What would happen to the passengers in a stationary bus if it were hit from behind?

Answer 1

The stationary bus will immediately move forward with that force by which it was struck. Those inside will tend to remain stationary until acted upon by parts of the now moving bus; this will be nearly immediate. As they are acted upon by the now moving bus, they will begin to move in the same direction, and will continue to move in that direction until some other force counters or alters that movement, typically some other structure in the bus. This will occur much that same for the bus that was struck.

This is the embodiement of Newton's three laws of Motion:

1. The bus is stationary and then struck. The bodies in the bus are stationary and then acted upon by the movement of the bus. If an object experiences no net force, then its velocity is constant: the object is either at rest (if its velocity is zero), or it moves in a straight line with constant speed (if its velocity is nonzero).
2. The bus is struck. The bodies in the bus are acted upon by the now moving bus. The acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass m of the body, i.e., F = ma.
3. When a first body (the moving bus) exerts a force F1 (the impact) on a second body (the stationary bus), the second body simultaneously exerts a force F2 = −F1 on the first body. This means that F1 and F2 are equal in magnitude and opposite in direction. - in short, if the two buses are equal in mass, the first bus is likely to stop as the second bus accelerates.