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The feet of the passengers are in contact with the bus (floor). If the passenger is sitting then he/she is contact with the bus at the seat. There is friction on the floor and on the seat. 

Let us say a passenger is standing with out holding any support. A passenger is sitting with the torso and head not holding  any support. No seat belt tied.

When the bus starts, there is an acceleration forward. The feet and the part of the body in contact with the bus quickly acquire this acceleration and speed due to friction. But head and torso are initially at rest and have the inertia of being at rest and at the same position, as they have been so far. So they appear to move backward as seen from the moving bus.

This effect is explained by the Newton's First Law of Inertia.

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