Vibration on Hard Acceleration-Stop and Drive.

Hi. I have recently bought 2009 FX50s- The problem is when car is accelerating too fast at stop and drive it kind of jerks and vibrates while shifting to next gear. This problem is not there while normal acceleration. Could you please tell me what is the problem. Is it a serious problem costing too much . Should i keep the car or sell it. Would be grateful if you can help. Tnx