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That's just fine.
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But suppose you are in a train
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and you're moving past me and you look at this piece of chalk.
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Of course, everything in my room is going backwards for you.
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But things which were at rest will move at a constant velocity,
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opposite of the velocity that you have relative to me.
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You will find that objects that are at constant initial velocity
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maintain the velocity.
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If I am an inertial observer,
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another person moving relative to me at constant velocity
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will also be an inertial observer.
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Why?