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A car starting from rest and moving with uniform acceleration on a straight road travels for sometime such that the paths described by in the last second and in the penultimate second of it's motion are in ratio 4:3 respectively. Calculate the total time taken by the car?
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A car starting from rest and moving with uniform acceleration on a str...
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A car starting from rest and moving with uniform acceleration on a str...
Given information:
- The paths described by the car in the last second and the penultimate second are in the ratio of 4:3.
- The car starts from rest and moves with uniform acceleration on a straight road.
Assumptions:
- Let the time taken by the car to cover the last second of motion be 't1' seconds.
- Let the time taken by the car to cover the penultimate second of motion be 't2' seconds.
- Let the uniform acceleration of the car be 'a' m/s^2.
Calculating distances:
- In the last second, the car covers a distance of 4d, where 'd' is the distance covered in the last second.
- In the penultimate second, the car covers a distance of 3d.
Using kinematic equations:
- The distance covered by the car in time 't' seconds with uniform acceleration 'a' starting from rest can be calculated using the equation:
- s = ut + 1/2 * a * t^2,
where 's' is the distance, 'u' is the initial velocity (which is 0 in this case), 'a' is the acceleration, and 't' is the time.
Calculating distances covered in the last second and penultimate second:
- In the last second, the distance covered can be calculated as:
- 4d = 0 + 1/2 * a * t1^2 (equation 1)
- In the penultimate second, the distance covered can be calculated as:
- 3d = 0 + 1/2 * a * t2^2 (equation 2)
Using the first equation to solve for time:
- Rearranging equation 1, we get:
- t1^2 = (8d)/a
Using the second equation to solve for time:
- Rearranging equation 2, we get:
- t2^2 = (6d)/a
Ratio of times:
- The ratio of times can be calculated as:
- t1/t2 = √((8d)/a) / √((6d)/a) = √(8/6) = √(4/3) = 2/√3
Calculating the total time:
- The total time taken by the car can be calculated as the sum of the times taken in the last second and the penultimate second.
- Total time = t1 + t2
Substituting the values:
- Since t1/t2 = 2/√3, we can write t1 = (2/√3) * t2.
- Substituting this value in the equation for total time:
- Total time = (2/√3) * t2 + t2 = (2 + √3) * t2
Conclusion:
- The total time taken by the car is (2 + √3) times the
- The paths described by the car in the last second and the penultimate second are in the ratio of 4:3.
- The car starts from rest and moves with uniform acceleration on a straight road.
Assumptions:
- Let the time taken by the car to cover the last second of motion be 't1' seconds.
- Let the time taken by the car to cover the penultimate second of motion be 't2' seconds.
- Let the uniform acceleration of the car be 'a' m/s^2.
Calculating distances:
- In the last second, the car covers a distance of 4d, where 'd' is the distance covered in the last second.
- In the penultimate second, the car covers a distance of 3d.
Using kinematic equations:
- The distance covered by the car in time 't' seconds with uniform acceleration 'a' starting from rest can be calculated using the equation:
- s = ut + 1/2 * a * t^2,
where 's' is the distance, 'u' is the initial velocity (which is 0 in this case), 'a' is the acceleration, and 't' is the time.
Calculating distances covered in the last second and penultimate second:
- In the last second, the distance covered can be calculated as:
- 4d = 0 + 1/2 * a * t1^2 (equation 1)
- In the penultimate second, the distance covered can be calculated as:
- 3d = 0 + 1/2 * a * t2^2 (equation 2)
Using the first equation to solve for time:
- Rearranging equation 1, we get:
- t1^2 = (8d)/a
Using the second equation to solve for time:
- Rearranging equation 2, we get:
- t2^2 = (6d)/a
Ratio of times:
- The ratio of times can be calculated as:
- t1/t2 = √((8d)/a) / √((6d)/a) = √(8/6) = √(4/3) = 2/√3
Calculating the total time:
- The total time taken by the car can be calculated as the sum of the times taken in the last second and the penultimate second.
- Total time = t1 + t2
Substituting the values:
- Since t1/t2 = 2/√3, we can write t1 = (2/√3) * t2.
- Substituting this value in the equation for total time:
- Total time = (2/√3) * t2 + t2 = (2 + √3) * t2
Conclusion:
- The total time taken by the car is (2 + √3) times the
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A car starting from rest and moving with uniform acceleration on a str...
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A car starting from rest and moving with uniform acceleration on a straight road travels for sometime such that the paths described by in the last second and in the penultimate second of it's motion are in ratio 4:3 respectively. Calculate the total time taken by the car?
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A car starting from rest and moving with uniform acceleration on a straight road travels for sometime such that the paths described by in the last second and in the penultimate second of it's motion are in ratio 4:3 respectively. Calculate the total time taken by the car? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A car starting from rest and moving with uniform acceleration on a straight road travels for sometime such that the paths described by in the last second and in the penultimate second of it's motion are in ratio 4:3 respectively. Calculate the total time taken by the car? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car starting from rest and moving with uniform acceleration on a straight road travels for sometime such that the paths described by in the last second and in the penultimate second of it's motion are in ratio 4:3 respectively. Calculate the total time taken by the car?.
A car starting from rest and moving with uniform acceleration on a straight road travels for sometime such that the paths described by in the last second and in the penultimate second of it's motion are in ratio 4:3 respectively. Calculate the total time taken by the car? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A car starting from rest and moving with uniform acceleration on a straight road travels for sometime such that the paths described by in the last second and in the penultimate second of it's motion are in ratio 4:3 respectively. Calculate the total time taken by the car? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car starting from rest and moving with uniform acceleration on a straight road travels for sometime such that the paths described by in the last second and in the penultimate second of it's motion are in ratio 4:3 respectively. Calculate the total time taken by the car?.
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