I think you are confusing Watts (power) and WattHour (energy capacity).
Watt = Volt x Amp
WattHour = Volt x Amp x Hours
Battery numbers are usually Wh (capacity). A 500Wh battery capacity only gives you that, its energy capacity, but it does not tell you the max power the battery can deliver.
For that, you need to know the sustained and Max Amps the battery can deliver, as well as its voltage.
For a 48V battery to deliver 1000W of power, it needs to be able to provide 20.83Amps (1000/48)
If the battery is able to deliver 20.83 Amps sustained, and if its capacity is 500Wh, it means it can deliver 500Watts of power for one hour, or 1000W of power for 1/2 hour.
When cruising around on flat ground at constant speed, you will likely be using a lot less than 1000Watt, and therefore will be able to sustain that for longer time.
For example you could sustain 250Watt for 2 hours.