Question

Why do we move backward when a bus suddenly starts moving

Answer 1

This is due to inertia of rest. As we are in contact with the bus, and the bus is in rest, our body is also in rest. When the bus suddenly moves, our body tends to stay at the original position, however since the leg is in contact with the floor, the friction pulls us forward against the tendency of the body. Since our body is deformable,I.e, not a strictly straight unbendable structure, our legs go along with the bus whereas the rest of the body remains at the original place but wrt the bus it seems as if we are falling backwards. After a small time, the muscles adjust and our body moves along with the bus completely. Main principle is Newton's first law of motion.

Answer 2

This happens because of newtons 1st law of motion - an object in rest tends to remain rest until acted upon by an unbalanced force.
It means that when the bus suddenly moves, and your body still tends to be in rest.so when the bus is moving forward you are staying still , so you move back when the bus accelerates.