Speed of the automobile,

\(v = 54\,km\,{h^{ - 1}} = 54 \times \frac{5}{{18}}\,m\,{s^{ - 1}} = 15\,m\,{s^{ - 1}}\)

Radius of the wheel of the automoblie, \(R = 0.45 m\)

Moment of inertia of the wheel about its axis of rotation, \(I = 3 \,kg\) \({m^2}\)

Time in which the vehicle brought to rest. \(t = 15\, s\)

The initial angular speed of the wheel is 

\(\omega i = \frac{v}{R} = \frac{{15\,m\,{s^{ - 1}}}}{{0.45\,m}} = \frac{{1500}}{{45}}rad\,{s^{ - 1}} = \frac{{100}}{3}rad\,{s^{ - 1}}\)

and its final angular speed is 

\({\omega _f} = 0\)        (as the vehicle comes to rest)

\(\therefore \) The angular retardation of the wheel is 

\(\alpha  = \frac{{{\omega _f} - {\omega _i}}}{t} = \frac{{0 - \frac{{100}}{3}}}{{15\,s}} =  - \frac{{100}}{{45}}\,rad\,{s^{ - 2}}\)

The magnitude of required torque is

\(\tau  = I\left| \alpha  \right| = \left( {3\,kg\,{m^2}} \right)\left( {\frac{{100}}{{45}}rad\,{s^{ - 2}}} \right)\)

\( = \frac{{20}}{3}\,kg\,{m^2}{s^{ - 2}} = 6.66\,kg\,{m^2}{s^{ - 2}}\)