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A body covers a distance of 4 m in 3rd second and 12 m in 5th second. If the motion is uniformly accelerated, how far will it travel in the next 3 seconds?
- a)10 m
- b)30 m
- c)40 m
- d)60 m
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A body covers a distance of 4 m in 3rd second and 12 m in 5th second. ...
On solving, u = −6ms−1, a = 4ms−2
Distance travelled in next 3 seconds = S8 − S5
Most Upvoted Answer
A body covers a distance of 4 m in 3rd second and 12 m in 5th second. ...
**Given Data:**
- Distance covered in the 3rd second = 4 m
- Distance covered in the 5th second = 12 m
**To Find:**
- Distance covered in the next 3 seconds
**Assumption:**
- The motion is uniformly accelerated.
**Explanation:**
The motion is uniformly accelerated, which means the acceleration is constant throughout the motion. Let's denote the acceleration as 'a' and the initial velocity as 'u'.
Using the equations of motion, we can relate the distance, time, initial velocity, and acceleration:
- Distance covered in the n-th second = (u + (n - 1)a) * (n - 1)
Using the given data:
- Distance covered in the 3rd second = (u + 2a) * 2 = 4
- Distance covered in the 5th second = (u + 4a) * 4 = 12
Solving these equations, we can find the values of 'u' and 'a'.
- 2u + 4a = 4 ----(1)
- 4u + 16a = 12 ----(2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get:
- 4u + 16a - 4u - 8a = 12 - 8
- 8a = 4
- a = 0.5 m/s²
Substituting the value of 'a' in equation (1), we get:
- 2u + 4(0.5) = 4
- 2u + 2 = 4
- 2u = 4 - 2
- 2u = 2
- u = 1 m/s
Now, we have the values of 'u' and 'a'. Let's find the distance covered in the next 3 seconds.
- Distance covered in the 6th second = (u + 5a) * 5 = (1 + 5(0.5)) * 5 = 15 m
- Distance covered in the 7th second = (u + 6a) * 6 = (1 + 6(0.5)) * 6 = 21 m
- Distance covered in the 8th second = (u + 7a) * 7 = (1 + 7(0.5)) * 7 = 28 m
Therefore, the distance covered in the next 3 seconds is 15 m + 21 m + 28 m = 64 m.
Hence, the correct answer is option 'D' - 60 m.
- Distance covered in the 3rd second = 4 m
- Distance covered in the 5th second = 12 m
**To Find:**
- Distance covered in the next 3 seconds
**Assumption:**
- The motion is uniformly accelerated.
**Explanation:**
The motion is uniformly accelerated, which means the acceleration is constant throughout the motion. Let's denote the acceleration as 'a' and the initial velocity as 'u'.
Using the equations of motion, we can relate the distance, time, initial velocity, and acceleration:
- Distance covered in the n-th second = (u + (n - 1)a) * (n - 1)
Using the given data:
- Distance covered in the 3rd second = (u + 2a) * 2 = 4
- Distance covered in the 5th second = (u + 4a) * 4 = 12
Solving these equations, we can find the values of 'u' and 'a'.
- 2u + 4a = 4 ----(1)
- 4u + 16a = 12 ----(2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get:
- 4u + 16a - 4u - 8a = 12 - 8
- 8a = 4
- a = 0.5 m/s²
Substituting the value of 'a' in equation (1), we get:
- 2u + 4(0.5) = 4
- 2u + 2 = 4
- 2u = 4 - 2
- 2u = 2
- u = 1 m/s
Now, we have the values of 'u' and 'a'. Let's find the distance covered in the next 3 seconds.
- Distance covered in the 6th second = (u + 5a) * 5 = (1 + 5(0.5)) * 5 = 15 m
- Distance covered in the 7th second = (u + 6a) * 6 = (1 + 6(0.5)) * 6 = 21 m
- Distance covered in the 8th second = (u + 7a) * 7 = (1 + 7(0.5)) * 7 = 28 m
Therefore, the distance covered in the next 3 seconds is 15 m + 21 m + 28 m = 64 m.
Hence, the correct answer is option 'D' - 60 m.
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A body covers a distance of 4 m in 3rd second and 12 m in 5th second. If the motion is uniformly accelerated, how far will it travel in the next 3 seconds?a)10 mb)30 mc)40 md)60 mCorrect answer is option 'D'. Can you explain this answer?
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A body covers a distance of 4 m in 3rd second and 12 m in 5th second. If the motion is uniformly accelerated, how far will it travel in the next 3 seconds?a)10 mb)30 mc)40 md)60 mCorrect answer is option 'D'. 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 A body covers a distance of 4 m in 3rd second and 12 m in 5th second. If the motion is uniformly accelerated, how far will it travel in the next 3 seconds?a)10 mb)30 mc)40 md)60 mCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body covers a distance of 4 m in 3rd second and 12 m in 5th second. If the motion is uniformly accelerated, how far will it travel in the next 3 seconds?a)10 mb)30 mc)40 md)60 mCorrect answer is option 'D'. Can you explain this answer?.
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