Drink driver Michelle Nelson was caught when she clipped an unmarked police car on Hucknall Road.
Before she was banned for a year, she told city magistrates: "I took my eye off the ball for a split second and went into the back of the car.
"There was no damage done," said Nelson, 56, of Fulwood Crescent, Aspley.
The collision took place at 12.35pm. She said she had a drink the night before and felt she was safe to drive. She had taken her father to hospital earlier.
"I am so sorry for what has happened. I had no idea I would be over the limit or I would not have done this," she added.
A £80 fine, £50 prosecution costs and a £30 government surcharge were ordered. She admitted driving with 46 micrograms of alcohol in 100 millilitres of breath, 11 over the legal limit.
Kwok Wan, prosecuting, told the court: "Mrs Nelson was in collision with an unmarked police vehicle.
"Uniformed officers attended and, as is usual, a roadside breath test was taken."
Nelson failed this and another test which was taken at a police station.
Presiding magistrate Anthony Burton told her: "Thank you for being frank with the court. Your early guilty plea has been taken into account."
If Nelson passes a course on the perils of drink driving, the disqualification will be reduced by a quarter.
