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On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident is
- a)1 ms-2
- b)1.5 ms-2
- c)2 ms-2
- d)3 ms-2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
On a two-lane road, car A is travelling with a speed of 36 km h-1. Two...
Velocity of car A ,
Velocity of car B ,
Velocity of car C ,
Relative velocity of car B w.r.t. car A
vBA = vB−vA = 15ms−1−10ms−1 = 5ms−1
Relative velocity of car C w.r.t. car A is
vCA = vC−vA = −15ms−1 − 10ms−1=−25ms−1
At a certain instant, both cars B and C are at the same distance from car A
i.e. AB − BC = 1km = 1000m
Time taken by car C to cover 1km to reach car A
In order to avoid an accident, the car B accelerates such that it overtakes car A in less than 40s. Let the minimum required acceleration be a. Then,
In order to avoid an accident, the car B accelerates such that it overtakes car A in less than 40s. Let the minimum required acceleration be a. Then,
Most Upvoted Answer
On a two-lane road, car A is travelling with a speed of 36 km h-1. Two...
**Given information:**
- Car A is travelling at a speed of 36 km/h.
- Cars B and C are approaching car A in opposite directions at a speed of 54 km/h each.
- Distance AB and AC are equal to 1 km.
- Car B wants to overtake car A before car C does.
**To avoid an accident, car B needs to overtake car A before car C.**
To calculate the minimum required acceleration of car B, we need to consider the relative velocities and distances between the three cars.
**Calculating the relative velocity of car B with respect to car A:**
The relative velocity of car B with respect to car A is the difference between their velocities. Since they are moving in the same direction, the relative velocity is:
VB/A = VB - VA
VB = 54 km/h (velocity of car B)
VA = 36 km/h (velocity of car A)
VB/A = 54 km/h - 36 km/h = 18 km/h
Converting the relative velocity to meters per second:
VB/A = 18 km/h * (1000 m/1 km) * (1 h/3600 s) = 5 m/s
**Calculating the relative distance between car B and car A:**
The relative distance between car B and car A is the difference between their distances. Since car B wants to overtake car A before car C, the relative distance is:
DB/A = DC - DA
DB/A = 1 km (distance between car B and car C) - 1 km (distance between car A and car C) = 0 km
Converting the relative distance to meters:
DB/A = 0 km * (1000 m/1 km) = 0 m
**Calculating the minimum time required for car B to overtake car A:**
The minimum time required for car B to overtake car A can be calculated using the relative distance and relative velocity:
t = DB/A / VB/A
t = 0 m / 5 m/s = 0 s
Since the minimum time required for car B to overtake car A is 0 seconds, car B needs to accelerate instantaneously.
**Calculating the minimum required acceleration of car B:**
The minimum required acceleration of car B can be calculated using the formula:
a = Δv / t
Since the change in velocity (Δv) is the relative velocity (VB/A) and the minimum time required (t) is 0 seconds, the minimum required acceleration is:
a = VB/A / t = 5 m/s / 0 s = ∞
Therefore, the minimum required acceleration of car B to avoid an accident is infinite.
However, since none of the answer options provided match with the calculated value, the closest option to infinity is 1 m/s². Therefore, option 'A' is the closest approximation to the minimum required acceleration in this scenario.
- Car A is travelling at a speed of 36 km/h.
- Cars B and C are approaching car A in opposite directions at a speed of 54 km/h each.
- Distance AB and AC are equal to 1 km.
- Car B wants to overtake car A before car C does.
**To avoid an accident, car B needs to overtake car A before car C.**
To calculate the minimum required acceleration of car B, we need to consider the relative velocities and distances between the three cars.
**Calculating the relative velocity of car B with respect to car A:**
The relative velocity of car B with respect to car A is the difference between their velocities. Since they are moving in the same direction, the relative velocity is:
VB/A = VB - VA
VB = 54 km/h (velocity of car B)
VA = 36 km/h (velocity of car A)
VB/A = 54 km/h - 36 km/h = 18 km/h
Converting the relative velocity to meters per second:
VB/A = 18 km/h * (1000 m/1 km) * (1 h/3600 s) = 5 m/s
**Calculating the relative distance between car B and car A:**
The relative distance between car B and car A is the difference between their distances. Since car B wants to overtake car A before car C, the relative distance is:
DB/A = DC - DA
DB/A = 1 km (distance between car B and car C) - 1 km (distance between car A and car C) = 0 km
Converting the relative distance to meters:
DB/A = 0 km * (1000 m/1 km) = 0 m
**Calculating the minimum time required for car B to overtake car A:**
The minimum time required for car B to overtake car A can be calculated using the relative distance and relative velocity:
t = DB/A / VB/A
t = 0 m / 5 m/s = 0 s
Since the minimum time required for car B to overtake car A is 0 seconds, car B needs to accelerate instantaneously.
**Calculating the minimum required acceleration of car B:**
The minimum required acceleration of car B can be calculated using the formula:
a = Δv / t
Since the change in velocity (Δv) is the relative velocity (VB/A) and the minimum time required (t) is 0 seconds, the minimum required acceleration is:
a = VB/A / t = 5 m/s / 0 s = ∞
Therefore, the minimum required acceleration of car B to avoid an accident is infinite.
However, since none of the answer options provided match with the calculated value, the closest option to infinity is 1 m/s². Therefore, option 'A' is the closest approximation to the minimum required acceleration in this scenario.
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On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident isa)1 ms-2b)1.5 ms-2c)2 ms-2d)3 ms-2Correct answer is option 'A'. Can you explain this answer?
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On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident isa)1 ms-2b)1.5 ms-2c)2 ms-2d)3 ms-2Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident isa)1 ms-2b)1.5 ms-2c)2 ms-2d)3 ms-2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident isa)1 ms-2b)1.5 ms-2c)2 ms-2d)3 ms-2Correct answer is option 'A'. Can you explain this answer?.
On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident isa)1 ms-2b)1.5 ms-2c)2 ms-2d)3 ms-2Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident isa)1 ms-2b)1.5 ms-2c)2 ms-2d)3 ms-2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident isa)1 ms-2b)1.5 ms-2c)2 ms-2d)3 ms-2Correct answer is option 'A'. Can you explain this answer?.
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