What is the World Record for most push ups in 1 second?
I don't believe anyone keeps records for that short a period. To quote from recordholders.org, referring to the number of push-ups in one minute:
it became impossible to judge about the correctness of the exercises at this speed. The last record that was accepted by the Guinness Book of Records were138, achieved by Roy Berger (Canada) in on 28 February 2004
Extrapolating from 138 in 60 seconds, you can probably safely set a lower bound to the record in one second of 2, but that's not particularly exciting.