How do we sense velocity intuitively?

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Loren Booda
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One may estimate acceleration by the force one experiences.

One may judge distance by several methods - such as parallax, focus, and sound/sight divergence.

What, however, is the most direct means of sensing one's velocity intuitively?
 
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Since velocity is only relative, the only way to judge velocity is relative to something that is "stationary". For example, you can get your velocity relative to the street when walking or riding in a car.
 
Then I guess displacement is also relative (the tests I mentioned for it being indirect), whereas acceleration is not.

If we were able to detect object redshift from an unshifted MBR reference point, would that provide an absolute (as opposed to relative) measure of velocity?

Is there a theoretical physical space where acceleration is relative in general?