Electric motors on bicycles are taking off now.
The electric motor is there to 'Assist' with hills or whatever, and when you are going down hills, you can flip a switch (instead of braking) and recharge your battery.
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Electric scooters are also taking off in densely packed urban areas and around small towns since the range is limited.
Easy to charge, but medium weight so you can't carry them around easily...
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Traditional 'Mopeds' are normally Internal Combustion Engines mounted on a bicycle chassis, you can pedal or use the engine, or both.
These normally didn't have batteries, and you started the engine by peddling like a bicycle and engaging the motor to start them.
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Gas engine 'Scooters' are taking over around here.
No pedals, so they are strictly gasoline powered and most have electric start so a battery is required.
Not the idea situation for a 'Survival' situation where fuel and batteries would be scarce.
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In the event of needing to travel long distances with heavy cargo (farm products, trade goods, ect.) in an 'On Your Own' situation,
One might consider an electric motor or moped engine on a train track cart.
Trains will be scarce to non existent in a natural or man made catastrophe, but the tracks will be very easy to use with a simple platform with rollers on the tracks and stops to the inside of the tracks to keep the rollers on the tracks.
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Now, as in traditional times, boats will be a very good way to move large loads.
As we have found out, just a few solar panels will power a trolling motor on our pontoon boat,
And for bigger loads, a gas engine could be used.
The two aren't mutually exclusive, the gas engine can be raised when not using gas, and the electric motor can be used when loads are light.
The canopy roof on a pontoon boat makes the perfect place for mounting solar panels.
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Golf carts with solar panels mounted as a hard top will recharger themselves over time...
You could park you cart under a carport roof made of solar panels to charge the batteries also.
Some places are making '4 wheelers' or ATV's with battery power also. Same rules apply, and a car port with solar panels would charge them also.