Trivia, how was a quarter mile chosen as the length of a dragstrip?

From Wally Parks:

We took some new (1949 model) cars down, and as part of the the regular Motor Trend road test, we ran these experimental runs. The purpose of the thing was to find out just how far you could race the average car that was available at the time before you had to start getting stopped. We had a runway down there that I think was 4700 feet long. We had probably 20 different cars running, of all types, including some dry lakes cars; and we found that if we extended the acceleration distance more than a quarter mile, some of them couldn't get stopped at the other end. It was on that basis that we (later) established the quarter-mile as the official (NHRA) competition distance.
Hot Rod Magazine Nov. 1978