JEE Exam  >  JEE Questions  >  A stone falls freely from rest and the total ... Start Learning for Free
A stone falls 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 three seconds of its motion. The stone remains in the air for
  • a)
    6 s
  • b)
    5 s
  • c)
    7 s
  • d)
    4 s
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A stone falls freely from rest and the total distance covered by it in...
u = 0
Free Test
Community Answer
A stone falls freely from rest and the total distance covered by it in...
Understanding the Problem
The stone falls freely from rest under the influence of gravity. We need to find the total time it remains in the air, given that the distance covered in the last second of its motion equals the distance covered in the first three seconds.

Key Concepts
- The distance covered by a freely falling object can be calculated using the formula:
\[ d = \frac{1}{2} g t^2 \]
where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)) and \( t \) is the time in seconds.
- The distance covered in the last second can be calculated as:
\[ d_{last} = \frac{1}{2} g t^2 - \frac{1}{2} g (t-1)^2 \]

Distance in First Three Seconds
- For the first three seconds:
\[ d_{3s} = \frac{1}{2} g (3)^2 = \frac{9g}{2} \]

Distance in Last Second
- For the last second:
\[ d_{last} = \frac{1}{2} g t^2 - \frac{1}{2} g (t-1)^2 \]
\[ = \frac{1}{2} g [t^2 - (t^2 - 2t + 1)] = \frac{1}{2} g (2t - 1) \]

Setting Distances Equal
- According to the problem, set \( d_{3s} = d_{last} \):
\[ \frac{9g}{2} = \frac{1}{2} g (2t - 1) \]
- Simplifying gives:
\[ 9 = 2t - 1 \]
\[ 2t = 10 \]
\[ t = 5 \, \text{s} \]

Conclusion
Thus, the stone remains in the air for **5 seconds**, confirming that the correct answer is option **B**.
Explore Courses for JEE exam
A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer?
Question Description
A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A stone falls 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 three seconds of its motion. The stone remains in the air fora)6 sb)5 sc)7 sd)4 sCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev