Physics: relation between 1/s and m/s^2 (confused)

A car is traveling to the right with a speed of 29m/s when the rider slams on the accelerator to pass another car. The car passes in 110m with constant acceleration and reaches a speed of 34m/s.
What was the acceleration of the car as it sped up?
I calculated the average velocity 31.5m/s, and I know the car will add 1m/s each 22m. I divided 31.5 by 22 and get the same answer as the acceleration 1.43 m/s^2. What I don't understand is the relationship in between, what 1/s in this case is. And from unit form, 1/s is not equaled to m/s^2. Or it is just a coincident that I am actually wrong.