Electric-assisted bicycles are treated as human-powered bicycles, while bicycles capable of propulsion by electric power alone face additional registration and regulatory requirements as mopeds. Requirements include electric power generation by a motor that cannot be easily modified, along with a power assist mechanism that operates safely and smoothly. In December 2008, The assist ratio was updated as follow:

We bought 2 of these to go along with our AW 26"x1.75" Front Wheel Electric Bicycle Motor Kits and they work perfectly! The batteries that came with and were recommended by the wheel manufacturer were "clunky", had to be mounted in hanging bags and just didn't work well. These Li-ion Battery with Battery Holders are sleek, fit our Beach Cruisers perfectly, give us a rack to carry our "beach stuff" and one of the best features is how easy they are to charge! They lock in place when we are out and about, but I can unlock them, slide them both out and take them into the RV for charging when we return. Very happy with these and would recommend to anyone looking to convert their current bike into e-bikes!
In a parallel hybrid motorized bicycle, such as the aforementioned 1897 invention by Hosea W. Libbey, human and motor inputs are mechanically coupled either in the bottom bracket, the rear wheel, or the front wheel, whereas in a (mechanical) series hybrid cycle, the human and motor inputs are coupled through differential gearing. In an (electronic) series hybrid cycle, human power is converted into electricity and is fed directly into the motor and mostly additional electricity is supplied from a battery.
An electric bicycle is a bicycle with an electric motor used to power the vehicle, or to assist with pedaling. In many parts of the world, electric bicycles are classified as bicycles rather than motor vehicles, so they are not subject to the same laws as motor vehicles. Electric bicycles are one type of motorized bicycle. However, electric bicycles are defined separately and treated as a specific vehicle type in many areas of legal jurisdiction.
None of this would matter if the VanMoof Electrified S2 (and its close relative the X2) wasn't fun to ride, but it is a blast. Like the Brompton, it pulls off the neat trick of powering you along but giving the illusion that you're doing the work, reacting quickly and cleverly to the speed of your pedalling and the difficulty of any incline you're on. 
E-bikes use rechargeable batteries, electric motors and some form of control. Battery systems in use include sealed lead-acid (SLA), nickel-cadmium (NiCad), nickel-metal hydride (NiMH) or lithium-ion polymer (Li-ion). Batteries vary according to the voltage, total charge capacity (amp hours), weight, the number of charging cycles before performance degrades, and ability to handle over-voltage charging conditions. The energy costs of operating e-bikes are small, but there can be considerable battery replacement costs. The lifespan of a battery pack varies depending on the type of usage. Shallow discharge/recharge cycles will help extend the overall battery life.
The Footloose has no chain, however -- it's entirely electrically driven. It takes very little effort to get to your destination, meaning you arrive at work without having broken a sweat. The downside is that when you run out of power, you're not going anywhere. And pedalling from a standstill, waiting for the motor to kick in, is an odd sensation that takes some getting used to.
We rode the Vado through the gauntlet, including some of the steepest hills in Palo Alto, and it easily handled everything we threw at it, maintaining a steady 20 miles per hour even on the most daunting of ascents. The bike also handles well on downhills and is both nimble and quick on city streets and paved trails. It’s even comfortable to ride for extended distances, which is vitally important for any bike built for urban settings.
Under Arizona law, motorized electric bicycles and tricycles meeting the definition under the applicable statute are not subject to title, licensing, insurance, or registration requirements, and may be used upon any roadway authorized for use by conventional bicycles,[77] including use in bike lanes integrated with motor vehicle roadways. Unless specifically prohibited, electric bicycles may be operated on multi-use trails designated for hiking, biking, equestrian, or other non-motorized usage, and upon paths designated for the exclusive use of bicycles. No operator's license is required, but anyone operating a bicycle on Arizona roads must carry proof of identity.[78] A "motorized electric bicycle or tricycle" is legally defined as a bicycle or tricycle that is equipped with a helper motor that may be self-propelled, which is operated at speeds of less than twenty miles per hour. Electric bicycles operated at speeds of twenty miles an hour or more, but less than twenty-five miles per hour may be registered for legal use on the roadways as mopeds, and above twenty-five miles per hour as a registered moped with an 'M' endorsement on the operator's driving license. However, mopeds in Arizona are prohibited from using bike lanes on motor vehicle roadways. The Arizona statute governing motorized electric bicycles does not prohibit local jurisdictions from adopting an ordinance that further regulates or prohibits the operation of motorized electric bicycles or tricycles.[79]

