The passengers in a bus tend to fall backward when it starts suddenly due to inertia as the passengers tend to remain in the state of rest while the bus starts to move. When the bus stops suddenly, people fall forward because their inertia as they are in state of motion even when the bus has come to rest.
Law of Inertia
The law of inertia states that:
An object will continue to be in the state of rest or in a state of motion unless an external force acts on it.
Inertia of motion
The inertia of motion states that:
When the resistance is offered by the body to continue to be in uniform motion unless an external force acts on it.
Inertia in a moving bus when the brake is applied
As the driver applies brakes, the bus comes to rest. But, the passenger tries to maintain the inertia of motion. As a result, a forward force is exerted on him. Similarly, the passenger tends to fall back when the bus accelerates from rest because when the bus accelerates, the passenger’s inertia tends to oppose the bus’s forward motion. Hence, the passenger tends to fall back when the bus accelerates forward.