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A boy is x distance behind the car when the car starts accelerating from rest with an acceleration a0. With what minimum constant velocity should the boy start running to catch the car? (1) √a0x (2) √3a0x (3) √2a0x (4) √a0x?
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A boy is x distance behind the car when the car starts accelerating fr...
Solution:
To catch the car, the boy has to cover the same distance as the car and should reach the same velocity as the car.
Let's assume the minimum velocity of the boy to catch the car as v.
Initial velocity of the car, u = 0
Final velocity of the car, v0 = ?
Acceleration of the car, a0 = given
From the equations of motion, we know that:
v0^2 = u^2 + 2a0x ------(1)
where x is the distance between the car and the boy.
Now, let's consider the velocity of the boy when he catches the car.
The time taken by the car to travel a distance x at an acceleration of a0 is given by:
t = sqrt(2x/a0)
In this time, the boy has to cover the same distance x to catch the car.
Therefore, the velocity of the boy is given by:
v = x/t = x/sqrt(2x/a0) = sqrt(2a0x)
Hence, the minimum constant velocity at which the boy should start running to catch the car is sqrt(2a0x).
Therefore, the correct option is (3) sqrt(2a0x).
To catch the car, the boy has to cover the same distance as the car and should reach the same velocity as the car.
Let's assume the minimum velocity of the boy to catch the car as v.
Initial velocity of the car, u = 0
Final velocity of the car, v0 = ?
Acceleration of the car, a0 = given
From the equations of motion, we know that:
v0^2 = u^2 + 2a0x ------(1)
where x is the distance between the car and the boy.
Now, let's consider the velocity of the boy when he catches the car.
The time taken by the car to travel a distance x at an acceleration of a0 is given by:
t = sqrt(2x/a0)
In this time, the boy has to cover the same distance x to catch the car.
Therefore, the velocity of the boy is given by:
v = x/t = x/sqrt(2x/a0) = sqrt(2a0x)
Hence, the minimum constant velocity at which the boy should start running to catch the car is sqrt(2a0x).
Therefore, the correct option is (3) sqrt(2a0x).
Community Answer
A boy is x distance behind the car when the car starts accelerating fr...
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A boy is x distance behind the car when the car starts accelerating from rest with an acceleration a0. With what minimum constant velocity should the boy start running to catch the car? (1) √a0x (2) √3a0x (3) √2a0x (4) √a0x?
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A boy is x distance behind the car when the car starts accelerating from rest with an acceleration a0. With what minimum constant velocity should the boy start running to catch the car? (1) √a0x (2) √3a0x (3) √2a0x (4) √a0x? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A boy is x distance behind the car when the car starts accelerating from rest with an acceleration a0. With what minimum constant velocity should the boy start running to catch the car? (1) √a0x (2) √3a0x (3) √2a0x (4) √a0x? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy is x distance behind the car when the car starts accelerating from rest with an acceleration a0. With what minimum constant velocity should the boy start running to catch the car? (1) √a0x (2) √3a0x (3) √2a0x (4) √a0x?.
A boy is x distance behind the car when the car starts accelerating from rest with an acceleration a0. With what minimum constant velocity should the boy start running to catch the car? (1) √a0x (2) √3a0x (3) √2a0x (4) √a0x? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A boy is x distance behind the car when the car starts accelerating from rest with an acceleration a0. With what minimum constant velocity should the boy start running to catch the car? (1) √a0x (2) √3a0x (3) √2a0x (4) √a0x? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy is x distance behind the car when the car starts accelerating from rest with an acceleration a0. With what minimum constant velocity should the boy start running to catch the car? (1) √a0x (2) √3a0x (3) √2a0x (4) √a0x?.
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