the difference between fast/quick/rapid

Quick is best, although fast is ok.

But at least for me, you can’t use rapid here; it doesn’t seem to apply directly to people like that.

I can't give reference, but just let you know that to my American ear, "quick" or "fast" are both good, but "rapid" seems unnatural in that context.

Macmillan Dictionary defines quick ("able to move fast or do something fast") and fast ("able to move quickly") in terms of each other, so there's not much to choose between them.

Either is a desirable trait in a striking art like karate; force equals mass times acceleration, after all.

On the other hand, Macmillan defines rapid as "happening, moving, or acting quickly," rather than being quick or fast.

I would prefer "Quick" as defined in Dictionary.com

1. done, proceeding, or occurring with promptness or rapidity, as an action, process, etc.; prompt; immediate: a quick response.

2. that is over or completed within a short interval of time: a quick shower.

3. moving, or able to move, with speed: a quick fox; a quick train.

4. swift or rapid, as motion: a quick flick of the wrist.

5. easily provoked or excited; hasty: a quick temper.

"Fast" is the best choice.

Quick and fast are almost identical in meaning, but quick also has the connotation in a sentence such as that of being quick on the uptake, quick to learn, etc., while fast does not and implies quick in movement only. Unless, of course, you want to express those other implications as well.

Rapid simply does not fit the context.

I see that you should be able to differentiate between the three now. But ever tried to use something else, all these words are relative, in other words, fast means do something like moving quickly but relative to something else.

I would recommend you taking your reader imagination a bit further and you relate for the reader.

She is a karate coach. She is not very powerful, but she is as fast as an eagle attacking a prey.

Fast and quick can be used here, and which one you use depends on the facts of the case. An article called The difference between FAST and QUICK in martial arts by ‘Anakonxx’ explains the difference in this context:

Being quick means delivering a technique with explosive speed. Fast is speed without the explosiveness. The former should be the goal of any combat sport devotee.

Some comments in the final paragraph of that article suggest that strength is an important element of quickness:

Lastly, let’s talk about strength in relation to being fast and quick. Once the student learns the mechanics of the technique, the timing is beautiful, your perception speed is marvelous, and your delivery is impeccable. You are only fast, but you are not quick yet. You need to add strength to the strike. ...

If you agree with the martial-arts article’s definitions of fast and quick and the comments about strength, then saying “She is not very powerful” might preclude calling her quick; she might merely be fast.

Some previous answers note that rapid isn't suitable. This is a matter of usage (see ngrams for she is... and he is...) rather than of grammar. I think rapid is commonly used to characterize actions or processes, but not people.

I am a Russian and English is not my mother tongue. Yet I have an idea. I think that 'quick' implies some motivation or stimulus. If you eat something quickly you do it because you want to do something else after eating. 'Rapid' implies 'no obstacles'. In this canteen you can eat rapidly because there will be no waiting time, there will be no obstacles to your eating. 'Swift" means 'in a great hurry'. If he eats swiftly his food, it means that he swallows his food with little chewing. And 'fast' means just 'with high-speed'. You must slow down your fast eating pace.

As an enthusiast of bikes, quickness is measured in terms of acceleration while fastness is considered in terms of speed.

As I understand:

1. Quick: refers to time, it describes something that is done in a short period of time or without any delay;
2. Fast: refers to speed, it describes something moving at high speeds;
3. Rapid: refers to time, but at which rate something changes, that is, either increases or decreases;

That being said:

She is a karate coach. She is not very strong, but she is very quick.

Means that she makes decisions in no time and her movements take short periods of time to be completed.

She is a karate coach. She is not very strong, but she is very fast.

Means that she can run at high speeds.

She is a karate coach. She is not very strong, but she is very rapid.

Is incomplete, and would not get to the original meaning you wanted. It to be changed to something like:

She is a karate coach. She is not very strong, but her students had rapid progress.