(a) 119.3 rad/s
The angular speed of the wheel is

we need to convert it into radiands per second. We know that

Therefore, we just need to multiply the angular speed of the wheel by this factor, to get the angular speed in rad/s:

(b) 596.5 rad
The angular displacement of the wheel in a time interval t is given by

where

and
t = 5 s is the time interval
Substituting numbers into the equation, we find

(c) 127.3 rad/s
At t=10 s, the angular speed begins to increase with an angular acceleration of

So the final angular speed will be given by

where
is the initial angular speed
is the angular acceleration
is the time interval
Solving the equation,

(d) 616.5 rad
The angle through which the wheel has rotated during this time interval is given by

Substituting the numbers into the equation, we find

(e) 222 m
The instantaneous speed of the center of the wheel is given by
(1)
where
is the average angular velocity of the wheel during the time t=10 s and t=15 s, and it is given by

and
R = 36 cm = 0.36 m is the radius of the wheel
Substituting into (1),

And so the displacement of the center of the wheel will be
