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The character 快 is usually used for the meaning of "fast", but it is also used in the sense of "pleasant" or "happy" - for example, in the words 痛快, 爽快. It seems that both meanings are quite ancient.

According to the morphology, you'd expect this character to originally have the "happy" meaning - it has a 忄 radical - but the "fast" meaning is also very ancient, e.g.

此马虽快,然力薄不堪苦行。——《晋书·王湛传》

How did this character pick up two meanings, which are not quite related?

And yes, 快 also has other meanings.

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  • quick seems to have come later. 說文解字: 喜也從心夬聲 – Mou某♦ Sep 8 '14 at 4:50
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    I'm afraid it's difficult to find a convincing answer for this question. 快，喜也。从心，夬聲 is the original text in Shuowen, so the core is why it can evolve to have a meaning "quick". I think there may be two possibilities: 1) some other character with a similar pronunciation had a meaning related to "quick", 快 was mistakenly written for that character, and then became popular; 2) 《說文新證》：“【夬】射箭時套在指上的扳指，分決為引申義。甲骨文从又，○形象扳指。＂ So if 夬 had a meaning related to a shooting arrow, it would be a reason for why 快 could have the meaning "quick". – Stan Sep 9 '14 at 18:37
  • Anyway there're too many theories for the explanation of 夬, but most of them have nothing to do with "quick". So I tend to consider 夬 is only the phonetic part in 快. – Stan Sep 9 '14 at 18:40
  • In Italian, allegro means cheerful/happy, but in music also denotes a faster pace, so I guess that the meaning evolved similarly in Chinese. – Gabriel Diego May 24 '19 at 20:13
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Not a very satisfying answer but anyway:

說文解字

喜也。从心夬聲。苦夬切

說文解字注

喜也。引申之義爲疾速。俗字作駃。从心。夬聲。苦夬切。十五部。

Notice the 引申之義爲疾速 from above, happiness extended to mean fast.

I don't know exactly the mentality of 喜 -> 引申 -> 疾速 but apparently people did think they were related at one point in time.

Maybe it has to do with 俗字作駃

大汉语词典

駃 kuài［1］快马。“参见駃马”。［2］同“快”。

Must have been some mix-up somewhere.

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Here is a note from the 古漢語常用字字典 concerning synonyms for ‘quick, fast’ in Classical Chinese:

[辨] 快, 速, 疾, 捷. 這幾個字都有快速的意思.

“快” 表示快速是後起意義, 在上古只做愉快講, 而”快速”這個意義卻常用"速"表示.

"疾” 一般比”速”快一些. “捷” 指動作輕快, 敏捷.

(See under entry for 速)

[Note: I misread this dictionary entry initially - it doesn't mean that 'kuai' occured in a compound with 'su' in CC. The comments that follow have been edited in this light.]

This is saying what others have posted - that originally (or in the pre-classical period) 快 meant happy, and only later took on the meaning of fast. It was 速 which did mean ‘fast’ at that early date, which makes sense given the ‘movement’ radical. I would suggest that the semantic range of 快 may have expanded due to use as an attributive. For example, speed was a desirable quality in horses, so 快馬 was a horse that made people happy. Perhaps 速 lost its adjectival role and other words were used to fill in. An analogous usage in English would be “a goodly pace.”

You could see how this would work with 疾 as well. This character in Classical Chinese meant to be sick – in comparison to 病, 疾 denoted a less serious illness. If it was used to modify other words in the sense of “a feverish pace” or very fast, a similar semantic shift seems plausible.

I don’t think this interpretation necessarily contradicts @Michaelyus’s idea that this is due to 假借borrowing. This kind of semantic shift is known from many languages, as the English examples I’ve given suggest.

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  • Indeed. "Quick" in English didn't originally mean "fast". (It didn't mean "happy" like in Chinese, that would be too much of a coincidence!) It meant "alive, lively", from the Germanic "keck", which, incidentally, is where our expression "the quick and the dead" comes from; nothing to do with speed. Perhaps there's a more general underlying association of haste and liveliness with happiness. – Matt S. May 26 '19 at 6:56
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It is just a word with more than 1 meaning; For example in english, the word degree could be a unit of temperature, an angle measurment, or certain education level. There is no why - it has multiple meanings and just the way it is.

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    The three meanings of "degree" you point at are obviously linked and there's absolutely no mystery... – vermillon Mar 15 '16 at 9:34
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There is some correlation of happiness, passion and faster pace in other languages too.

In Italian, the word allegro both denotes cheerful and also the brisk paced music style.

In Latin, the word alacer (from which allegro came from), means exactly both happy and fast.

In English also cheer means both to become happy or when a crowd starts moving in a positive attitude.

So I guess that it is just normal that natural languages observe a correlation with livid movements and happiness as opposed to a depressed, quiet mood.

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because the happy time always felt short like the time is running fast

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when 快 exist alone it means fast when it bundles with 乐（happy) like 快乐 it meaning happyness.

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