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micromobility - Ebikes, scooters, longboards: Whatever floats your goat, this is micromobility
Ebikes, bicycles, scooters, skateboards, longboards, eboards, motorcycles, skates, unicycles: Whatever floats your goat, this is all things micromobility!
"Transportation using lightweight vehicles such as bicycles or scooters, especially electric ones that may be borrowed as part of a self-service rental program in which people rent vehicles for short-term use within a town or city.
micromobility is seen as a potential solution to moving people more efficiently around cities"
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It's a little sad that we need to actually say this, but:
Don't be an asshole or you will be permanently banned.
Respectful debate is totally OK, criticizing a product is fine, but being verbally abusive will not be tolerated.
Focus on discussing the idea, not attacking the person.
That price will be very difficult to meet. For that money it'll probably have to be an AliExpress special. Get a front hub. You probably want a torque arm but I don't think you'll find any in that price range. You can get away without one if you run the motor at low power, like 250W. Unfortunately I don't think you can get a non-hazardous battery anywhere close to that price range. Perhaps look for LiFePO4 (LFP) battery since the chemistry is inherently safer and it's cheaper to make. It's heavier than standard Li-ion.
Otherwise I'd get:
With all that said, steep gradients can kill geared hubs so a direct-drive hub or a mid drive like BBS02/HD might be better suited. Most DD hubs are more powerful so you'd either have to use torque arm/a or run it at low wattage. In general aluminum frames can't handle a lot of torque at their dropouts without spreading or cracking. The rear dropouts can handle 500-700W when the nuts are correctly torqued. You can read about that on ebikes.ca.