Why, with a sharp increase in the speed of the bus, do passengers deviate backward and when suddenly stop, forward?

Passengers are inside the transport and move at the same speed, however, at the moment when the bus sharply changes its speed, this change is transmitted to passengers through their points of contact with the bus surface and spreads through the bodies of passengers not instantly, but with some delay. Thus, with a decrease in speed (braking), the passenger’s speed at the moment of time turns out to be higher than the speed of his environment and he moves forward inside the bus relative to him. And with a sharp acceleration, on the contrary, the passenger’s body is delayed and he moves back. The passenger retains by inertia the vector (speed) of movement that he possessed a moment earlier.