We tend to put some adverbials in front of the verb but others after the verb. It depends on many factors.
It's hard to come up with a reasonable explanation why we say:
(！indicates an imperative sentence, 。 a declarative sentence, and ， an incomplete sentence.)
Sometimes both are used:
Apparently, 地 is preferred when the verb is long or followed by something else.
I think the word that comes after the verb is usually the focus or new information. If you omit the adverbs,
do not sound like complete sentences, which means the adverbs probably contain important information. That's why we tend to place them at the end of a sentence. On the other hand,
are complete sentences, so
I think 了 is what makes all the difference--it means a new event has happened, which by itself contains significant information. We may first use 了 to notify a new event, then use 得 to add some details.
Not all adverbs/adjectives can appear in both positions, and not all of them need 得 or 地. For example, 快 itself is an adverb.
他快吃完了。 = He almost finished eating -> He is eating.
快吃。 -- 快 is more like “hurry up” or “come on”