Find out the reasons:

When a bus at rest suddenly moves forward, the passengers, standing in the bus, fall backward.

When the bus is at rest the passengers standing in the bus are also at rest but the passengers possess inertia of rest also, as we know that when a person is in a bus it will travel with the same velocity as that of the bus. So when a bus is suddenly moves forward from rest , it possesses some force to move it from rest and this force is applied to bus not passengers , the lower part of human body is in contact with the bus but the upper half part of human body possesses more inertia of rest than lower half part because it is more heavy(mass) , hence our lower part moves with the bus easily than the upper part because upper part has more inertia of rest , so it is likely that the upper part will remain at rest . Actually the passengers do not move backward but their lower part is carried in forward direction with the bus and the upper part wants to stay at it’s position due to inertia of rest.

The same can be done for brakes and deceleration or retardation.

ADDITIONAL INFORMATION – We can do same experiment with a long rod placed vertically on a wooden plank. When we try to slide the plank with considerable force the lower part of the rod will move with the plank but the upper part remains where it was initially placed. Hence due to inertia of rest.