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A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) is
- a)3.3%
- b)4.8%
- c)5.3%
- d)6.8%
Correct answer is option 'B'. Can you explain this answer?
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Problem statement:
A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) is
Solution:
Given:
Initial velocity of the vehicle, u = 60 km/h
Ratio of lag to brake distance = 6:5
Total reaction time of the driver, tr = 2.5 s
Coefficient of longitudinal fraction, μ = 0.36
Let,
The ascending gradient of the highway = θ
Distance travelled by the vehicle during the total reaction time = Sr
Distance travelled by the vehicle during the lag time = 6x
Distance travelled by the vehicle during the brake time = 5x
Where x is the common factor
We know that,
Total stopping distance (SD) = Sr + lag distance + brake distance
The distance travelled by the vehicle during the total reaction time can be calculated as:
Sr = u × tr = (60 × 1000) / (60 × 60) × 2.5 = 416.67 m
The lag distance and brake distance can be calculated by using the following formula:
Lag distance = (u² / 2g) × μ × tr²
Brake distance = (u² / 2g) × μ × (1 + v/u)²
Where g is the acceleration due to gravity and v is the final velocity of the vehicle, which is zero in this case.
The lag distance and brake distance are in the ratio of 6:5
6x = (u² / 2g) × μ × tr²
5x = (u² / 2g) × μ × (1 + v/u)²
Dividing the above two equations, we get:
6/5 = (tr² / (1 + v/u)²)
Substituting the given values, we get:
6/5 = (2.5² / (1 + 0/60)²)
Solving the above equation, we get:
v = 36 km/h
The brake distance can be calculated as:
5x = (60² / 2 × 9.81) × 0.36 × (1 + 0/60)²
x = 53.3 m
The total stopping distance can be calculated as:
SD = Sr + lag distance + brake distance
SD = 416.67 + 6x + 5x
SD = 416.67 + 11x
SD = 416.67 + 11 × 53.3
SD = 1079.97 m
The value of gradient θ can be calculated as:
θ = (SD / 100) / (2 × u² / 2g)
θ = (1079.97 / 100) / (2 × 60² / 2 × 9.81)
θ = 4.8%
Therefore, the value of ascending gradient is 4.8%.
A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) is
Solution:
Given:
Initial velocity of the vehicle, u = 60 km/h
Ratio of lag to brake distance = 6:5
Total reaction time of the driver, tr = 2.5 s
Coefficient of longitudinal fraction, μ = 0.36
Let,
The ascending gradient of the highway = θ
Distance travelled by the vehicle during the total reaction time = Sr
Distance travelled by the vehicle during the lag time = 6x
Distance travelled by the vehicle during the brake time = 5x
Where x is the common factor
We know that,
Total stopping distance (SD) = Sr + lag distance + brake distance
The distance travelled by the vehicle during the total reaction time can be calculated as:
Sr = u × tr = (60 × 1000) / (60 × 60) × 2.5 = 416.67 m
The lag distance and brake distance can be calculated by using the following formula:
Lag distance = (u² / 2g) × μ × tr²
Brake distance = (u² / 2g) × μ × (1 + v/u)²
Where g is the acceleration due to gravity and v is the final velocity of the vehicle, which is zero in this case.
The lag distance and brake distance are in the ratio of 6:5
6x = (u² / 2g) × μ × tr²
5x = (u² / 2g) × μ × (1 + v/u)²
Dividing the above two equations, we get:
6/5 = (tr² / (1 + v/u)²)
Substituting the given values, we get:
6/5 = (2.5² / (1 + 0/60)²)
Solving the above equation, we get:
v = 36 km/h
The brake distance can be calculated as:
5x = (60² / 2 × 9.81) × 0.36 × (1 + 0/60)²
x = 53.3 m
The total stopping distance can be calculated as:
SD = Sr + lag distance + brake distance
SD = 416.67 + 6x + 5x
SD = 416.67 + 11x
SD = 416.67 + 11 × 53.3
SD = 1079.97 m
The value of gradient θ can be calculated as:
θ = (SD / 100) / (2 × u² / 2g)
θ = (1079.97 / 100) / (2 × 60² / 2 × 9.81)
θ = 4.8%
Therefore, the value of ascending gradient is 4.8%.
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A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer?
Question Description
A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer?.
A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer?.
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A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A vehicle moving at 60 km/h on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6:5. Considering total reaction time of the driver as 2.5 s and the coefficient of longitudinal fraction as 0.36, the value of ascending gradient (%) isa)3.3%b)4.8%c)5.3%d)6.8%Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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