The $3,099 MSRP is a bit daunting if you've not shopped for high-end bikes before, but it compares favorably with, say, Trek's electric bike lineup. That said, you can get a solid urban/commuter bike without a motor for well under $1,000. You can even score an e-bike for under a grand, but you'll likely be looking at a battery range of less than 40 miles, along with lower-quality components.
Firstly there's a magnetically-fired locking pin in the rear wheel, triggered by kicking a button on the hub. This is fairly secure in itself and almost impossible to remove without destroying the bike. In London, we'd pair it with a more traditional bike lock so there's a more obvious visual deterrent, though a LED matrix screen on the frame does issue a warning to would-be tea-leafs.
The Ancheer comes with outstanding Shimano Tourney gears in 6 x speeds. This gear system is one of the best in the business. Similarly the front-rear disc brakes are perfectly effective and will bring you to a safe stop even from speed. Speaking of speed, the maximum is 16mph and the bike will travel anywhere between 17-23 miles on a single charge. The battery charges up in 4-6 hours, which is the same for virtually all e-bikes.
No endorsement is required on a driver license in order to operate a motorized bicycle, thus the motorized bicycle may be operated by anyone with a valid driver license. Goggles, windshields and other special equipment required for motorcycles and motor-driver cycles are not required for operation of a motorized bicycle. However, crash helmets are required regardless of operators age. Minors between the ages of 14 and 16 may apply for a restricted license to operate a motorized bicycle, just as they would to operate a motor-driver cycle. For instance, they must take a written test, vision tests and demonstrate their ability to operate the motorized bicycle. The license issued will be restricted to a motorized bicycle only. The license is valid only during daylight hours and within a seven-mile (11 km) radius of the driver's home. Applicants for any type of license less than eighteen (18) years old, must complete a Minor/Teen-age Affidavit and Cancellation form making the parent or legal guardian financially liable for the applicants action. [57]
"Medical Exemptions" are also a standard right in the State of Texas for motorcycles & even bicyclists. Through Texas's motorcycle helmet law (bicycle helmet laws from city ordinances), it is only required for those 21 years old or younger to wear a helmet. However, a medical exemption, [59][60][61][62][63][64] written by a certified licensed medical physician or licensed chiropractor, which exempts one from wearing a helmet, can be used for bicyclists if helmets are required.
Oklahoma the following restrictions on the operation of Electric-Assisted Bicycle in 47 O.S. 11-805.2 [123] as follows: 1. Possess a Class A, B, C or D license, but shall be exempt from a motorcycle endorsement; 2. Not be subject to motor vehicle liability insurance requirements only as they pertain to the operation of electric-assisted bicycles; 3. Be authorized to operate an electric-assisted bicycle wherever bicycles are authorized to be operated; 4. Be prohibited from operating an electric-assisted bicycle wherever bicycles are prohibited from operating; and 5. Wear a properly fitted and fastened bicycle helmet which meets the standards of the American National Standards Institute or the Snell Memorial Foundation Standards for protective headgear for use in bicycling, provided such operator is eighteen (18) years of age or less.
Battery – in combination with the motor, this determines how far you can get before your bike needs a recharge. Some don’t provide adequate support on even gentle hills, while the best will comfortably take the strain as the gradient shoots up. Range also varies, with the best e-bike systems we’ve tested able to take you nearly twice the distance of lesser models.
A new electric cyclist will likely experience two conflicts of thought: 1). Will the general public accept my use of this power assist technology, or Will they ridicule and reject me as being lazy? 2). Will I stand out to law enforcement by the look of my bike or riding a bit faster than other cyclist on hills and roads? Grappling with these two thoughts will tempt most folks to try and remain unnoticed and ride more responsibly. After I became an advocate of e-transportation on two wheels, enjoying the benefits of power assist commuting, I eventually was a bit put off by this federal law, especially the 20mph limitation. Is 20 mph really practical and justified? Is it not true that many active young people on typical road bicycles are able to actively ride in the 20-25mph range? I discovered that ebikes, with larger tires and disk brakes, can comfortably and safety cruise in that range of speed. The standard 2001 Federal law of 20mph, eventually became a practical limitation for an ebike commuter of over 20 miles a day, and caused me to get a bike beyond the federal limits, making me more alert and sensitive when riding in the presence of the police.

The federal Consumer Product Safety Act defines a "low speed electric bicycle" as a two or three wheeled vehicle with fully operable pedals, a top speed when powered solely by the motor under 20 mph (32 km/h) and an electric motor that produces less than 750 W (1.01 hp). The Act authorizes the Consumer Product Safety Commission to protect people who ride low-speed electric vehicles by issuing necessary safety regulations.[63] The rules for e-bikes on public roads, sidewalks, and pathways are under state jurisdiction, and vary.