@Traviskpshelton You should tell us what YOU are trying to DO. So far, all you have mentioned is a smallish 360 W∙hr battery rated at 36 V and capable of delivering 10 A∙hr of current into a 1000 W LED load. You wanted to know how long a fully charged battery would run the LED lamp load. Ideally, that would 360 W∙hr / 1000 W or roughly 0.36 hours, about 21.6 minutes. In actuality, the run time will be much less than that, for reasons
@kellys_eye stated in his post #2. He also mentioned that an alternator would have to supply 1000 W / 36 V = 27.78 A to power your super-max LED to 1000 W power level. In doing so, the alternator would need at least 1000 W of mechanical power input, roughly 1.34 HP. Round this up to 2 HP to account for conversion losses and to have some power left over for charging the battery.
So, then you come back and ask:
Or can you give me instruction as to what I should do?
This, after asking about attaching an alternator to a BIKE!? If you mean a human-powered pedal bike, you need to realize that a well-conditioned athlete will have trouble maintaining a power output of 50 watts for any significant length of time on a bicycle. A kilowatt is simply not possible. OTOH, if you mean a motorbike or motorcycle, good luck retrofitting an alternator to one of those. Most already have an alternator fitted to provide power for the lights, ignition system, and to keep the battery charged. It is unlikely that you will find a one kilowatt alternator that can be shoe-horned into ANY motorcycle. And most "bikes" today are fitted with 12 V NOT 36 V batteries.
So, as
@davenn said: YOU tell us what you are trying to DO. It sounds to me like you don't have a clue, and are probably wandering into very dangerous territory, as
@BobK intimated in post #3. Do you even know how to provide sufficient cooling for a 1000 watt LED?