When the running bus stops suddenly, the passengers are jerked forward because due to inertia of motion the passengers tend to remain in their state of motion even though the bus has come to rest.
The Illusion Of Control: Some People Simply Think They'll Exit Faster. Another scientific explanation is people's urgency to take control of their lives. Moreover, many people believe that standing in the aisle as soon as the plane lands will help them get off and collect their luggage quicker.
When a bus abruptly starts moving, the passengers tend to slide backward due to inertia, as the passenger's inertia tends to oppose the bus's forward motion. Hence, the passenger tends to fall back when the bus accelerates forward.
When a bus stops suddenly, its passengers tend to fall forward because due to their inertia the passengers tend to remain in a state of motion even though the bus has come to rest.