These are exactly the questions Einstein was asking himself, which led him to his theory of relativity. The phenomenon you are referring to is called time dilation and is one of the consequences of this theory. If you had on a watch while you were running faster and faster, you would notice that your watch was slowing down compared to a clock on the wall. This is true for all relative motion, so technically, just by walking or driving in a car, you experience this time dilation. However, it is so small that you cant notice it in everyday activities. As your speed approaches the speed of light, time dilation gets larger. At the speed of light, time dilation is infinite. This means that time doesnt move at this velocity.
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