Correct, but it isn't just a number printed. It is possible to measure continuous rated power, but only under specific conditions, mentioned in the EN15194:2017. Also you need a lot more time to measure that.As far as I know limit is on continuous rated power as specified by manufacturer.
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...which is just a number printed on motor. Real power is determined by controller and there is no legal limit on it, so why would police try to measure it? For fun?...
Measuring "continuous rated power" on site isn't possible, that is why they (relative easy and fast) measure speed only.
Not for fun, but they try to prevent dangerous behaviour of kids with high speeds.
Here (0:32 and 1:18) on YT you can see this how the police do this and there you can see how these kids use these ebikes.
imho with "real power"you mean "maximum achievable power" and this could be indeed a lot more.
Very short summary of EN15194:2017:
......
This European Standard is intended to cover electrically power assisted bicycles of a type which have a
maximum continuous rated power of 0,25 kW, of which the output is progressively reduced and finally
cut off as the EPAC reaches a speed of 25 km/h, or sooner, if the cyclist stops pedalling.
.....
3.20
continuous rated power
output power specified by manufacturer, at which the motor reaches its thermal equilibrium at given ambient conditions
3.21
thermal equilibrium
temperatures of motor parts which do not vary more than 2K per h
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