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Student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms−2, the students starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:?
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Student is standing at a distance of 50 metre from the bus. As soon as...
Given data:
- Initial distance between student and bus, \( s_0 = 50 \, \text{m} \)
- Acceleration of the bus, \( a = 1 \, \text{ms}^{-2} \)
Analysis:
- The relative speed between the student and the bus should be equal to the speed of the bus for the student to catch the bus.
- The student is running towards the bus with a uniform velocity \( u \).
Approach:
- Calculate the time taken by the bus to cover the initial distance, \( s_0 \), using the equation of motion: \( s = ut + \frac{1}{2}at^2 \).
- Use the time calculated to determine the speed of the bus when the student starts running.
- Set up an equation for the relative speed between the student and the bus to find the minimum value of \( u \) required for the student to catch the bus.
Calculations:
1. Calculate time taken by the bus to cover initial distance:
\( s_0 = ut + \frac{1}{2}at^2 \)
\( 50 = 0 + \frac{1}{2} \times 1 \times t^2 \)
\( t^2 = 100 \)
\( t = 10 \, \text{s} \)
2. Calculate speed of the bus when the student starts running:
\( v_{bus} = u_{bus} + at \)
\( v_{bus} = 0 + 1 \times 10 \)
\( v_{bus} = 10 \, \text{ms}^{-1} \)
3. Set up equation for relative speed:
\( v_{rel} = v_{bus} - u \)
For the student to catch the bus, \( v_{rel} = 0 \).
\( 0 = 10 - u \)
\( u = 10 \, \text{ms}^{-1} \)
Conclusion:
The minimum value of \( u \) required for the student to catch the bus is \( 10 \, \text{ms}^{-1} \).
- Initial distance between student and bus, \( s_0 = 50 \, \text{m} \)
- Acceleration of the bus, \( a = 1 \, \text{ms}^{-2} \)
Analysis:
- The relative speed between the student and the bus should be equal to the speed of the bus for the student to catch the bus.
- The student is running towards the bus with a uniform velocity \( u \).
Approach:
- Calculate the time taken by the bus to cover the initial distance, \( s_0 \), using the equation of motion: \( s = ut + \frac{1}{2}at^2 \).
- Use the time calculated to determine the speed of the bus when the student starts running.
- Set up an equation for the relative speed between the student and the bus to find the minimum value of \( u \) required for the student to catch the bus.
Calculations:
1. Calculate time taken by the bus to cover initial distance:
\( s_0 = ut + \frac{1}{2}at^2 \)
\( 50 = 0 + \frac{1}{2} \times 1 \times t^2 \)
\( t^2 = 100 \)
\( t = 10 \, \text{s} \)
2. Calculate speed of the bus when the student starts running:
\( v_{bus} = u_{bus} + at \)
\( v_{bus} = 0 + 1 \times 10 \)
\( v_{bus} = 10 \, \text{ms}^{-1} \)
3. Set up equation for relative speed:
\( v_{rel} = v_{bus} - u \)
For the student to catch the bus, \( v_{rel} = 0 \).
\( 0 = 10 - u \)
\( u = 10 \, \text{ms}^{-1} \)
Conclusion:
The minimum value of \( u \) required for the student to catch the bus is \( 10 \, \text{ms}^{-1} \).
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Student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms−2, the students starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:?
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Student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms−2, the students starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms−2, the students starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms−2, the students starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:?.
Student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms−2, the students starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms−2, the students starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms−2, the students starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:?.
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