Q135 / 150 · MHT CET 2020 (15 Oct Shift 2) · Physics

A vehicle moving with $15 \mathrm{~km} / \mathrm{hr}$ comes to rest by covering $5 \mathrm{~m}$ distance by applying brakes. If the same vehicle moves at $45 \mathrm{~km} / \mathrm{hr}$, then by applying brakes, it will come to rest by covering a distance

  • A
    $15 \mathrm{~m}$
  • Correct answer
    B
    $45 \mathrm{~m}$
  • C
    $60 \mathrm{~m}$
  • D
    $30 \mathrm{~m} .$

Solution

\(\mathrm{u}=15 \mathrm{~km} / \mathrm{hr}=\frac{15 \times 1000}{60 \times 60}=\frac{150}{36} \mathrm{~m} / \mathrm{s}\) \(\mathrm{v}^{2}=\mathrm{u}^{2}-2 \mathrm{as}\) \(\therefore \mathrm{a} \frac{u^{2}}{2 \mathrm{~s}}=\frac{150 \times 150}{36 \times 36 \times 2 \times 5} \mathrm{~m} / \mathrm{s}^{2}\) Next \(\mathrm{s}=\frac{u^{2}}{2 a}=\frac{45000}{60 \times 60} \times \frac{45000}{60 \times 60} \times \frac{1}{2} \times \frac{36 \times 36}{150 \times 15}\) \(=45 \mathrm{~m}\)

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

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