Question

Why do you fall in the forward direction when a moving bus brakes to a stop and fall

backward when it accelerates from rest.

Answer 1

when bus is in rest and we are also in rest when the bus accelerate we are in rest so we move backwards and vice versa .
It is very good question

Answer 2

When brakes are applied to stop a moving bus, the bus comes to the rest position but because of the tendency to be in the motion a person falls in forward direction.

Similarly when bus accelerates from rest, the tendency of the person in bus is to be at rest but due to the sudden acceleration the person falls backward direction.

Hope it is useful.