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A body of mass 2 kg is moving along positive X-axis with a constant speed of 8 m/s. If a force of 20 N is acting on the body along the (-)ve X-axis then calculate the time when body will be at rest after applying the force and calculate the displacement covered by the body during this time interval.?
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A body of mass 2 kg is moving along positive X-axis with a constant sp...
Given Data
- Mass of the body (m) = 2 kg
- Initial velocity (u) = 8 m/s
- Force (F) = -20 N (acting in the negative X-axis)
Calculating Acceleration
Using Newton's second law, we can find the acceleration (a):
- Formula: \( F = m \cdot a \)
- Rearranging gives: \( a = \frac{F}{m} = \frac{-20 \, \text{N}}{2 \, \text{kg}} = -10 \, \text{m/s}^2 \)
This indicates that the body is decelerating at a rate of 10 m/s².
Calculating Time to Rest
To find the time (t) when the body comes to rest (final velocity \( v = 0 \)), we use the equation:
- Formula: \( v = u + a \cdot t \)
- Setting \( v = 0 \):
\( 0 = 8 \, \text{m/s} - 10 \, \text{m/s}^2 \cdot t \)
- Rearranging gives:
\( t = \frac{8 \, \text{m/s}}{10 \, \text{m/s}^2} = 0.8 \, \text{s} \)
Calculating Displacement
To calculate the displacement (s) during this time, we use the equation:
- Formula: \( s = u \cdot t + \frac{1}{2} a \cdot t^2 \)
- Substituting values:
\( s = 8 \, \text{m/s} \cdot 0.8 \, \text{s} + \frac{1}{2} \cdot (-10 \, \text{m/s}^2) \cdot (0.8 \, \text{s})^2 \)
- Calculating:
\( s = 6.4 \, \text{m} - 3.2 \, \text{m} = 3.2 \, \text{m} \)
Final Results
- Time to come to rest: 0.8 seconds
- Displacement covered: 3.2 meters
- Mass of the body (m) = 2 kg
- Initial velocity (u) = 8 m/s
- Force (F) = -20 N (acting in the negative X-axis)
Calculating Acceleration
Using Newton's second law, we can find the acceleration (a):
- Formula: \( F = m \cdot a \)
- Rearranging gives: \( a = \frac{F}{m} = \frac{-20 \, \text{N}}{2 \, \text{kg}} = -10 \, \text{m/s}^2 \)
This indicates that the body is decelerating at a rate of 10 m/s².
Calculating Time to Rest
To find the time (t) when the body comes to rest (final velocity \( v = 0 \)), we use the equation:
- Formula: \( v = u + a \cdot t \)
- Setting \( v = 0 \):
\( 0 = 8 \, \text{m/s} - 10 \, \text{m/s}^2 \cdot t \)
- Rearranging gives:
\( t = \frac{8 \, \text{m/s}}{10 \, \text{m/s}^2} = 0.8 \, \text{s} \)
Calculating Displacement
To calculate the displacement (s) during this time, we use the equation:
- Formula: \( s = u \cdot t + \frac{1}{2} a \cdot t^2 \)
- Substituting values:
\( s = 8 \, \text{m/s} \cdot 0.8 \, \text{s} + \frac{1}{2} \cdot (-10 \, \text{m/s}^2) \cdot (0.8 \, \text{s})^2 \)
- Calculating:
\( s = 6.4 \, \text{m} - 3.2 \, \text{m} = 3.2 \, \text{m} \)
Final Results
- Time to come to rest: 0.8 seconds
- Displacement covered: 3.2 meters
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A body of mass 2 kg is moving along positive X-axis with a constant speed of 8 m/s. If a force of 20 N is acting on the body along the (-)ve X-axis then calculate the time when body will be at rest after applying the force and calculate the displacement covered by the body during this time interval.?
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A body of mass 2 kg is moving along positive X-axis with a constant speed of 8 m/s. If a force of 20 N is acting on the body along the (-)ve X-axis then calculate the time when body will be at rest after applying the force and calculate the displacement covered by the body during this time interval.? 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 A body of mass 2 kg is moving along positive X-axis with a constant speed of 8 m/s. If a force of 20 N is acting on the body along the (-)ve X-axis then calculate the time when body will be at rest after applying the force and calculate the displacement covered by the body during this time interval.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 2 kg is moving along positive X-axis with a constant speed of 8 m/s. If a force of 20 N is acting on the body along the (-)ve X-axis then calculate the time when body will be at rest after applying the force and calculate the displacement covered by the body during this time interval.?.
A body of mass 2 kg is moving along positive X-axis with a constant speed of 8 m/s. If a force of 20 N is acting on the body along the (-)ve X-axis then calculate the time when body will be at rest after applying the force and calculate the displacement covered by the body during this time interval.? 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 A body of mass 2 kg is moving along positive X-axis with a constant speed of 8 m/s. If a force of 20 N is acting on the body along the (-)ve X-axis then calculate the time when body will be at rest after applying the force and calculate the displacement covered by the body during this time interval.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 2 kg is moving along positive X-axis with a constant speed of 8 m/s. If a force of 20 N is acting on the body along the (-)ve X-axis then calculate the time when body will be at rest after applying the force and calculate the displacement covered by the body during this time interval.?.
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