Quote by mananvpanchal
Hello,
Suppose, A and B is clocks at both end of train. A is at left and B is at right. Observer O is at middle of train at point M. Observer R is on platform.
Train is at rest and O synchronize both clock. The clock is synchronized with respect to both observer.

Yes, both clocks are synchronised for both reference systems according to the standard synchronisation convention.
Now, train starts moving to right. It accelerate and after some time it runs with constant speed. Now, the clock is still synchronized with respect to O.

No, that is wrong: according to the standard synchronisation convention, the clocks are now out of synch with respect to O.
But what about R? Is clocks synchronized with respect to R? If no, then which clock is ahead A or B?
Thanks.

 Both moving clocks are now very slightly behind according to R.
 According to O, clock B in the front is now ahead on clock A in the rear.
This is quickly understood with a simplified analysis from the platform: neglecting the small effect from length contraction, both clocks are about equally behind. If O sends a signal to both A and B, clock A is moving towards the signal while B is running away from it. Thus the signals will reach A before B. Consequently, A will indicate less time than B at these events which O defines as simultaneous.
Harald