A cyclist accelerates from rest. After 6 s, the wheels have made 5 rev.

A cyclist accelerates from rest. After 6 s, the wheels have made 5 rev.

(a) What is the angular acceleration of the wheels?
______rad/s2
(b) What is the angular velocity of the wheels after 6 s?
______rad/s

there are 2π radians per revolution so the wheels have turned through 10π radians after 6 s, which is an average angular velocity = 10π/6 = 1.67π rad/s
and
we know that in constantly accelerated motion: average velocity = 1/2 final velocity
so
final angular velocity of wheels = (2)(1.67π) = 10.5 rad/s <= ANS (b)
since the wheels started from 0 rad/s, the change in angular speed = 10.5 rad/s,
which means the angular acceleration = 10.5/6 = 1.75 rad/s² <= ANS (a)