I'm not familiar with that way of describing the ampacity, but it looks like it would provide a maximum of 35 amps per minute? for one hour. If it's a 35 amp hour battery, you would need to know the amt. of current the motor draws while in use.
This sounds like a battery designed for an emergency exit light or something of the sort. If it is, I seriously doubt you will get much use out of it.
See if you can determine from literature with your motor the max. amp draw. Once you determine that, look at the amp hour rating for the battery. You can safely use 80% of the battery's potential without damaging it.