Whenever the person in possession or control of any private property used by the public for purposes of vehicular traffic by permission of the owner shall cause to be posted at each entrance thereto a permanently lettered, clearly legible sign with the following legend:

TRAFFIC REGULATIONS OF THE CITY OF TOPEKA ENFORCED ON THIS PROPERTY. SPEED LIMIT 12 M.P.H. (OR AS POSTED).

Then such private property shall thereafter be deemed to be under the traffic regulations of the City as provided by law. (Code 1981 § 43-87. Code 1995 § 142-2.)