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A man is s= 9 m behind the door of a train when it starts moving with a = 2m/s² . The man runs full speed .How far does he have to run to and after how much time does he get into train ? What is his full speed ?
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A man is s= 9 m behind the door of a train when it starts moving with ...
Suppose, the man catches the train after that train moves a distance ‘x’.
So, distance moved by the man is, S = 9+x
Let, u be the speed of the man with which he runs to catch the train. If ‘t’ is the time after which he catches then,
S = ut
=> 9+x = ut ………………..(1)
Now, the train starts from rest with an acceleration 2 m/s2. So, it travels a distance ‘x’ before the man boards it in time ‘t’.
x = 0 + 1/2 X 2 X t2
=> x = t2 …………………….(2)
Since, the man is just able to get into the train, it means the man catches the train when the speed of the train becomes ‘u’. (for speed of the train more than ‘u’ the man will miss it)
Using first kinematics equation,
u = 0 + 2 X t
=> u = 2t ………………….(3)
(1) & (3) => 9+x = (2t)t
=> 9+x = 2t2
=> 9+x = 2x [Using (2)]
=> x = 9 m
(2) => x = t2
=> t = 3 s
(3) => u = 2t
=> u = 6 m/s
So, the speed with which the man has to run to catch the train is 6 m/s.
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A man is s= 9 m behind the door of a train when it starts moving with ...
The problem states that a man is standing 9 meters behind the door of a train when it starts moving. The train has an acceleration of 2 m/s². The man decides to run at full speed to catch the train. We need to determine how far the man has to run to get onto the train and how long it takes him to do so. Additionally, we need to find out what his full speed is.
Let's break down the problem into different components and solve them step by step.
1. Initial Position:
- The man starts 9 meters behind the door of the train.
- We'll consider this position as the origin, so the initial position of the train would be 0 meters.
2. Acceleration:
- The train has an acceleration of 2 m/s².
- This means that its velocity increases by 2 m/s every second.
3. Distance to Cover:
- The man needs to reach the door of the train, which is at position 0 meters.
- Since he starts 9 meters behind the door, he needs to cover a distance of 9 meters to reach the door.
4. Time to Reach the Train:
- To find the time it takes for the man to reach the train, we can use the equation:
- s = ut + (1/2)at², where s is the distance, u is the initial velocity, t is the time, and a is the acceleration.
- Since the man starts from rest, his initial velocity (u) is 0.
- The distance (s) he needs to cover is 9 meters, and the acceleration (a) is 2 m/s².
- Plugging the values into the equation, we get:
- 9 = 0 + (1/2)(2)(t²)
- 9 = t²
- Taking the square root of both sides, we find that t = 3 seconds.
5. Full Speed of the Man:
- To find the full speed of the man, we can use the equation:
- v = u + at, where v is the final velocity, u is the initial velocity, t is the time, and a is the acceleration.
- Since the man starts from rest, his initial velocity (u) is 0.
- The final velocity (v) would be his full speed.
- The acceleration (a) is 2 m/s², and the time (t) is 3 seconds.
- Plugging the values into the equation, we get:
- v = 0 + (2)(3)
- v = 6 m/s
Therefore, the man needs to run a distance of 9 meters to reach the moving train, and it takes him 3 seconds to do so. His full speed is 6 m/s.
Let's break down the problem into different components and solve them step by step.
1. Initial Position:
- The man starts 9 meters behind the door of the train.
- We'll consider this position as the origin, so the initial position of the train would be 0 meters.
2. Acceleration:
- The train has an acceleration of 2 m/s².
- This means that its velocity increases by 2 m/s every second.
3. Distance to Cover:
- The man needs to reach the door of the train, which is at position 0 meters.
- Since he starts 9 meters behind the door, he needs to cover a distance of 9 meters to reach the door.
4. Time to Reach the Train:
- To find the time it takes for the man to reach the train, we can use the equation:
- s = ut + (1/2)at², where s is the distance, u is the initial velocity, t is the time, and a is the acceleration.
- Since the man starts from rest, his initial velocity (u) is 0.
- The distance (s) he needs to cover is 9 meters, and the acceleration (a) is 2 m/s².
- Plugging the values into the equation, we get:
- 9 = 0 + (1/2)(2)(t²)
- 9 = t²
- Taking the square root of both sides, we find that t = 3 seconds.
5. Full Speed of the Man:
- To find the full speed of the man, we can use the equation:
- v = u + at, where v is the final velocity, u is the initial velocity, t is the time, and a is the acceleration.
- Since the man starts from rest, his initial velocity (u) is 0.
- The final velocity (v) would be his full speed.
- The acceleration (a) is 2 m/s², and the time (t) is 3 seconds.
- Plugging the values into the equation, we get:
- v = 0 + (2)(3)
- v = 6 m/s
Therefore, the man needs to run a distance of 9 meters to reach the moving train, and it takes him 3 seconds to do so. His full speed is 6 m/s.
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A man is s= 9 m behind the door of a train when it starts moving with a = 2m/s² . The man runs full speed .How far does he have to run to and after how much time does he get into train ? What is his full speed ?
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A man is s= 9 m behind the door of a train when it starts moving with a = 2m/s² . The man runs full speed .How far does he have to run to and after how much time does he get into train ? What is his full speed ? 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 A man is s= 9 m behind the door of a train when it starts moving with a = 2m/s² . The man runs full speed .How far does he have to run to and after how much time does he get into train ? What is his full speed ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is s= 9 m behind the door of a train when it starts moving with a = 2m/s² . The man runs full speed .How far does he have to run to and after how much time does he get into train ? What is his full speed ?.
A man is s= 9 m behind the door of a train when it starts moving with a = 2m/s² . The man runs full speed .How far does he have to run to and after how much time does he get into train ? What is his full speed ? 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 A man is s= 9 m behind the door of a train when it starts moving with a = 2m/s² . The man runs full speed .How far does he have to run to and after how much time does he get into train ? What is his full speed ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is s= 9 m behind the door of a train when it starts moving with a = 2m/s² . The man runs full speed .How far does he have to run to and after how much time does he get into train ? What is his full speed ?.
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