An automobile moves on a road with a speed of $54\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$ . The radius of its wheels is $0.45\text{m}$ and the moment of inertia of the wheel about its axis of rotation is $3\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }{\mathrm{m}}^2$ . If the vehicle is brought to rest in $\text{15 s}$, the magnitude of average torque transmitted by its brakes to the wheel is:

• A

  $8.58\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }{\mathrm{m}}^{\mathrm{2 }}{\mathrm{s}}^{-2}$
• B

  $10.86\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }{\mathrm{m}}^2\mathrm{ }{\mathrm{s}}^{-2}$
• C

  $2.86\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }{\mathrm{m}}^{2\mathrm{ }}{\mathrm{s}}^{-2}$
• Correct answer
  D

  $6.66\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }{\mathrm{m}}^{\mathrm{2 }}{\mathrm{s}}^{-2}$

Hence, the correct answer is option: 'D'.