In Ontario, Canada, may I pedal my e-bike up to the road's posted speed limit without motor assistance?
Like if my bike does 31 mph but the speed limit is higher, can I travel to that speed without motor assistance?
I think your question is "can I go as fast as the speed limit of the road if I'm not using the electric motor?" The answer, in Ontario (thank you Google) appears to be yes.
No modifications to the motor to allow it to exceed a power output greater than 500W and a speed greater than 32 km/h.
But this seems to apply specifically to operating the bike on motor power, though it's not clear from the quote.
Digging a bit further, the governing law (the "Highway Traffic Act") defines a "power-assisted bicycle" as:
“power-assisted bicycle” means a bicycle that,
(a) is a power-assisted bicycle as defined in subsection 2 (1) of the Motor Vehicle Safety Regulations made under the Motor Vehicle Safety Act (Canada),
(b) bears a label affixed by the manufacturer in compliance with the definition referred to in clause (a),
(c) is fitted at all times with pedals that are operable to propel the bicycle, and
(d) is capable at all times of being propelled on level ground solely by using muscular power to operate the pedals;
That appears to defer to a parent law (the "Motor Vehicle Safety Act (Canada)") in the parent jurisdiction. The relevant portion of the "Motor Vehicle Safety Regulations" states:
power-assisted bicycle means a vehicle that:
(a) has steering handlebars and is equipped with pedals,
(b) is designed to travel on not more than three wheels in contact with the ground,
(c) is capable of being propelled by muscular power,
(d) has one or more electric motors that have, singly or in combination, the following characteristics:
(i) it has a total continuous power output rating, measured at the shaft of each motor, of 500 W or less,
(ii) if it is engaged by the use of muscular power, power assistance immediately ceases when the muscular power ceases,
(iii) if it is engaged by the use of an accelerator controller, power assistance immediately ceases when the brakes are applied, and
(iv) it is incapable of providing further assistance when the bicycle attains a speed of 32 km/h on level ground,
(e) bears a label that is permanently affixed by the manufacturer and appears in a conspicuous location stating, in both official languages, that the vehicle is a power-assisted bicycle as defined in this subsection, and
(f) has one of the following safety features,
(i) an enabling mechanism to turn the electric motor on and off that is separate from the accelerator controller and fitted in such a manner that it is operable by the driver, or
(ii) a mechanism that prevents the motor from being engaged before the bicycle attains a speed of 3 km/h; (bicyclette assistée)
So the actual requirement in governing law is that the motor can no longer provide assistance beyond a speed of 32km/h, not that the electric bicycle can't go faster than that.
The ebike speed limits are about the velocity where the motor has to stop assisting you.
You're welcome to ride at any speed over that motor limit but it has to be under your own power, or that of gravity, or possibly assisted by draughting.
Consider that if the velocity was limited to 32 km/h, the bike would have to brake to keep you under that speed, and no electric-assist pedal bike does that.