the 1939 Worlds Fair had a bumper cars ride and a co cart ride on an oval track (thank you Terry!) in the "Amusement Zone"

'39 World's Fair bumper cars illustrations from the Popular Science magazine which ran illustrations by artists to give an idea of what was to come

so I went on a google search to see what the internet knows about the '39 Worlds Fair having bumper cars

those are clips from the video at https://archive.org/details/0639_HM_Medicus_collection_New_York_Worlds_Fair_1939-40_Reel_6_15_01_00_00

Which surprising to me, is NSFW, as the amount of topless beautiful young women is astonishing. The mermaids were topless, the "sun worshipers" had transparent bikinis, the ballerinas were topless, the burlesque dancers were transparent bikini tops, and there was one dancing women show that had a half dozen styles of night club topless stripper dances, frankly, that surprises me... that the '39 worlds fair has never had any mention of all the breasts and nipples in anything I've ever heard about it. 

"News reporters found it difficult to understand the role of the Amusement Zone. "The smell of popcorn and hamburgers mixed with wiffs from Frank Buck's fauna display gave the place a Coney Island air." "Culture seems to be having a struggle with Entertainment at the fair. The tendency among visitors is to draw the line along World's Fair Boulevard, which geographically separates the (the Amusement zone from the exhibit area)." 

And seemingly ignoring the constant controversy over the "nude shows,"

 "It is a credit to the management that none of the obscene exhibits in the Chicago Midway were permitted. It was all good and wholesome fun reflecting the changed public sentiment."

https://www.1939nyworldsfair.com/worlds_fair/wf_tour/zone-7/zone-7.htm

Wait, what? Obscene exhibits at the Chicago Worlds Fair? Hell, I've never heard of that either!

and the ubiquitous bumper car that stayed familiar for a couple decades after the fair  https://www.worthpoint.com/worthopedia/1939-york-worlds-fair-advertising-2951412655

George Smith, the man in charge of the Amusement Zone concessions, began his World's Fair career as a chair pusher at Buffalo's Pan-American Exposition in 1901.