QUOTE(MJB @ May 31 2008, 09:03 PM)

Suppose person was at position A and camera was at position B and distance between them is d. As the bus started moving, camera started moving as well whereas upper part of the person remained staionary for a time t, during this time bus moved a distance x, so the camera lower part of the person also travelled a distance x, whereas the upper part of the person travelled 0 distance. So camera will record same distance d for the lower part of the person whereas a distance d+x for the upper part of the person, after time t, his body will be stabilized and distance will become again d between camera and his upper part, so during recording, this differnce of distance and then covering this distance will show that he was falling at the start of bus
ahn very nice u r right ,,The reason I posted this question is because often people say that the bus moves and they use inertia to explain why the passenger should fall backward. But, in camera's frame of reference, the bus never moves.
Your explanation is correct. You have used two frames of reference (ground and camera). There is another explanation, which requires the frame of reference to be put only on the camera.
Camera is tied to the bus. So, camera's frame is the same as the bus's frame. When driver starts the bus, then tyres rotate. Tyres push ground in the backward direction. By Newton's 3rd law, ground pushes tyres and thus the bus in the forward direction. This is force of friction. Bus moves because of this force of friction. Since there is a net external force on the bus, the bus's frame of reference is non-inertial and hence camera's frame is also non-inertial. The acceleration of this frame is in the forward direction.
When we study a system in non-inertial frame, then together with real forces, we should also consider pseudo force. The pseudo force is in the opposite direction of the direction of the frame's acceleration.
In our problem, system is passenger, frame of reference is on the camera (or we can also say, on the bus), frame's acceleration is in the forward direction. So, the pseudo force on the passenger is in the backward direction. Because of this pseudo force, the passenger falls backward.
The pseudo force acts on the lower portion of the passenger's body also. But this part does not move because when it tries to move, then the friction between the seat and the passenger body prevents the lower part of the body to move. If the seat is very smooth, then even the lower part will move somewhat.