Why should passenger hold on to a support to prevent himself from swaying in a turning bus???
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A person travelling in a bus shares the motion of the bus. When the bus takes a turn, it changes its direction of motion. The passenger due to his inertia of motion, however, continues to move in the original direction. So, if the passenger does not hold on to a support, he will be swayed away.
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The bus is moving In a straight line so the person will tend to move in a straight line. Even as the bus turns, the person has the tendency to keep moving in straight path. He can thus fall on the adjacent or behind seat. So to avoid swaying, the person has to apply force to cling on with the motion of the bus.
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