It's a good and fair question.
First of all, I think that it is important to know that, the reason that the living in Christ will simply be changed into their immortal and glorified bodies, is because they will not be dead in order to be resurrected. That said, it is also important to understand what the word 'anastasis' translated as 'Resurrection' means.
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Strong's Concordance
anastasis: a standing up, i.e. a resurrection, a raising up, rising
Original Word: ἀνάστασις, εως, ἡ
Part of Speech: Noun, Feminine
Transliteration: anastasis
Phonetic Spelling: (an-as'-tas-is)
Definition: a standing up, a resurrection, a raising up, rising
Usage: a rising again, resurrection.
HELPS Word-studies
386 anástasis (from
303 /aná, "up, again" and
2476 /hístēmi, "to stand") – literally, "stand up" (or "stand again"), referring to
physical resurrection (of the body).
Christ's
physical resurrection is the foundation of Christianity, which also guarantees the future resurrection of all believers (see Jn 6:39,40,44).
[
386 /anástasis ("resurrection") refers to the
physical,
bodily resurrection of Christ – and people (both of the redeemed and the unredeemed).]
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So, according to the definition of anastasis/resurrection, it properly means to stand up again in the same physical body. Jesus is our example of this. For when He appeared to His disciples behind locked doors, they thought that He was a spirit, but He comforts them by showing them His hands and feet (nail marks) that it is Him. Then the Lord says, "A spirit does not have flesh and bone as you see I have." So the resurrection is a physical standing up again.
Those who have died in Christ from the on-set of the church up until the resurrection, their ashes, atoms, molecules, etc. will be reanimated into an immortal and glorified body.
Those in Christ who are still living, wherever they are and whatever they are doing at that moment, will be changed/transformed i.e. into their immortal and glorified bodies.
"Listen, I tell you a mystery: We will not all sleep, but we will all be changed—
in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed.
The word 'atomos' translated as in a flash, moment or instant, is defined as a period of time to short to divide. So, you are correct in that it is the change of our bodies that will take place in an instant. However, I believe that this atomos can be applied to the entire process that takes place, which includes o9ur transformation and being caught up.
Since we know that this change will be a transformation into a physical body with heavenly characteristics, then when this event takes place, whether a believer is driving their car, sleeping, flying on plane, at work, talking with a friend, giving a speech, etc., they are going to be changed on the spot. And as I said earlier, I believe that instant change can be applied to the whole process, so that the change that takes place and their being caught up will be one instantaneous event. In other words, if a believer is speaking to an unbeliever at the time of them being change, there is not going to be a delay in their being caught up to have a conversation with the unbeliever as to what just happened. By that's just my understand of this.
When this event takes place, the entire church from beginning to end, will be gathered in one place at the same time to meet the Lord in the air. Where in fulfillment of John 14:1-3, the Lord will take us all back to the Father's house to those places that He prepared for us so that where He is, we may be also.
So to answer the question, I would say that if a believer is driving a car when they are changed and caught up, then that car will be without a driver. The same goes for flying a plane, speaking in front of a large or small group of people, etc. To the unbeliever, I would suggest that to them and at the speed in which they are changed and are caught up, it will appear that the person has just disappeared before their very eyes. It makes one think about what kind of a world-wide stir that's going to cause. It might cause more mask mandates
Those who have been chosen to be the great tribulation saints, will become believers at that time and will know that the church has been caught up and will prepare themselves for what is coming, pouring over the scriptures, specifically the book of Revelation to understand the events of God's wrath via the seals, trumpets and bowl judgments, as well as information regarding the antichrist/beast. For they will be trapped in the worst time of the history of the world, the Day of the Lord.