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This is known as inertia. When the bus is acted upon by an unbalanced force the inertia of the bus differs but not of the person who is standing. So the person continues to be moving forward even if the bus decelerates suddenly until friction acts upon the person or the person catch holds of something and vice versa when the bus accelerates.

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Q: Why does a person standing on a bus is thrown towards the rear of the bus as it starts to move forwards and to the front as it slows down?
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