Answer:
distance moved by the center of the wheel during time
to
is 145.32 m
Explanation:
Given that :
The radius of the wheel R = 28 cm
Initial angular speed of the wheel 
= 
= 
= 100.5 rad/s
At time t = 9 s ; the angle rotated by wheel 
= 32 π × 9
= 905 rad
At time
; the angular speed is definitely the same and the initial velocity
is 
However ; after time
; the angular acceleration of the wheel ∝ = 1.3 rad/s²
At time
; angular speed of wheel 


Now; the angle rotated by the wheel during time
to
is expressed as:

From the question; we are being told that :
This zero-velocity condition implies that vCM=ωR, where ω is the angular speed of the object, since the instantaneous speed of the contact point is vCM-ωR.
i.e 
then we can say :
acceleration
and
linear distance
indicating how far did the center of the wheel move
So; distance moved by the center of the wheel during time
to
is ;
= 0.28 × 519
s = 145.32 m
Therefore; distance moved by the center of the wheel during time
to
is 145.32 m