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Two buses A and B are at positions 60 m and 160 m from the origin at time t=0. They start moving in the same direction simultaneously with uniform speed 54km/h and 36km/h. Determine the time and position at which A overtaken B?
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Two buses A and B are at positions 60 m and 160 m from the origin at t...
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Two buses A and B are at positions 60 m and 160 m from the origin at t...
Given information:
- Bus A is initially at a position of 60 m from the origin.
- Bus B is initially at a position of 160 m from the origin.
- Both buses start moving in the same direction simultaneously.
- The speed of Bus A is 54 km/h.
- The speed of Bus B is 36 km/h.
Approach:
To determine the time and position at which Bus A overtakes Bus B, we need to calculate the time it takes for Bus A to cover the distance between them. Since both buses are moving in the same direction, the relative speed between the two buses will be the difference in their speeds.
Calculating the relative speed:
Relative speed = Speed of A - Speed of B
Relative speed = (54 km/h) - (36 km/h)
Relative speed = 18 km/h
Converting relative speed to meters per second:
1 km/h = (1000 m) / (3600 s)
Relative speed = (18 km/h) * (1000 m) / (3600 s)
Relative speed = 5 m/s
Calculating the time it takes for Bus A to cover the distance:
Distance = Initial distance between the buses = 160 m - 60 m = 100 m
Time = Distance / Relative speed
Time = 100 m / 5 m/s
Time = 20 seconds
Calculating the position at which Bus A overtakes Bus B:
Position = Initial position of Bus B + Distance covered by Bus A
Position = 160 m + (20 s * 36 km/h)
Position = 160 m + (20 s * 10 m/s)
Position = 160 m + 200 m
Position = 360 m
Conclusion:
Bus A will overtake Bus B after 20 seconds at a position of 360 meters from the origin.
- Bus A is initially at a position of 60 m from the origin.
- Bus B is initially at a position of 160 m from the origin.
- Both buses start moving in the same direction simultaneously.
- The speed of Bus A is 54 km/h.
- The speed of Bus B is 36 km/h.
Approach:
To determine the time and position at which Bus A overtakes Bus B, we need to calculate the time it takes for Bus A to cover the distance between them. Since both buses are moving in the same direction, the relative speed between the two buses will be the difference in their speeds.
Calculating the relative speed:
Relative speed = Speed of A - Speed of B
Relative speed = (54 km/h) - (36 km/h)
Relative speed = 18 km/h
Converting relative speed to meters per second:
1 km/h = (1000 m) / (3600 s)
Relative speed = (18 km/h) * (1000 m) / (3600 s)
Relative speed = 5 m/s
Calculating the time it takes for Bus A to cover the distance:
Distance = Initial distance between the buses = 160 m - 60 m = 100 m
Time = Distance / Relative speed
Time = 100 m / 5 m/s
Time = 20 seconds
Calculating the position at which Bus A overtakes Bus B:
Position = Initial position of Bus B + Distance covered by Bus A
Position = 160 m + (20 s * 36 km/h)
Position = 160 m + (20 s * 10 m/s)
Position = 160 m + 200 m
Position = 360 m
Conclusion:
Bus A will overtake Bus B after 20 seconds at a position of 360 meters from the origin.
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Two buses A and B are at positions 60 m and 160 m from the origin at time t=0. They start moving in the same direction simultaneously with uniform speed 54km/h and 36km/h. Determine the time and position at which A overtaken B?
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Two buses A and B are at positions 60 m and 160 m from the origin at time t=0. They start moving in the same direction simultaneously with uniform speed 54km/h and 36km/h. Determine the time and position at which A overtaken B? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two buses A and B are at positions 60 m and 160 m from the origin at time t=0. They start moving in the same direction simultaneously with uniform speed 54km/h and 36km/h. Determine the time and position at which A overtaken B? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two buses A and B are at positions 60 m and 160 m from the origin at time t=0. They start moving in the same direction simultaneously with uniform speed 54km/h and 36km/h. Determine the time and position at which A overtaken B?.
Two buses A and B are at positions 60 m and 160 m from the origin at time t=0. They start moving in the same direction simultaneously with uniform speed 54km/h and 36km/h. Determine the time and position at which A overtaken B? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two buses A and B are at positions 60 m and 160 m from the origin at time t=0. They start moving in the same direction simultaneously with uniform speed 54km/h and 36km/h. Determine the time and position at which A overtaken B? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two buses A and B are at positions 60 m and 160 m from the origin at time t=0. They start moving in the same direction simultaneously with uniform speed 54km/h and 36km/h. Determine the time and position at which A overtaken B?.
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