Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?

This phenomenon can be explained using the concept of inertia, which is described in Newton's First Law of Motion.

Explanation:

Inertia: Inertia is the property of an object to resist changes in its state of motion or rest. When you are on a bus, your body tends to maintain its current state of motion (or rest) unless acted upon by an external force.

Falling forward when the bus brakes:

While the bus is moving, both you and the bus are in motion at the same speed.
When the bus suddenly brakes, the lower part of your body (in contact with the bus) slows down due to the frictional force from the seat or floor.
However, the upper part of your body tends to continue moving forward because of inertia.
As a result, you feel like you are falling forward.
Falling backward when the bus accelerates:

When the bus starts accelerating from rest, the lower part of your body, which is in contact with the bus, is pushed forward by the force of the seat or floor.
The upper part of your body, however, resists this forward motion due to inertia and tends to stay in its previous state of rest.
This creates the sensation of falling backward.
In both cases, your body’s tendency to maintain its original state of motion (or rest) explains why you experience a forward or backward movement relative to the bus.