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GATE 2024 CE (CE1) – Question 22

Transportation Infrastructure · Geometric design of roadways: cross-section, sight distance, alignments · 1 mark · Multiple choice

A car is travelling at a speed of 60 km/hr on a section of a National Highway having a downward gradient of 2%. The driver of the car suddenly observes a stopped vehicle on the car path at a distance 130 m ahead, and applies brake. If the brake efficiency is 60%, coefficient of friction is 0.7, driver's reaction time is 2.5 s, and acceleration due to gravity is 9.81 m/s$^2$, the distance (in meters) required by the driver to bring the car to a safe stop lies in the range

  1. 126 to 130
  2. 41 to 45
  3. 33 to 37
  4. 75 to 79

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Correct answer: (D) 75 to 79

Explanation

The speed is $v = \frac{60}{3.6} = 16.67$ m/s. The distance covered during the reaction time is $16.67 \times 2.5 = 41.7$ m. The effective friction is $0.6 \times 0.7 = 0.42$ and on a 2% downgrade the deceleration is $g(0.42 - 0.02) = 0.40g$. The braking distance is $\frac{v^2}{2 \times 0.40g} = \frac{277.8}{7.848} = 35.4$ m. The total stopping distance is $41.7 + 35.4 = 77.1$ m, in the range 75 to 79 m.