Bomb you for your question.
To thoroughly answer your question might require far more education than the scope of time and energy that might be put into a forum post.
The short answer is yes, you should be able to use a 36v battery pack on a 48v kit.
You can typically plug a lower voltage battery pack into a kit that can handle higher voltage. The likely only issue you may have is the low voltage cutoff programmed into the controller.
What output the battery you are referring can handle is relative or completely dependent on the battery, the answer is not all the same no matter the battery. A .5c or 1c battery 36v10ah pack would be negatively effected by drawing more watts or amps from it than it can handle. To give you a bit of understanding, To find a packs capacity, you multiply it's voltage(V) by it's amp hours(AH). Assuming your battery pack is something like a 36v10ah pack, you'd end up with a capacity of 360 watt hour(WH) capacity. The C rating(capacity rating) is a multiple of capacity. To help you understand some of this, a watt meter while running your motor might be useful.