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A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?
Verified Answer
A stone is falling freely from rest and the total distance covered by ...
The distance travelled by the stone in the nth second is given by,
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5th second is the last second. So, the stone will remain in air for 5 seconds.
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A stone is falling freely from rest and the total distance covered by ...
The Problem
A stone is falling freely from rest, and we need to determine how long it remains in the air. We are given that the distance covered by the stone in the last second of its motion is equal to the distance covered in the first 3 seconds.
Analysis
Let's break down the problem and analyze it step by step.
1. Initial Motion
- The stone is falling freely from rest, which means it starts from rest and falls under the influence of gravity.
- We can apply the equation of motion:
- Distance covered, s = ut + 0.5 * a * t^2, where u is initial velocity, a is acceleration, and t is time.
- Since the stone starts from rest, the initial velocity (u) is 0.
2. First 3 Seconds
- We are given that the distance covered in the first 3 seconds is equal to the distance covered in the last second.
- Let's represent the distance covered in the first 3 seconds as s1 and the distance covered in the last second as s2.
- According to the given condition, s1 = s2.
3. Last Second of Motion
- Let's consider the last second of motion, from t = 2s to t = 3s.
- As per the given condition, the distance covered in this one-second interval is equal to the distance covered in the first 3 seconds.
- We can represent this distance as s2 = s1.
4. Calculating Distance Covered
- To calculate the distance covered in the first 3 seconds, we substitute t = 3s in the equation of motion.
- s1 = 0 + 0.5 * a * (3^2) = 4.5a.
- Similarly, for the last second, s2 = 0 + 0.5 * a * (1^2) = 0.5a.
5. Equating Distances
- As per the given condition, s1 = s2.
- 4.5a = 0.5a.
- Dividing both sides by a gives us 4.5 = 0.5.
- This is not possible unless a = 0.
- Therefore, the acceleration (a) must be zero.
6. Duration of Motion
- If the acceleration is zero, it means the stone is not experiencing any external force and is moving with a constant velocity.
- The stone will continue to move at this constant velocity until it hits the ground.
- Since there is no acceleration, the stone will remain in the air indefinitely.
Conclusion
In this problem, we found that the stone remains in the air indefinitely. This is because the distance covered in the first 3 seconds is equal to the distance covered in the last second, which is only possible when the acceleration is zero. Therefore, the stone continues to move with a constant velocity until it hits the ground.
A stone is falling freely from rest, and we need to determine how long it remains in the air. We are given that the distance covered by the stone in the last second of its motion is equal to the distance covered in the first 3 seconds.
Analysis
Let's break down the problem and analyze it step by step.
1. Initial Motion
- The stone is falling freely from rest, which means it starts from rest and falls under the influence of gravity.
- We can apply the equation of motion:
- Distance covered, s = ut + 0.5 * a * t^2, where u is initial velocity, a is acceleration, and t is time.
- Since the stone starts from rest, the initial velocity (u) is 0.
2. First 3 Seconds
- We are given that the distance covered in the first 3 seconds is equal to the distance covered in the last second.
- Let's represent the distance covered in the first 3 seconds as s1 and the distance covered in the last second as s2.
- According to the given condition, s1 = s2.
3. Last Second of Motion
- Let's consider the last second of motion, from t = 2s to t = 3s.
- As per the given condition, the distance covered in this one-second interval is equal to the distance covered in the first 3 seconds.
- We can represent this distance as s2 = s1.
4. Calculating Distance Covered
- To calculate the distance covered in the first 3 seconds, we substitute t = 3s in the equation of motion.
- s1 = 0 + 0.5 * a * (3^2) = 4.5a.
- Similarly, for the last second, s2 = 0 + 0.5 * a * (1^2) = 0.5a.
5. Equating Distances
- As per the given condition, s1 = s2.
- 4.5a = 0.5a.
- Dividing both sides by a gives us 4.5 = 0.5.
- This is not possible unless a = 0.
- Therefore, the acceleration (a) must be zero.
6. Duration of Motion
- If the acceleration is zero, it means the stone is not experiencing any external force and is moving with a constant velocity.
- The stone will continue to move at this constant velocity until it hits the ground.
- Since there is no acceleration, the stone will remain in the air indefinitely.
Conclusion
In this problem, we found that the stone remains in the air indefinitely. This is because the distance covered in the first 3 seconds is equal to the distance covered in the last second, which is only possible when the acceleration is zero. Therefore, the stone continues to move with a constant velocity until it hits the ground.
Community Answer
A stone is falling freely from rest and the total distance covered by ...
6 seconds
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A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?
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A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?.
A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?.
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