What is your guess at the real-world distance? Using a 408 motor, no head wind, 48V controller, 26" tires, at around 2.00" thick, around 800g tires, the rider is 180lbs., no pedalling, no hills, FULL Throttle.
using " wh " or Watt/Hour is the easiest way to figure this out.
on a setup as you describe, expect 10 to 12 wh per km ( make it 15 if you do stop and go at ever block )
A 48v 10ah lithium battery, cobalt, manganese, iron phosphate, will give you between 8ah to 9ah depending on who's rating it.. so let's say 8ah to be nice and to avoid 100% discharge per cycle..
48v x 8ah = 384wh
384 / 10 to 12 wh per km = 38 to 32 km per charge.
Apply that to 10ah SLA's.. that can only deliver 5ah or so and you get 48 x 5 = 240wh
D cell nimh or F cell nicad is good for 6ah ( 8 if you push them hard )
But when talking lithium, with a 408, and a 20 amp controller, C rate is not that big a deal.. as it will only be 20 amps at the most. 2C for a 10ah pack.
I'd guess about 15 miles tops. My aotema will take me about 10-11 miles full speed on a 8 ah 48v nicad pack full throttle. Since a 408 might be a tad slower, it might go a tad further. Add 3-4 miles more for 2 more ah and I come up with 13-15 miles. I weigh 180. The wind resistance is a big factor, but my bike is very upright and un aerodynaminc. If you ride something more like a road race bike, or recumbent, then the range could be much higher.
I have about the exact same system (lot of us have) and my real world stop&go average was indeed 10-12 wh/km like Ypedal said. and my distance was also about 40 KM ideal conditions.
But most of us pedal some when we go up hills and take-off from a stop light.
I always bring a light charger with me and do opportunity charging so there is no chance of ever reaching LVC cut out. It makes a 10amp/hr battery pack a usable and safe size factor.