Pretty much the question itself
In: Physics
Yes. The bee is is moving at at a speed relative to the car and is heavier than the air it displaces, so when the car stops suddenly, the bee will continue to move at the speed the car was previously moving and in the same direction, resulting in hitting the windshield. If an object is lighter than air (ex: a helium balloon) it will move backwards when the car stops suddenly.
Think of it this way: If it weren’t for your seatbelt, you would also hit the windshield if the car came to a sudden stop. Same exact thing happens to the bee. Everything in the car: you, the air, the bee—they’re all moving forward together with the car, and will keep that momentum if the car suddenly stops.
And yes, if a bee flew into your car while it was stopped, and you accelerated rapidly, the bee would hit the back windshield. If you accelerate gradually enough, the air resistance and the bee’s own flying would be enough for it to keep speed with the car as it gets up to speed and not hit anything. The back of your car seat does that for you, which is why you feel your back pressing into the seat as you accelerate.
A moving car is essentially moving all its content inside of it, along with the air.
If the car suddenly stops (in a car crash for example), its content will keep moving forward, until stopped by something that is still; because the crash starts with the car exterior entering in contact with a still obstacle, things that are directly connected to it, will also stop moving first.
Because the driver is not solidly attached with to car, his body will keep moving, while the steering wheel will stop, resulting in collision (which is why we created seatbelts).
A bee flying inside the car has initially been pushed by the air inside of it, and stays moving along with the air transported and displaced by the car. If the car suddenly stops, the air inside will not stop the bee from moving because it is not hard/dense enough; so the bee will certainly move, and might hit the front window if the car was moving fast enough.
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