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Force acts on a 100 g particle in such a way that the position of the particle as a function of time is given by x = 6t-2t² + 2, where x is in metres and t is in seconds. The work done during the first 2 second is:-?
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Force acts on a 100 g particle in such a way that the position of the ...
Understanding the Problem
To determine the work done on a particle given its position function, we first need to find the force acting on the particle and then calculate the work done over a specified time interval.
Position Function
The position of the particle as a function of time is given by:
- x(t) = 6t - 2t² + 2
Calculating Velocity and Acceleration
To find the force, we need to calculate the velocity and acceleration:
- Velocity (v) = dx/dt = 6 - 4t
- Acceleration (a) = dv/dt = -4 m/s² (constant acceleration)
Finding Force
Using Newton's second law (F = ma):
- Mass (m) = 100 g = 0.1 kg
- Force (F) = m * a = 0.1 kg * (-4 m/s²) = -0.4 N
Calculating Work Done
Work done (W) can be calculated using the formula:
- W = F * d, where d is the displacement over the time interval.
First, determine displacement from t = 0 to t = 2:
- x(0) = 6(0) - 2(0)² + 2 = 2 m
- x(2) = 6(2) - 2(2)² + 2 = 6 m
Displacement (d) = x(2) - x(0) = 6 m - 2 m = 4 m
Now, substituting into the work formula:
- W = F * d = -0.4 N * 4 m = -1.6 J
Conclusion
The work done during the first 2 seconds is -1.6 Joules. This negative value indicates that the force acts opposite to the direction of displacement.
To determine the work done on a particle given its position function, we first need to find the force acting on the particle and then calculate the work done over a specified time interval.
Position Function
The position of the particle as a function of time is given by:
- x(t) = 6t - 2t² + 2
Calculating Velocity and Acceleration
To find the force, we need to calculate the velocity and acceleration:
- Velocity (v) = dx/dt = 6 - 4t
- Acceleration (a) = dv/dt = -4 m/s² (constant acceleration)
Finding Force
Using Newton's second law (F = ma):
- Mass (m) = 100 g = 0.1 kg
- Force (F) = m * a = 0.1 kg * (-4 m/s²) = -0.4 N
Calculating Work Done
Work done (W) can be calculated using the formula:
- W = F * d, where d is the displacement over the time interval.
First, determine displacement from t = 0 to t = 2:
- x(0) = 6(0) - 2(0)² + 2 = 2 m
- x(2) = 6(2) - 2(2)² + 2 = 6 m
Displacement (d) = x(2) - x(0) = 6 m - 2 m = 4 m
Now, substituting into the work formula:
- W = F * d = -0.4 N * 4 m = -1.6 J
Conclusion
The work done during the first 2 seconds is -1.6 Joules. This negative value indicates that the force acts opposite to the direction of displacement.
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Force acts on a 100 g particle in such a way that the position of the particle as a function of time is given by x = 6t-2t² + 2, where x is in metres and t is in seconds. The work done during the first 2 second is:-?
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Force acts on a 100 g particle in such a way that the position of the particle as a function of time is given by x = 6t-2t² + 2, where x is in metres and t is in seconds. The work done during the first 2 second is:-? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Force acts on a 100 g particle in such a way that the position of the particle as a function of time is given by x = 6t-2t² + 2, where x is in metres and t is in seconds. The work done during the first 2 second is:-? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Force acts on a 100 g particle in such a way that the position of the particle as a function of time is given by x = 6t-2t² + 2, where x is in metres and t is in seconds. The work done during the first 2 second is:-?.
Force acts on a 100 g particle in such a way that the position of the particle as a function of time is given by x = 6t-2t² + 2, where x is in metres and t is in seconds. The work done during the first 2 second is:-? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Force acts on a 100 g particle in such a way that the position of the particle as a function of time is given by x = 6t-2t² + 2, where x is in metres and t is in seconds. The work done during the first 2 second is:-? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Force acts on a 100 g particle in such a way that the position of the particle as a function of time is given by x = 6t-2t² + 2, where x is in metres and t is in seconds. The work done during the first 2 second is:-?.
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