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A skater wearing in line skates (no friction) standing in the bus holding nothing. What direction will the skater move when the bus moves?

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If the bus moves forward the skater will roll towards the back.

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The body will move backward and the skates forward?
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Only if the body loses balance.
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Center of gravity, action and reaction?
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I don't know the exact reason, I just know from having things roll around in my car/SUV.
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From riding a bus and subway. Top goes one way bottom goes the opposite. Hence the shoulders go back and the feet go up (forward). A balancing act.
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backwards

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tword the back if the bus is going forward and vice versa

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Backwards

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He won't move at all. He will stay in the same place until the bus finally leaves (if the bus moves fast enough). A good example would be a treadmill. If you roll a ball onto a moving treadmill, it will stay in one general place. It will eventually fall off because it will stop rolling.

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