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A particle is moving at a constant speed in a circular trajectory centered at the origin of an xy co-ordinate system. at one point (x=4m, y=0m) the particle has a velocity -5.0 j m/s. determine acceleration of particle.?
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A particle is moving at a constant speed in a circular trajectory cent...
The acceleration of the particle is given by the formula a = v^2/r, where a is the acceleration, v is the velocity of the particle, and r is the radius of the circular trajectory. Since the velocity of the particle at the point (x=4m, y=0m) is -5.0 j m/s, and the radius of the circular trajectory is 4m, the acceleration of the particle is given by a = (-5.0 j m/s)^2 / 4m = (-25 j m^2/s^2)/4m = -6.25 j m/s^2. Therefore, the acceleration of the particle is -6.25 j m/s^2.
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A particle is moving at a constant speed in a circular trajectory cent...
Given information:
- The particle is moving at a constant speed in a circular trajectory centered at the origin of an xy-coordinate system.
- At one point (x=4m, y=0m), the particle has a velocity of -5.0 j m/s.
Understanding the problem:
We need to determine the acceleration of the particle at the given point. Since the particle is moving in a circular trajectory, it experiences centripetal acceleration towards the center of the circle.
Calculating centripetal acceleration:
The centripetal acceleration can be calculated using the formula:
a = v²/r
where a is the centripetal acceleration, v is the velocity of the particle, and r is the radius of the circular trajectory.
Identifying key values:
- The given velocity of the particle is -5.0 j m/s. Since the velocity is given in vector form, it has a magnitude of 5.0 m/s and is directed in the negative y-direction.
- The x-coordinate of the particle is 4m, which gives us the radius of the circular trajectory, r = 4m.
Calculating centripetal acceleration:
Using the formula above, we can calculate the centripetal acceleration as follows:
a = (5.0 m/s)² / 4m
a = 25 m²/s² / 4m
a = 6.25 m/s²
Therefore, the acceleration of the particle at the given point is 6.25 m/s². This acceleration is directed towards the center of the circular trajectory.
Explanation:
The centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and its magnitude depends on the velocity of the object and the radius of the circle. In this case, the particle has a velocity of -5.0 j m/s, which means it is moving in the negative y-direction. The x-coordinate of the particle is 4m, which gives us the radius of the circular trajectory. By substituting these values into the formula for centripetal acceleration, we can calculate the acceleration as 6.25 m/s². This acceleration indicates that the particle is accelerating towards the center of the circular trajectory.
- The particle is moving at a constant speed in a circular trajectory centered at the origin of an xy-coordinate system.
- At one point (x=4m, y=0m), the particle has a velocity of -5.0 j m/s.
Understanding the problem:
We need to determine the acceleration of the particle at the given point. Since the particle is moving in a circular trajectory, it experiences centripetal acceleration towards the center of the circle.
Calculating centripetal acceleration:
The centripetal acceleration can be calculated using the formula:
a = v²/r
where a is the centripetal acceleration, v is the velocity of the particle, and r is the radius of the circular trajectory.
Identifying key values:
- The given velocity of the particle is -5.0 j m/s. Since the velocity is given in vector form, it has a magnitude of 5.0 m/s and is directed in the negative y-direction.
- The x-coordinate of the particle is 4m, which gives us the radius of the circular trajectory, r = 4m.
Calculating centripetal acceleration:
Using the formula above, we can calculate the centripetal acceleration as follows:
a = (5.0 m/s)² / 4m
a = 25 m²/s² / 4m
a = 6.25 m/s²
Therefore, the acceleration of the particle at the given point is 6.25 m/s². This acceleration is directed towards the center of the circular trajectory.
Explanation:
The centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and its magnitude depends on the velocity of the object and the radius of the circle. In this case, the particle has a velocity of -5.0 j m/s, which means it is moving in the negative y-direction. The x-coordinate of the particle is 4m, which gives us the radius of the circular trajectory. By substituting these values into the formula for centripetal acceleration, we can calculate the acceleration as 6.25 m/s². This acceleration indicates that the particle is accelerating towards the center of the circular trajectory.
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A particle is moving at a constant speed in a circular trajectory centered at the origin of an xy co-ordinate system. at one point (x=4m, y=0m) the particle has a velocity -5.0 j m/s. determine acceleration of particle.?
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A particle is moving at a constant speed in a circular trajectory centered at the origin of an xy co-ordinate system. at one point (x=4m, y=0m) the particle has a velocity -5.0 j m/s. determine acceleration of particle.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is moving at a constant speed in a circular trajectory centered at the origin of an xy co-ordinate system. at one point (x=4m, y=0m) the particle has a velocity -5.0 j m/s. determine acceleration of particle.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving at a constant speed in a circular trajectory centered at the origin of an xy co-ordinate system. at one point (x=4m, y=0m) the particle has a velocity -5.0 j m/s. determine acceleration of particle.?.
A particle is moving at a constant speed in a circular trajectory centered at the origin of an xy co-ordinate system. at one point (x=4m, y=0m) the particle has a velocity -5.0 j m/s. determine acceleration of particle.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is moving at a constant speed in a circular trajectory centered at the origin of an xy co-ordinate system. at one point (x=4m, y=0m) the particle has a velocity -5.0 j m/s. determine acceleration of particle.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving at a constant speed in a circular trajectory centered at the origin of an xy co-ordinate system. at one point (x=4m, y=0m) the particle has a velocity -5.0 j m/s. determine acceleration of particle.?.
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