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A car is moving towards check Post with velocity 54 km per hour when car is at 400 metre from checkpost driver applies break which is cost of a solution of 0.3 metre per second find the distance of car from checkpost for 2 minutes after applying the brakes?
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A car is moving towards check Post with velocity 54 km per hour when c...
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A car is moving towards check Post with velocity 54 km per hour when c...
Initial Conditions:
- Initial velocity of the car = 54 km/h
- Distance of the car from the checkpost = 400 meters
- Deceleration (braking) of the car = 0.3 m/s²
Conversion:
To solve the problem, we need to convert the initial velocity from km/h to m/s as the deceleration is given in m/s².
1 km/h = 1000 m/3600 s = 5/18 m/s
So, the initial velocity of the car can be calculated as follows:
54 km/h * (5/18) m/s = 15 m/s
Calculating the Stopping Distance:
To find the distance of the car from the checkpost after 2 minutes, we need to determine the stopping distance first.
The stopping distance can be calculated using the equation:
v² = u² + 2as
where:
- v is the final velocity (0 m/s when the car stops)
- u is the initial velocity (15 m/s)
- a is the deceleration (-0.3 m/s², as it opposes the motion)
- s is the stopping distance (which we need to find)
Plugging in the values into the equation:
0² = 15² + 2 * (-0.3) * s
0 = 225 - 0.6s
0.6s = 225
s = 225 / 0.6
s = 375 meters
Calculating the Distance after 2 minutes:
Now, we can calculate the distance of the car from the checkpost after 2 minutes (120 seconds).
The distance traveled by the car after applying the brakes can be calculated using the equation:
s = ut + (1/2)at²
where:
- s is the distance traveled
- u is the initial velocity (15 m/s)
- t is the time (120 seconds)
- a is the deceleration (-0.3 m/s²)
Plugging in the values into the equation:
s = 15 * 120 + (1/2) * (-0.3) * (120)²
s = 1800 - 2160
s = -360 meters
Explanation:
After applying the brakes, the car covers a distance of 375 meters to come to a complete stop. However, after 2 minutes, the car would have traveled in the opposite direction due to the deceleration. Therefore, the distance from the checkpost after 2 minutes would be -360 meters, indicating that the car has moved back 360 meters from its initial position.
It's important to note that the negative sign indicates the direction of motion, which is opposite to the initial direction of the car.
Final Answer:
The distance of the car from the checkpost after 2 minutes of applying the brakes is -360 meters.
- Initial velocity of the car = 54 km/h
- Distance of the car from the checkpost = 400 meters
- Deceleration (braking) of the car = 0.3 m/s²
Conversion:
To solve the problem, we need to convert the initial velocity from km/h to m/s as the deceleration is given in m/s².
1 km/h = 1000 m/3600 s = 5/18 m/s
So, the initial velocity of the car can be calculated as follows:
54 km/h * (5/18) m/s = 15 m/s
Calculating the Stopping Distance:
To find the distance of the car from the checkpost after 2 minutes, we need to determine the stopping distance first.
The stopping distance can be calculated using the equation:
v² = u² + 2as
where:
- v is the final velocity (0 m/s when the car stops)
- u is the initial velocity (15 m/s)
- a is the deceleration (-0.3 m/s², as it opposes the motion)
- s is the stopping distance (which we need to find)
Plugging in the values into the equation:
0² = 15² + 2 * (-0.3) * s
0 = 225 - 0.6s
0.6s = 225
s = 225 / 0.6
s = 375 meters
Calculating the Distance after 2 minutes:
Now, we can calculate the distance of the car from the checkpost after 2 minutes (120 seconds).
The distance traveled by the car after applying the brakes can be calculated using the equation:
s = ut + (1/2)at²
where:
- s is the distance traveled
- u is the initial velocity (15 m/s)
- t is the time (120 seconds)
- a is the deceleration (-0.3 m/s²)
Plugging in the values into the equation:
s = 15 * 120 + (1/2) * (-0.3) * (120)²
s = 1800 - 2160
s = -360 meters
Explanation:
After applying the brakes, the car covers a distance of 375 meters to come to a complete stop. However, after 2 minutes, the car would have traveled in the opposite direction due to the deceleration. Therefore, the distance from the checkpost after 2 minutes would be -360 meters, indicating that the car has moved back 360 meters from its initial position.
It's important to note that the negative sign indicates the direction of motion, which is opposite to the initial direction of the car.
Final Answer:
The distance of the car from the checkpost after 2 minutes of applying the brakes is -360 meters.
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A car is moving towards check Post with velocity 54 km per hour when car is at 400 metre from checkpost driver applies break which is cost of a solution of 0.3 metre per second find the distance of car from checkpost for 2 minutes after applying the brakes?
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A car is moving towards check Post with velocity 54 km per hour when car is at 400 metre from checkpost driver applies break which is cost of a solution of 0.3 metre per second find the distance of car from checkpost for 2 minutes after applying the brakes? 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 car is moving towards check Post with velocity 54 km per hour when car is at 400 metre from checkpost driver applies break which is cost of a solution of 0.3 metre per second find the distance of car from checkpost for 2 minutes after applying the brakes? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car is moving towards check Post with velocity 54 km per hour when car is at 400 metre from checkpost driver applies break which is cost of a solution of 0.3 metre per second find the distance of car from checkpost for 2 minutes after applying the brakes?.
A car is moving towards check Post with velocity 54 km per hour when car is at 400 metre from checkpost driver applies break which is cost of a solution of 0.3 metre per second find the distance of car from checkpost for 2 minutes after applying the brakes? 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 car is moving towards check Post with velocity 54 km per hour when car is at 400 metre from checkpost driver applies break which is cost of a solution of 0.3 metre per second find the distance of car from checkpost for 2 minutes after applying the brakes? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car is moving towards check Post with velocity 54 km per hour when car is at 400 metre from checkpost driver applies break which is cost of a solution of 0.3 metre per second find the distance of car from checkpost for 2 minutes after applying the brakes?.
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