When your body is accelerated, each part of your body is accelerated individually. The seat pushes on your back, the muscles in your back push on some organs and those organs push on other organs. This is why you feel the ride with your whole body.
Normally, all the parts of your body are pushing on each other because of the constant force of gravity. However in the "free-fall" state of plummeting down a hill, there is hardly any net force acting on you. In this case, the various pieces of your body are not pushing on each other as much but are all falling individually inside your body. You would then feel a sinking sensation in your stomach as it is suddenly very light because there is less force pushing on it.
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