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Robbers in a car travelling at
20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake the car
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20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake the car
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Verified Answer
Robbers in a car travelling at 20m/s pass a policemen on a ...
The distance covered by the policeman in 12 sec
s = ut + 1/2 at2
= 0 x12 + 0.5 x3 x 12x12 = 216m
v = u + at = 0 + 12x3 = 36m/s
The distance covered by the robber in 12 sec
s = 20 x 12 = 240m
Suppose he over takes in 12 + t sec, in which he travels = 216 + 36 * t
r robbers will travel in the same time 20 * ( 12+t) m
216 + 36 t = 240 + 20 t
t = 24 / 16 = 1.5 s
Distance travelled by policeman in 12 + 1.5 = 13.5 s
= 216 + 36 x 1.5 = 270 m
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
Robbers in a car travelling at 20m/s pass a policemen on a ...
Given information:
- Initial speed of the car: 20 m/s
- Initial speed of the policeman: 0 m/s (rest)
- Acceleration of the policeman: 3 m/s²
- Time for which the policeman accelerates: 12 seconds
Analysis:
To find the distance covered by the policeman before he overtakes the car, we need to determine the time it takes for the policeman to catch up with the car and then calculate the distance using the formula for distance traveled during constant acceleration.
Step 1: Finding the time taken for the policeman to catch up with the car
- The car is initially ahead of the policeman by the distance it traveled during the 12 seconds of acceleration.
- The distance traveled by the car during this time can be calculated using the formula:
Distance = Initial velocity * Time + 0.5 * Acceleration * Time²
Distance = 20 m/s * 12 s + 0.5 * 0 (since the car travels at a constant velocity after passing the policeman) * (12 s)²
Distance = 240 m
- Therefore, the car is initially ahead of the policeman by 240 meters.
- The relative speed between the car and the policeman is the difference between their velocities. Since the policeman is chasing the car, the relative speed is 20 m/s.
- The time taken for the policeman to catch up with the car can be calculated using the formula:
Time = Distance / Relative speed
Time = 240 m / 20 m/s
Time = 12 s
Step 2: Finding the distance covered by the policeman
- The distance covered by the policeman during the 12 seconds of acceleration can be calculated using the formula:
Distance = Initial velocity * Time + 0.5 * Acceleration * Time²
Distance = 0 m/s * 12 s + 0.5 * 3 m/s² * (12 s)²
Distance = 216 m
- The distance covered by the policeman after the acceleration phase is the product of his constant velocity and the remaining time until he catches up with the car. The remaining time can be calculated as:
Remaining time = Total time - Acceleration time
Remaining time = 12 s - 12 s
Remaining time = 0 s
- Therefore, the distance covered by the policeman after the acceleration phase is:
Distance = Constant velocity * Remaining time
Distance = 20 m/s * 0 s
Distance = 0 m
Step 3: Calculating the total distance covered by the policeman
- The total distance covered by the policeman is the sum of the distances covered during the acceleration phase and after the acceleration phase.
Total distance = Distance during acceleration + Distance after acceleration
Total distance = 216 m + 0 m
Total distance = 216 m
Conclusion:
The policeman covers a distance of 216 meters before he overtakes the car.
- Initial speed of the car: 20 m/s
- Initial speed of the policeman: 0 m/s (rest)
- Acceleration of the policeman: 3 m/s²
- Time for which the policeman accelerates: 12 seconds
Analysis:
To find the distance covered by the policeman before he overtakes the car, we need to determine the time it takes for the policeman to catch up with the car and then calculate the distance using the formula for distance traveled during constant acceleration.
Step 1: Finding the time taken for the policeman to catch up with the car
- The car is initially ahead of the policeman by the distance it traveled during the 12 seconds of acceleration.
- The distance traveled by the car during this time can be calculated using the formula:
Distance = Initial velocity * Time + 0.5 * Acceleration * Time²
Distance = 20 m/s * 12 s + 0.5 * 0 (since the car travels at a constant velocity after passing the policeman) * (12 s)²
Distance = 240 m
- Therefore, the car is initially ahead of the policeman by 240 meters.
- The relative speed between the car and the policeman is the difference between their velocities. Since the policeman is chasing the car, the relative speed is 20 m/s.
- The time taken for the policeman to catch up with the car can be calculated using the formula:
Time = Distance / Relative speed
Time = 240 m / 20 m/s
Time = 12 s
Step 2: Finding the distance covered by the policeman
- The distance covered by the policeman during the 12 seconds of acceleration can be calculated using the formula:
Distance = Initial velocity * Time + 0.5 * Acceleration * Time²
Distance = 0 m/s * 12 s + 0.5 * 3 m/s² * (12 s)²
Distance = 216 m
- The distance covered by the policeman after the acceleration phase is the product of his constant velocity and the remaining time until he catches up with the car. The remaining time can be calculated as:
Remaining time = Total time - Acceleration time
Remaining time = 12 s - 12 s
Remaining time = 0 s
- Therefore, the distance covered by the policeman after the acceleration phase is:
Distance = Constant velocity * Remaining time
Distance = 20 m/s * 0 s
Distance = 0 m
Step 3: Calculating the total distance covered by the policeman
- The total distance covered by the policeman is the sum of the distances covered during the acceleration phase and after the acceleration phase.
Total distance = Distance during acceleration + Distance after acceleration
Total distance = 216 m + 0 m
Total distance = 216 m
Conclusion:
The policeman covers a distance of 216 meters before he overtakes the car.
Community Answer
Robbers in a car travelling at 20m/s pass a policemen on a ...
270 m
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Robbers in a car travelling at 20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake the car ?
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Robbers in a car travelling at 20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake 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 Robbers in a car travelling at 20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake the car ? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Robbers in a car travelling at 20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake the car ?.
Robbers in a car travelling at 20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake 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 Robbers in a car travelling at 20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake the car ? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Robbers in a car travelling at 20m/s pass a policemen on a motorcycle at rest. The policeman immediately starts chasing the robbers the robbers . The policeman accelerate at 3m /second square for 12 second and thereafter travels at a constant velocity . Calculate the distance covered by the policeman before he overtake the car ?.
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