But Deputy Chief Constable Andy McDyer said the officers were taking a break on the last day of the annual fair, which saw just four arrests during the eight-day event.
Mr McDyer said: "On the final day of the 2017 Hull Fair, our officers, who were policing the event, took a five-minute break to have some fun and engage with the fairground organisers by taking to the dodgems.
"Our officers, PCSOs and volunteer special constables worked long, hard hours during the event, some working nine consecutive 10-hour shifts, and they were able to enjoy a ride before the fair leaves Hull for another year.
"Throughout the week-long event, where Hull hosts one of the largest travelling fairs in Europe, we have received overwhelming positive feedback from both visitors to the fair and those following us on social media."
He continued: "We helped create a family-friendly and safe environment for all those attending and this is borne out by the fact that, of the half a million people that attended this year's event, there were only four arrests.
"I am incredibly proud of our teams that worked hard to engage with members of the public and ensure that the fair was safe for the people that attended."
Chief Superintendent Darren Downs posted a picture of himself on the ride on Twitter, with the caption: "Apparently I look too competitive, but I might as well have put a target on my back. Fantastic afternoon at the fair."
Inspector Scott Snowden also tweeted a photograph and wrote: "Great fun!"
The tweets received a mixture of responses from the public.
In reply to Mr Downs, a Twitter user named Thunder Road wrote: "Please don't ever complain again of shortage of police."
Lord Ealing said: "I wish that amount of police could be deployed to my area to combat the now crime that won't be investigated!!"
But others voiced their support.
Matt tweeted: "You all do an amazing job under great pressure and need some stress relief."
And Debbie wrote: "You guys deserve two minutes of fun at a quiet time like anyone else. Why not? Keep up the good work."
World's scariest theme park rides
World's scariest theme park rides
With a 127ft head-first drop straight under the wing of a genuine plane wreckage, followed by gut-wrenching near misses that take you terrifyingly close to a flaming fire truck, rotating helicopter blades and the walls of a life-size church, The Swarm is Europe's tallest winged roller coaster, and Thorpe Park's newest attraction.
Swings aren't scary, right? Wrong. How do you fancy one that reaches speeds of up to 50mph and 3G force? Sky Ride - the fastest swing in Europe - recently opened at Tree Top Adventure in North Wales. It's Europe’s first five-seater giant swing, elevated 80ft above the Conway Valley. Adrenaline seekers are suspended above the tree tops before being released to soar back and forth, with their feet dangling as the rush hits. Sky Ride is the highest swing-based ride of its kind in the UK.
According to legend, stars of the silver screen stayed at the Hollywood Tower Hotel during the golden age of Hollywood. But the story goes that in 1939, five guests were riding in the Hotel's maintenance service elevator when lightning struck the building - and they were never seen again. You can still see scorch marks on the exterior of the building. Only brave souls ride the Twilight Zone Tower of Terror at Disney's Hollywood Studios Theme Park.
Balder, at Liseberg Amusement Park in Sweden's Gothenburg, is one of the largest wooden roller coasters in the world and reaches speeds of up to 90km an hour.
Ferrari World in Abu Dabhi is world’s largest indoor theme park. Created around the classic double-curve body shell design of a Ferrari car, the park features over 20 rides and attractions, including the world’s fastest rollercoaster, Formula Rossa, which powers to 240 kmh in less than five seconds, and requires riders to wear safely goggles.
When it opened in 1996, Megafobia was Europe's largest wooden roller coaster. But you'll have to take a trip on this fast turning, heart tumbling, wild wooden roller coaster to find out why it's been voted the best ride in the UK, and the third best ride in the world.
Tree Top Adventure in the heart of Snowdonia in Wales is home to the world's highest Powerfan parachute simulator, the Powerfan Plummet. Thrill-seekers can scale a height of 106ft for a panoramic view, before plummeting to the ground aided by revolutionary new technology which ensures a feather light landing.
The Tower of Power at Siam Park, Costa Adeje in Tenerife offers the ultimate adrenaline rush. The 28 metre-high drop features a nearly vertical slide and a jaw-dropping drop at a speed of around 25mph. If that doesn’t seem enough, the ride then propels any brave takers through a clear underwater flume set in a giant tank... filled with sharks.
The Phoenix is a famous wooden roller coaster located at the Knoebels Amusement Resort in Elysburg, Pennsylvania. When it opened in 1947, the Phoenix was the largest roller coaster in the world, with 3200 feet of track and a 78ft hill. Gulp.
At Busch Gardens in Tampa Bay, Florida, North America's first dive coaster takes you 200ft up then hurtles you 90 degrees straight down at speeds of up to 70mph. There's nothing above you but air, and nothing below you but the ground.