question about a person and a bus while driving.

You go forward if you jump while the bus is slowing down, because your velocity relative to earth is still at 80 mph, where the bus has a velocity less than that. Thats a simple as I can describe it for somewhere with no air resistance.

I would say it has to do with three things: air pressure, air resistance and motion. A known example of this is called g-force.

If you use hooded car, the interior creates a "vacuum" and when you move the car at a steady speed with only minimal/slight accelerating/braking or sideway motion, you usually sense very minimal changes with your body if none at all, which means the vacuum little by little is adjusting to the motion that is in the outside world.

This means you can even jump inside the car without smashing into the back of the car or throw a paper aeroplane inside the car without it piercing thru your head immidiately, as there is no additional air resistance caused by the air that is passing by the car at 80km/h compared to what you would face when you use a convertible car or for example open the door of the car, that causes a sucking motion torwards the door because of the air pressure difference.

If you drive a hotrod racing car where in the beginning you try to accelerate as fast as a nerd can wank to a .jpg, you are pretty much glued to the seat because of the g-forces. Even if you brake a little harder without crashing into anything and you are standing, you might lose your footing in the bus if you win at failing, so that means that there is too sudden change in the motion between the inside and outside motion.

or something like that
With a racing car, you are pinned to the seat because an object while at rest stays at rest untill a force is applied. In this case the forces that matter are the friction on the seat and the reaction force on the back of the seat, acting against the forward movement. If there was no back and no friction on the seat, the car would drive off and you would remain where you were :lol: There is no air resistance on you when you are in the car (or minimal air resistance because air has very little mass, so force is minimal becasue of the equation f=ma (f=force, m=mass, a=acceleration)

Try throwing a ball in the air and catching it while at constant speed, it acts as though the car is stationary. then throw it while violently accelerating or decelerating, the ball remains at the forward velocity when it was thrown, but the cars changes, and the ball goes backwards if accelerating and forwards if decelerating.