I assume that you left out the word light. It would not be possible to travel AT light speed. But a large fraction of it, say 99.99%, is technically possible. Though of course far beyond our present abilities. Your hand moving forward would not go faster, or even at, the speed of light. You would be experiencing what's known as relativistic time dilation. For you it may seem that your hand is moving at normal speed. But to an outside observer you would be moving in slow motion, due to the time dilation, and your hand would never be going fast enough to reach the speed of light. The closer you come to the speed of light the more time would be slowed down for you. Not to mention at near light speeds wierd things happen. You would actually be compressed, and your mass would increase, of course you would not notice this. It sounds far out but relativistic time dilation has been proven in experiments. It is part of the THEORY of relativity, but time dilation is FACT.
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you wouldn't be able to all the force will force your head back, theirs this ride called Alien and what it does is it goes in circles super fast and it doesnt even let you move if you mange to stand up youll be standing on the wall.
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Your hand would move forward, just as it does when riding on an airplane or train or car.
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When I drive on the freeway.. I can still move my hand..