can a object be in motion and rest simultaneously for different observer? Give an example and consequence?

Yes. An objects can be in motion and rest simultaneously for different observer according to their reference frame.
If You are in Space example in Space station, when you look The Earth and it's all objects like trees, buildings etc look moving; but same time if your friend on the Earth observe that trees and buildings are not moving. ( Theory of relativity )
When you are in train(A); even it your train-A is not yet started , but if some other train-B is on near by track and start to move on near by track, we think that our train-A start moving - that in opposite direction than other train (B). Actually our train-A is still on platform not moving in any direction. Secondly when our train-A start moving forward we notice that things and people inside train are at rest but platform and thing outside start moving backward.
 

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