"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.[58] 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[0] on a highway that is used primarily by motor vehicles. The department or a local authority may prohibit the use of an electric bicycle[0] on a highway used primarily by pedestrians.
Übrige "Motorfahrräder": “E-Bikes mit einer Leistung zwischen 500 und 1000 Watt oder einer bauartbedingten Höchstgeschwindigkeit von 20 bis 30 km/h oder einer Tretunterstützung, die auch bei einem Tempo von 25 – 45 km/h wirkt, gelten als Motorfahrräder und benötigen ein entsprechendes Kontrollschild.”. You can use any bicyle path and also hiking roads forbidden to motorbikes if you drive slowly.

Vehicles exceeding any of the criteria above must be registered and titled as a motorcycle. Other types of vehicles, such as electric scooters, "pocket rockets" and mini-choppers, may fit the definition of a moped or a motorcycle, but cannot be registered by the Department of State if they lack the equipment required by law to legally drive on public roads.[101]
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.
And let’s not forget the economic advantages of owning an e-bike. The annual cost of running a new family car is, on average, about $9,000 per year. Running an electric bike costs around $400 per year. And while filling a gas tank costs around $30, recharging an electric bike battery costs only about 50 cents. A tank of gas may get you further, but not 60 times further!
Around the turn of the 20th century, bicycles reduced crowding in inner-city tenements by allowing workers to commute from more spacious dwellings in the suburbs. They also reduced dependence on horses. Bicycles allowed people to travel for leisure into the country, since bicycles were three times as energy efficient as walking and three to four times as fast.
Electric bicycles are considered as "bicycles" under Montana law as the law defines bicycles in a two part definition where the first part of the definition describes a conventional bicycle propelled solely by human power and the second part of the definition describes a bicycle equipped with an independent power source for propulsion in addition to foot pedals to permit muscular propulsion. (Montana Code 61-8-102).[104]
The European Committee for Standardization (CEN) also has a specific Technical Committee, TC333, that defines European standards for cycles. Their mandate states that EN cycle standards shall harmonize with ISO standards. Some CEN cycle standards were developed before ISO published their standards, leading to strong European influences in this area. European cycle standards tend to describe minimum safety requirements, while ISO standards have historically harmonized parts geometry.[55]

Electric-assisted bicycles, also referred to as "e-bikes," are a subset of bicycles that are equipped with a small attached motor. To be classified as an "electric-assisted bicycle" in Minnesota, the bicycle must have a saddle and operable pedals, two or three wheels, and an electric motor of up to 1,000 watts, as well as meet certain federal motor vehicle safety standards. The motor must disengage during braking and have a maximum speed of 20 miles per hour (whether assisted by human power or not). Minn. Stat. §169.011, subd. 27.

I eventually got used to it over time, but at first having both kids behind me made the bike feel like it would sway to or fro perilously. I think it was just too much weight to navigate safely, and would be fine with younger kids that didn’t come close to the 120-pound weight limit for the rear cargo area. Overall I’m still a bit partial to a box-style bike if I’m hauling multiple kids and want to be able to see what they’re doing. 

If a car is at fault in an accident with a bicycle or ebike, their motor vehicle insurance will likely cover your cost for repair and hopefully medical expenses. But what happens if you are at fault, riding an ebike illegally because you did not register it as a Moped? At best, you could be prosecuted under the law. At worst, you could be financially liable for neglect or reckless endangerment via a law suit.
When last checked, no E-bikes satisfied this requirement, so ebikes cannot be registered in New Jersey.[108] However, NJ Bill A2581, introduced March 22, 2010, would permit the use of low-speed electric bicycles upon the roadways and bicycle paths in NJ, where a low-speed electric bicycle is defined as a two-wheeled vehicle with fully operable pedals for human propulsion and an electric motor of less than 100 pounds and 750 watts, whose maximum speed on a paved level surface is less than 20 miles per hour.[109] The bill has been referred to the state's Assembly Transportation, Public Works and Independent Authorities Committee.[110]

Recent legislation has passed putting Maryland ebike laws in line with the popular class 1,2,3 systems previously implemented in states such as California. This legislation becomes effective October 2019. The most significant portion of this change is the increased max limit on power and speed. It will be increased from a max of 500w / 20mph to 750w / 28mph (assuming the ebike in question meets class 3 criteria)
Power assisted bicycles are classified in two categories in Saskatchewan. An electric assist bicycle is a 2 or 3-wheeled bicycle that uses pedals and a motor at the same time only. A power cycle uses either pedals and motor or motor only. Both must have engines with 500 watt power or less, and must not be able exceed 32 km/h (20 mph), i.e., electric motor cuts out at this speed or cycle is unable to go this fast on a level surface. The power cycle has to meet the Canadian Motor Vehicle Safety Standards (CMVSS) for a power-assisted bicycle. The power cycle requires at least a learner's driving licence (class 7), and all of the other classes 1–5 may operate these also. The electric assist bicycle does not require a licence. Helmets are required for each. Both are treated as bicycles regarding rules of the road. Gas powered or assisted bicycles are classified as motorcycles regardless of engine size or if using pedals plus motor. Stickers identifying the bicycle's compliance with the Federal classification may be required for power cycles by some cities or municipalities.[31]
Hmm, I think it depends on the forest. My experience has been that if you have a Class 1 ebike and are riding respectfully, most places allow it. I have a sensitive knee and carry a doctor’s note citing disability laws in Colorado and have never been approached or asked by a ranger or fellow rider about the legality of my bike. That said, I have been using the really quiet and hidden Brose motor and I ride carefully and am friendly with everyone

Brock had been running his esoteric shop on Cambie St. for over 30 years, pioneering the sale and production of recumbent bikes, tricycles, velomobiles, unicycles, and of course electric bicycles well before any of these things were popular. He was dabbling with early ebike conversions in the 1990's when we were still in grade school and has been for many years one of the few shops always willing to say yes to electric retrofits. We hope to still see him riding around streets of Vancouver in a white velomobile. 
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I would advocate you ride legal within the laws of your state. I would also look into some kind of liability rider or umbrella policy with your home owner’s policy, which covers your personal liability and theft. Get your bike registered; wear your helmet, eye protection, whatever is required by state law so that if an accident occurs and you are at fault, there is no legal recourse. Even if you own a 750W/20mph ebike that meets the definition of a bicycle, any at-fault cyclist may still be denied coverage by stingy insurance companies who want to support their clients. Your health insurance will usually cover your medical bills, but the costs of an expensive ebike may be lost.