Akitten pushes a ball of yarn rolling toward it at 1.00 cm/s with its nose, displacing the ball of yarn 17.5 cm in the opposite direction in 2.00 s. what is the acceleration of the ball of yarn?

The problem is very unclear.  The way I understand it is like this: 
The yarn is rolling toward the cat, and from the instant the cat first touches
the yarn, it moves 17.5 cm 2 sec, in the direction opposite to the way it was
rolling.

Average speed during the 2 seconds after the bump = 17.5 / 2 = 8.75 cm/s .

Average speed = (1/2) (final speed away from the cat - 1 cm/sec towards the cat)

8.75 cm/s = (1/2) (final speed + 1)
Multiply each side by 2 :
17.5 = final speed + 1
Final speed = 16.5 cm/s

Acceleration = (change in speed) / (time for the change)

Acceleration = (16.5 + 1) / (20) = 0.875 cm/s² .

My confidence level in this one is not excessive, but I'll submit it anyway,
and somebody else can explain to me where I went wrong.