I took a car for a test drive and It vibrated while accelerating but drives fine at 40 or faster speed the guy said he had a drive shaft custom made so it is not that. I has an auto trans. Does anyone no what this could be?

Vibration when accellerating is definitely a driveline issue. It could be a U joint, broken motor/tranny mount, balance in the driveshaft or the pinion angle (An angle induced vibration will be high frequency, twice engine RPM in direct drive. It may show up only on acceleration or deceleration. Adjust the pinion down to correct acceleration and up to correct deceleration vibrations, plus or minus one degree is usually enough. Before adjusting anything, make sure the U-bolts holding the driveshaft to the pinion yoke are not overtightened. Correct torque is 17 foot pounds and no more) could be off with relationship to the engine output shaft. Check all of these first.

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Steve Jack
-Concept One Pulleys and Brackets
-Marketing Technologies Limited
-Northern/Southern Rodder Magazine's "Jack'Stands" technical column author/originator