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As an object accelerates toward the speed of light it's mass (and weight) increases, at the speed of light (c) the objects mass would be infinite, making it impossible for any object to accelerate to light speed. So, "no" an object does not weigh less by moving faster in a vacuum, the faster it goes the more it weighs and the slower time goes. The change in mass and time occurs because near light speed the variable "c" is more fixed and the remaining variables (time and mass) must change to maintain balance.

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Q: If a car is traveling in a vacuum does it weigh less the faster it goes?
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