Is it possible that the train in which you are sitting appears to move while it is at rest?

Hint: The given condition or circumstance asks for the situation when we sit in the train it feels like moving while it is at rest, it is completely possible. When there is some other train passing by right beside the train in which we are sitting, it may seem like our train is moving too.

Complete answer:
Yes it is possible because the train may be motion (moving) for the person who is outside the train but for passengers inside the train may be at rest (idle) as motion and rest are relative terms.

Just think that you are sitting on a train. There is another train on the railway track by your right side. Suppose you are looking at the train to your right side by a window. If that train starts to move. While sitting in the train you will feel that the train in which you are sitting is moving in a forward direction. But, the truth is that the train on your left side is moving in forward direction so we can say that motion is subject to reference.

This happens due to relative motion which is defined by the theory of Relativity which is given by Einstein. The relative velocity is achieved by the train. And other thing is inertia (inactive), which furthers defines relative motion or rest

Note:The above statement completely depends upon the relative velocity. According to relative velocity the velocity of an object or observer B in the rest frame of another object or observer.