Here, Speed of the automobile,

$v = 54\,km{h^{ - 1}} = 54 \times {5 \over {18}}m{s^{ - 1}} = 15m{s^{ - 1}}$

Radius of the wheel of the automobile, R = 0.45 m
Moment of inertia of the wheel about its axis of rotation, I = 3 kg m²

Time in which the vehicle brought to rest, t = 15 s
The initial angular speed of the wheel is

${\omega _i} = {v \over R} = {{15m{s^{ - 1}}} \over {0.45\,m}} = {{1500} \over {45}}rad\,{s^{ - 1}} = {{100} \over 3}rad\,{s^{ - 1}}$

and its final angular speed is ${\omega _f}$ = 0 (as the vehicle comes to rest)

$\therefore$ The angular retardation of the wheel is

$\alpha = {{{\omega _f} - {\omega _i}} \over t} = {{0 - {{100} \over 3}} \over {15\,s}} = - {{100} \over {45}}rad\,{s^{ - 1}}$

The magnitude of required torque is

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

$= {{20} \over 3}kg\,{m^2}{s^{ - 2}} = 6.66\,kg\,{m^2}{s^{ - 2}}$