Here, Speed of the automobile,
v=54kmh−1=54×‌ms−1=15ms−1Radius of the wheel of the automobile,
R=0.45mMoment of inertia of the wheel about its axis of rotation,
I=3‌kg‌m2Time in which the vehicle brought to rest,
t=15 sThe initial angular speed of the wheel is
ωi=‌=‌=‌rads−1=‌rads−1and its final angular speed is
ωf=0 (as the vehicle comes to rest)
∴ The angular retardation of the wheel is
α=‌=‌=−‌rads−1The magnitude of required torque is
τ=I|α|=(3‌kg‌m2)(‌‌rad‌ s−2)=‌‌kg‌m2‌ s−2=6.66‌kg‌m2‌ s−2