Velocity of an object with respect to the same object

Question

I know that velocity of an object with respect to the same object is a null vector but I'm not able to get a grasp of it.

Whatever I had thought till now is that if I'm sitting in a train (which may be moving with respect to ground) and I have a reference frame attached with me, the coordinates of every particle of train remain same (with respect to my reference frame) with time therefore with respect to me whole train is at rest and therefore we can say that every particle of train is a rest with respect to every other particles of train and therefore whole train is at rest with respect to whole train.

Is above reasoning true or it can be refined with better explanations?

Answer 1

Yes the description is generally correct. If two objects have the same velocity (in vector form) in the frame of absolute time and space, they are resting with respect to each other. Therefore the relative velocity of these two objects is null vector.

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In your description, one of the objects is yourself sitting on the train, another is the particles on the train. Regardless of Brownian motion, the particles stay resting with respect to yourself. Therefore the relative velocity between yourself and a particle is null vector.