Yes, I have experienced it.

My train had halted at a station. I was looking out of the window. Another train came and stopped between me and the platform. After 3 minutes or so, the other train suddenly started moving. However, I felt for about  5 seconds that my train had started moving. I felt sure that we were at rest at the station only when I had seen the platform again.

The reason for this is that motion is a relative concept. I can say that the other train is at motion while we are rest. The people on the other train can rightly say that they were at rest and the station and my train was moving backwards. 

Thus we need a reference point for specifying motion.

Yes,I have experienced it, While my train is temporarily halted,the train on beside track is appears to me as the train is moving.
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