Go at a mad rate (4)

I believe the answer is:

tear

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'go at' is the definition.
The answer and definition can be both acts as well as being singular nouns.
Maybe there's an association between them I don't understand?

'a mad rate' is the wordplay.
'a mad' indicates an anagram.
'rate' anagrammed gives 'TEAR'.

Can you help me to learn more?

(Other definitions for tear that I've seen before include "Secretion of the lacrymal glands" , "Small globule of sorrow" , "speed" , "Shred" , "Secretion of the lachrymal glands" .)

I've seen this clue in the Evening Standard.

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