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A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.
Correct answer is '30'. Can you explain this answer?
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Verified Answer
A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consi...
Given: grade = +4%
V1 = 20 m/sec.
f = 0.46
g = 10 m/sec.
V1 = 10 m/sec.
We know,
⇒
V1 = 20 m/sec.
f = 0.46
g = 10 m/sec.
V1 = 10 m/sec.
We know,
⇒
Most Upvoted Answer
A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consi...
Calculation of Required Braking Distance
Given parameters:
Grade of road = 4%
Speed of vehicle = 20 m/s
Coefficient of rolling friction = 0.46
Acceleration due to gravity = 10 m/s^2
Final speed = 10 m/s
Step 1: Calculate the force acting on the vehicle due to gravity.
Force due to gravity = m * g * sin(θ)
where m = mass of the vehicle, g = acceleration due to gravity, and θ = grade of the road
Force due to gravity = m * 10 * sin(4)
Force due to gravity = 0.0698 * m (approx.)
Step 2: Calculate the force required to stop the vehicle.
Force required to stop the vehicle = m * a
where m = mass of the vehicle and a = deceleration
a = (v_f^2 - v_i^2) / (2 * d)
where v_f = final speed, v_i = initial speed, and d = braking distance
a = (10^2 - 20^2) / (2 * d)
a = -50 / d (approx.)
Force required to stop the vehicle = m * (-50 / d)
Force required to stop the vehicle = -0.46 * (0.0698 * m)
Force required to stop the vehicle = -0.0322 * m (approx.)
Step 3: Equate the force acting on the vehicle due to friction and the force required to stop the vehicle.
Force due to friction = Force required to stop the vehicle
m * g * 0.46 = -0.0322 * m
g * 0.46 = -0.0322
g = -0.07 m/s^2 (approx.)
Step 4: Calculate the braking distance.
a = (v_f^2 - v_i^2) / (2 * d)
-0.07 = (10^2 - 20^2) / (2 * d)
d = 30 m (approx.)
Therefore, the required braking distance along the horizontal is 30 meters (rounded off to the nearest integer).
Given parameters:
Grade of road = 4%
Speed of vehicle = 20 m/s
Coefficient of rolling friction = 0.46
Acceleration due to gravity = 10 m/s^2
Final speed = 10 m/s
Step 1: Calculate the force acting on the vehicle due to gravity.
Force due to gravity = m * g * sin(θ)
where m = mass of the vehicle, g = acceleration due to gravity, and θ = grade of the road
Force due to gravity = m * 10 * sin(4)
Force due to gravity = 0.0698 * m (approx.)
Step 2: Calculate the force required to stop the vehicle.
Force required to stop the vehicle = m * a
where m = mass of the vehicle and a = deceleration
a = (v_f^2 - v_i^2) / (2 * d)
where v_f = final speed, v_i = initial speed, and d = braking distance
a = (10^2 - 20^2) / (2 * d)
a = -50 / d (approx.)
Force required to stop the vehicle = m * (-50 / d)
Force required to stop the vehicle = -0.46 * (0.0698 * m)
Force required to stop the vehicle = -0.0322 * m (approx.)
Step 3: Equate the force acting on the vehicle due to friction and the force required to stop the vehicle.
Force due to friction = Force required to stop the vehicle
m * g * 0.46 = -0.0322 * m
g * 0.46 = -0.0322
g = -0.07 m/s^2 (approx.)
Step 4: Calculate the braking distance.
a = (v_f^2 - v_i^2) / (2 * d)
-0.07 = (10^2 - 20^2) / (2 * d)
d = 30 m (approx.)
Therefore, the required braking distance along the horizontal is 30 meters (rounded off to the nearest integer).
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A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. Can you explain this answer?
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A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. 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 is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. 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 is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. Can you explain this answer?.
A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. 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 is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. 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 is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. Can you explain this answer?.
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A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. Can you explain this answer?, a detailed solution for A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. Can you explain this answer? has been provided alongside types of A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s2. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.Correct answer is '30'. Can you explain this answer? theory, EduRev gives you an
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