My car vibrates when I try to quickly accelerate?

it very well could be the crankshaft problem, worn bearing or warped crank. that would deffiantly cause the car to shake, especially when flooring it because it is spinning faster and with more energy. take it to a shop to check it, its usually a semi easy check, they just got to remove the oil pan and they may have to take it out. that will cost some money. especially if it has to be replaced.