump on and start riding. Some bikes have multiple settings, while others have just one setting with the addition of a throttle control. Depending on the setting, pedal-assistance can help a little – or a lot. At lower settings, pedal-assist is barely noticeable but helps extend your range. At higher settings, the power is quite obvious and feels like a strong wind at your back with the motor doing most of the work while you pedal along.
On the other hand, the battery doesn’t lock into the bike, which means you can’t just leave it on your bike when you park at the bike rack. Anyone could walk by and simply remove your battery. That seems like an oversight to me, though perhaps the designers assumed that such a small battery would just be easy to take with you. And it is. My wife could probably lose this battery in her purse.