Rumble from the back of car at ~15mph

[pdmjr1]

I just bought an '86 325e and when I'm accelerating past 15 mph there is a vibration/shaking from the back of the car, but it stops as quickly. This vibration/shaking happens only for a split second when accelerating through 15mph, but doesn't happen when decelerating. The guy I bought it from said he though it was a drive shaft issue, please help?

[packratbimmer]

Check rear sub-frame mounts and rear U-joint