Translation:What is observed as the velocity increases?
"Speed" is the best translation here. Скорость is used for both speed and velocity (and also rate in some contexts) in scientific Russian. Basically, you need to know the context to know which is the correct translation. There are many other examples of a term in Russian that correspond to different terms in English, for example, экспонента is used for both an exponential function and an exponent. Similarly, there are examples of a term in English that could be different terms in Russian, depending on the context; for example, type might be вид, тип или род. Then there are terms for which there is an exact translation but no immediately obvious relation: статистическая сумма is a partition function.
I rarely encounter such a strange concept as a velocity increasing. Usually, it is the norm, modulus, absolute value, or magnitude of a velocity that increases.
увеличение is a noun derived from the verb увеличить(ся). You don't have to always translate a noun as a noun and a verb as a verb. Feel free to convert parts of speech if you need to. Nouns derived from verbs are commonly used with the preposition при in Russian. Such phrases mean "as the process goes on" or "while the process is going on"
In real life I would feel free to produce a free translation. Here, I get tired of getting dinged, and having to figure out whether my translation was actually legitimate or simply wasn't coded in.
I answered "what was observed with the increase in velocity?", which is normal scientific English and much closer to the Russian. It should at least be accepted.
Do we really need 4 new words out of 5 in a sentence? I think it is kind of discouraging.
The issue here is that the "preferred" answer is asking for agency "...as you increase the speed" when there is no agency in the Russian version. A more appropriate English translation would be "What is observed as the speed increases?" or "What is observed with an increase in speed?"
"Increase of speed" exists in English. For example:
"limit jerk implies linear increase of acceleration to the limit acceleration, quadratic increase of speed" (https://en.wikipedia.org/wiki/Jerk_(physics)#In_motion_control)
"Increase of speed" exists in English dictionaries. For example:
"noun 1. the act of accelerating; increase of speed or velocity." (http://www.dictionary.com/browse/acceleration)
"При" may mean "in the process of", "as [something goes on]", "in the case of", "in front of (=in the presence of)", "during someone's rule", "attached to", "having", "accompanying", "assuming" or "as long as you have". The following noun/pronoun is put in the preposionsl case. "Про" is synonymous with "о/об" when the latter means "about". "Про" is less formal than "о" and is often used after the verbs думать, говорить, рассказывать and nouns such as сказка, рассказ, песня, книга. The objects of "про" are always put in the accusative form (unlike those of "о" which are put in the prepositional form when "о" means "about"). In some occasions про means "for", but this usage is dated.
It is neither. Увеличение (nominative case form) = increase / increasing. The preposition при requires putting the following noun in the prepositional case, hence при увеличении. When a verb+object phrase is transformed into a noun+noun phrase in which the first noun is derived from the verb, the second noun (the one that denotes the object) is always put in the genitive case. So we have the following transformation: увеличить скорость —> увеличение скорости —> при увеличении скорости
Probably just an omission. But even better would be "What is observed with an increase in speed?" Closer to the Russian and also close to another normal phrasing in science/engineering (in my experience, YMMV). This may already be accepted - I believe you were correct, Mr Chekhov.