Does an accelerating object shrinks?
What you asked is completely out of your course.
However if you must know, the question you asked is in the realm of Special theory of Relativity.
The shrinking of size has got nothing to do with the acceleration on it but it happens due to the speed of that object. Even if an object has no acceleration but is speeding then its size will shrink. It happens due to the famous postulate of that theory that speed of light is constant in all frames of references.
So when an object speeds up, the speed of light going in the same direction, relative to an observer in the objects frame of reference should be lesser according to Newtons relativistic mechanics (if an object of velocity a goes in the same direction as an object of velocity b then the relative velocity of those two objects is a-b).
But according to special theory of relativity speed of light is a constant and in order to preserve this we change the definition of time in that frame of reference. This causes the length, mass, velocity and few other physical parameters to change in that frame.
The details are currently way above the scope of your level.