a)

Distance for one revolution  = 2*pi*r

                                        = 2*pi*0.25

                                        =pi/2

Number of revolution to travel 150m = 150/(pi/2)

                                                     = 95.49 rev

b)

One revolution have 2*pi radians.

Therefore the number of radians it turns = 2*pi*95.49

                                                           = 600

c)

average angular velocity = (total radians turned)/time taken

                                   = 600/30

                                   =20 rad/s

d)

From equations for angular motion;

` `` ``theta = omega*t+0.5*alpha*t^2`

Since the bicycle starts from rest ` ``omega` = 0

at time t=30 theta = 600 rad

Therefore;

  ` 600 = 0*30+0.5*alpha*30^2`

`alpha = 1.33333`

Angular accelaration = 1.3333 rad/s^2

e)

From equations for angular motion;

`omega = omega_0+alpha*t`

when t=30;

`omega` = 0+1.33333*30 = 40rad/s

So angular velocity at end=40 rad/s

f)

Tangential velocity (v)       = `r*omega`

tangential accalaration (a) = `r*omega^2`

consider final velocity;

v = 0.25*40 = 10m/s

a = 0.25*40^2 = 400m/s