There are several causes why a blue smoke will comes out your car tail pipe but the main reason is only the same, the engine is burning oil inside the combustion chambers.However, it will differ on what causes why the engine burns oil, with that said lets do some car problem diagnosis.

When blue smoke from exhaust while accelerating comes out the tail pipe then this indicates that the engine is burning oil, but why did the engine is burning oil? Usually a blue smoke that is presence when the car accelerates will tell you that the engine has a bad valve stem seals. The valve stem seals is the one that keeps the oil from entering the engine combustion chambers, hence when the valve stem is gone bad it will not prevent the engine oil from entering the combustion chamber, and in this case it will burn inside the combustion chambers thus causing the blue smoke to comes out the tail pipe.

How are you going to fix the problem?

Simple, just replace the valve stem seals, but how to replace it is a different story. Replacing the valve stem seals is costly not unless you know how to do it yourself. However if your car is under warranty then need not worry because it will be covered, if not then be ready to face an expensive repair. Only the valve stem seals is needed to be replace and nothing more, after this is done the problem will be fixed. It is necessary to have your car subjected to a complete valve job.

Blue smoke is one of the indication a car has problem, there are other color of the smoke which indicate problem like white smoke or black smoke from exhaus of car and its  good practice to monitor what color is the smoke that comes out your car exhaust to know if the car is needed some repair work.