If Quicksilver can go that fast, if he didn't hold the person’s neck while running with them would his sudden burst of speed snap their neck? Or would they just have whiplash like in X-Men: Days Of Future Past?
This video (Game Theory: Hookshot) discusses the degree of acceleration a human body can withstand (starting at around the 12-minute mark), and the mathematics thereof.
Judging from physics and human physiology, rather than any canon source, it doesn't seem possible that Quicksilver could move a person as quickly as we see in the film without causing them severe injury.
The maximum acceleration a human has ever survived was a peak of 46G on a rocket sled which accelerated to Mach 0.9 (source). However, there is also the un-cited claim that such acceleration caused permanent vision problems.
- Mach 1 is just over 761Mph.
- The muzzle velocity of a 9mm bullet is 1029Mph.
In the film, we see Quicksilver easily outrunning what appears to be 9mm ammunition (although it could be 45 caliber); if he is accelerating a passenger to anywhere near those speeds, he would almost certainly kill them.
TL;DR: yes, Quicksilver cannot run (alone or with someone) without a bunch of implicit secondary powers (which would be very useful, but that he never uses)
This is a typical case of secondary powers required...
Like for Superman, Flash and all others who go to great speed, they have to have some implicit powers in order to achieve what they do without breaking all laws of physics... They need:
a sort of energy field that remove the inertia (to suppress the acceleration and not crush whatever they are holding, or themselves)
a superforce to support all the efforts they need to make to run this fast and resist acceleration
a super resistant mcostume (or else it would shred immediately)
a way to harden the floor, or else they would create big holes (every time they start or stop running, they apply a demential force to the ground)
super eyes to see what's coming in the way
super rapid thinking to have the time to react
Although the question offers two possible outcomes (snapped neck or whiplash), a third outcome seems most likely (and terminal): the person being transported would suffer fatal internal injuries because the forces of acceleration don't play only upon the outer husk of our bodies and our fragile necks, but upon each and every component therein.
The brain of a "shaken baby" is injured by bouncing against the inside of the skull. People in closed spaces exposed to the shock waves of explosions suffer internal injuries at least partly because the shock waves act upon their organs as well as their limbs, trunks, heads, etc. Thus, not only would the head be snapped backwards if unsupported, but the brain within would be snapped back into the back of the skull even if the head were supported. The stomach, kidneys, liver, lungs etc. would be pressed back against the spinal column with pulping force... and you get the picture.
The only way this could play out and end up with a living passenger at the end would be if there were some sort of "magical" or "super science" chamber effect surrounding their person which slowed the effects of acceleration similar to the way a decompression chamber slows the body's treatment of dissolved inert gases in his/her blood and joints when surfacing from a deep dive. If the person being transported could be held within a delaying sphere of some influence that allowed the compression forces to be played out over a few moments before and after arrival instead of taking place nearly instantly, the forces on the entire body could perhaps be absorbed in a less injurious way.
Of course, this seems unlikely since the force is the movement, and thus the delay, would have to be in space as well as time - kind of eliminating the speed of the transport and thus the premise of the question. Oh well... but fun to think about.
On DC comics, they explained this type of effects on Flash (and Flash-like characters) through Speed Force.
Quicksilver is somewhat a copycat of Flash, but by the moment Quicksilver have been created, DC hadn't explained Flash' powers through the point that physics were a problem yet, so by the time this happened, Marvel had two options: clearly find a similar explanation (which would have made the copy absolutely blatant), look for a totally different explanation or just ignore the physics completely and let the disbelief suspension do the hard work. As far as I know, this last option is what Marvel had used so far.