Short answer why do the passengers fall backward when the bus suddenly starts
Answers
When the bus is in uniform motion along a straight line or at rest then the bus is a inertial frame of reference and there is no pseudo force acts on this frame of reference. But when the bus stop suddenly or start suddenly that means it's a accelerated frame of reference ie non inertial frame of reference, and in non inertial frame of reference there is always a pseudo force different from real force(action & reaction force) whose direction is in the direction opposite to acceleration. So if bus stop suddenly that means it is deaccelerated so acceleration is in the backward direction and pseudo force is the front direction so man fall in the front direction not backward as in question.
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The passengers in a bus tend to fall backward when it starts suddenly due to inertia as the passengers tend to remain in the state of rest while the bus starts to move. When the bus stops suddenly, people fall forward because their inertia as they are in state of motion even when the bus has come to rest.
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