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What is the braking distance (in meters, round off to 2 decimal places) required for a bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop? Assume coefficient of longitudinal friction as 0.30 and gradient of road as +5%.
- a)17.50
- b)17.90
Correct answer is between '17.50,17.90'. Can you explain this answer?
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What is the braking distance (in meters, round off to 2 decimal place...
Braking distance = 
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What is the braking distance (in meters, round off to 2 decimal place...
Given information:
- Initial velocity (u) = 40 km/hr
- Final velocity (v) = 5 km/hr
- Coefficient of longitudinal friction (μ) = 0.30
- Gradient of road (θ) = 5%
Converting velocities to m/s:
- Initial velocity (u) = 40 km/hr = (40 * 1000) / (60 * 60) m/s = 11.11 m/s
- Final velocity (v) = 5 km/hr = (5 * 1000) / (60 * 60) m/s = 1.39 m/s
Calculating acceleration (a):
The formula for acceleration (a) is given by:
a = (v^2 - u^2) / (2s)
Where,
a = acceleration
v = final velocity
u = initial velocity
s = braking distance
Rearranging the formula, we get:
s = (v^2 - u^2) / (2a)
Calculating deceleration (a):
The formula for deceleration (a) is given by:
a = g * sin(θ) - μ * g * cos(θ)
Where,
a = deceleration
g = acceleration due to gravity (9.81 m/s^2)
θ = gradient of road
μ = coefficient of longitudinal friction
Plugging in the values, we get:
a = (9.81) * sin(5) - (0.30) * (9.81) * cos(5)
a ≈ 0.84 m/s^2
Calculating braking distance (s):
s = (v^2 - u^2) / (2a)
s = (1.39^2 - 11.11^2) / (2 * 0.84)
s ≈ 17.70 meters (rounded to 2 decimal places)
Therefore, the braking distance required for the bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop is approximately 17.70 meters. Thus, the correct answer is between 17.50 and 17.90 meters.
- Initial velocity (u) = 40 km/hr
- Final velocity (v) = 5 km/hr
- Coefficient of longitudinal friction (μ) = 0.30
- Gradient of road (θ) = 5%
Converting velocities to m/s:
- Initial velocity (u) = 40 km/hr = (40 * 1000) / (60 * 60) m/s = 11.11 m/s
- Final velocity (v) = 5 km/hr = (5 * 1000) / (60 * 60) m/s = 1.39 m/s
Calculating acceleration (a):
The formula for acceleration (a) is given by:
a = (v^2 - u^2) / (2s)
Where,
a = acceleration
v = final velocity
u = initial velocity
s = braking distance
Rearranging the formula, we get:
s = (v^2 - u^2) / (2a)
Calculating deceleration (a):
The formula for deceleration (a) is given by:
a = g * sin(θ) - μ * g * cos(θ)
Where,
a = deceleration
g = acceleration due to gravity (9.81 m/s^2)
θ = gradient of road
μ = coefficient of longitudinal friction
Plugging in the values, we get:
a = (9.81) * sin(5) - (0.30) * (9.81) * cos(5)
a ≈ 0.84 m/s^2
Calculating braking distance (s):
s = (v^2 - u^2) / (2a)
s = (1.39^2 - 11.11^2) / (2 * 0.84)
s ≈ 17.70 meters (rounded to 2 decimal places)
Therefore, the braking distance required for the bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop is approximately 17.70 meters. Thus, the correct answer is between 17.50 and 17.90 meters.
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What is the braking distance (in meters, round off to 2 decimal places) required for a bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop? Assume coefficient of longitudinal friction as 0.30 and gradient of road as +5%.a)17.50b)17.90Correct answer is between '17.50,17.90'. Can you explain this answer?
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What is the braking distance (in meters, round off to 2 decimal places) required for a bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop? Assume coefficient of longitudinal friction as 0.30 and gradient of road as +5%.a)17.50b)17.90Correct answer is between '17.50,17.90'. 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 What is the braking distance (in meters, round off to 2 decimal places) required for a bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop? Assume coefficient of longitudinal friction as 0.30 and gradient of road as +5%.a)17.50b)17.90Correct answer is between '17.50,17.90'. 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 What is the braking distance (in meters, round off to 2 decimal places) required for a bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop? Assume coefficient of longitudinal friction as 0.30 and gradient of road as +5%.a)17.50b)17.90Correct answer is between '17.50,17.90'. Can you explain this answer?.
What is the braking distance (in meters, round off to 2 decimal places) required for a bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop? Assume coefficient of longitudinal friction as 0.30 and gradient of road as +5%.a)17.50b)17.90Correct answer is between '17.50,17.90'. 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 What is the braking distance (in meters, round off to 2 decimal places) required for a bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop? Assume coefficient of longitudinal friction as 0.30 and gradient of road as +5%.a)17.50b)17.90Correct answer is between '17.50,17.90'. 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 What is the braking distance (in meters, round off to 2 decimal places) required for a bus to slow down from 40 km/hr to 5 km/hr as it approaches a bus stop? Assume coefficient of longitudinal friction as 0.30 and gradient of road as +5%.a)17.50b)17.90Correct answer is between '17.50,17.90'. Can you explain this answer?.
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