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Battery life

#2
It depends on how much current (amps) the motor and prop combination are pulling. Slow motors turning a small prop will have a low current draw can run damn near forever, where as fast motors with big props might only run for a couple of minutes; these are the extremes however and you don't pair them in this way.

Typically, slower motors swinging larger props tend to be more current efficient than fast motors swinging medium size props. My Super Cub runs for 35 minutes on a 1800mAh 3S battery with a slow motor and a medium size prop; the same motor/prop should run for about 15 minutes on a 850mAh battery. The setup for the Duster runs for 18 minutes on a 1300mAh 3S, so for a 850mAh it would run for about 10 minutes.
 
#6
900KV swinging a 13x8 prop (a large prop) will run for about 5 minutes cruising around on a 850mAh 3S. You'll want a 30A ESC for that setup. Make sure the motor is rated to handle at least 250 watts of power.