why the passengers sitting inside a bus pushed back when the bus suddenly moves forward
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Inertia in a moving bus when brake is applied
But, the passenger tries to maintain the inertia of motion. As a result, a forward force is exerted on him. ... Hence, the passenger tends to fall back when the bus accelerates forward.
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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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