The four-piece group and their manager, who were aged between 19 and 32, died in the early hours of 13 February following a gig in Stockholm.
Their car crashed into a raised section of a bridge and plummeted into a canal.
The inquest heard no alcohol or drugs was found in the blood of manager Craig Tarry, 32, who was driving.
Post-mortem examinations also showed the four band members had not taken drugs and had only consumed small amounts of alcohol.
The band's agent Graham Bennett told the inquest at Warrington Coroner's Court that the up-and-coming group were in Sweden for a festival showcasing young artists.
Viola Beach had already played at the Reading and Leeds festivals last year and the Stockholm event was their first gig outside the UK.
After the performance, they were travelling in a black Nissan Qashqai near the SÃ¶dertÃ¤lje Canal, about 18 miles from the capital, when a bridge was raised to let a boat pass underneath.
The inquest heard that the car was slightly over the speed limit as it was travelling at 108km/h (67mph) in a 100km/h zone.
Flashing lights signalled that the bridge was about to be raised with the middle section of the road lifted horizontally, the inquest heard.
Mr Tarry drove down a verge past stationary queuing traffic and through the first set of barriers, about 120m from the bridge, the court heard.
The car then travelled in a "controlled manner" at between 70 and 90km/h down the centre of the road.
It continued through a second set of barriers - 30m from the drop into the canal - and hit the raised section of the bridge before plummeting 25m, hitting the water within 15 seconds.
The court heard a tanker using the canal, which had requested the bridge to be lifted, then passed over the crash spot and "contact" with the car could not be ruled out.
The crew of a passing boat saw the car fall but initially thought it was ice.
Technical examinations did not find any errors with the car, barrier system or the procedure for raising the bridge.
One warning light on the bridge was out of order but there were at least 10 warning lights and flashing signals, the inquest heard.
Although the road was wet, it was not frozen with ice.
Post-mortem examinations found that all died from head injuries apart from Mr Lowe whose cause of death was given as drowning.
The court heard that the three band members sitting in the back of the car were not wearing seatbelts but those in the front were, and had to be cut from the vehicle.
Cheshire Coroner Nicholas Rheinberg said "none of the young men will have suffered" as they died.
The Swedish authorities have recommended improvements to the crossing, including LED signs and cameras on the bridge.
In the wake of their deaths, the band's first single Swings & Waterslides reached number 11, while their song Boys That Sing was performed by Coldplay in a tribute at Glastonbury.
Posthumously, Viola Beach scored a number one album in August.
The self-titled debut was compiled by the band's families, using live sessions and studio recordings, many of which were originally bound for an EP.
After the crash, a statement from the families of the band said: "We are tremendously proud of everything the boys achieved in such a short space of time.
"Craig, Jack, Kris, River and Tom shared a huge passion, talent and dedication to music."
An inquest into the deaths of British band Viola Beach after a crash in Sweden has heard that "none of the young men will have suffered".