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A car is going around a circular track. It is currently moving with a speed of 16.5 m/s and it is speeding up at a rate of 2.7 meters per second squared. As viewed from above, the car is moving in a counter-clockwise direction 122 degrees in a counter- clockwise direction from the positive x-axis. The situation is shown in the diagram above. The track has a radius of 77.5 meters. In units of meters and it is currently located at an angle of theta per second squared, what is the magnitude of the acceleration of the car?

A car is going around a circular track. It is currently moving with a speed of 16.5 m/s and it is speeding up at a rate of 2.7 meters per second squared. As viewed from above, the car is moving in a counter-clockwise direction 122 degrees in a counter- clockwise direction from the positive x-axis. The situation is shown in the diagram above. The track has a radius of 77.5 meters. In units of meters and it is currently located at an angle of theta per second squared, what is the magnitude of the acceleration of the car?

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### Circular Motion of a Car The diagram illustrates a car moving around a circular track. Key elements of the diagram include: - **Circular Track**: The track is shown as a circle with the car's path represented around its circumference. - **Axes**: The diagram includes x and y axes for determining the car's position. - **Velocity and Acceleration**: - The car has a velocity vector **\(v\)** tangential to the track, indicating its direction and speed. - A yellow rectangle represents the car on the track. - **Angular Position**: The angle **\(\theta\)** is measured from the positive x-axis, representing the car's position at 122 degrees in a counter-clockwise direction. ### Problem Statement A car is traveling along a circular track with the following parameters: - **Speed**: 16.5 meters per second (m/s) - **Acceleration**: The car is accelerating at a rate of 2.7 meters per second squared (m/s²). - **Angle**: The car is positioned at an angle of \(\theta = 122\) degrees from the positive x-axis. - **Radius of the Track**: 77.5 meters #### Task Calculate the magnitude of the car's acceleration, expressed in meters per second squared (m/s²).
Transcribed Image Text:### Circular Motion of a Car The diagram illustrates a car moving around a circular track. Key elements of the diagram include: - **Circular Track**: The track is shown as a circle with the car's path represented around its circumference. - **Axes**: The diagram includes x and y axes for determining the car's position. - **Velocity and Acceleration**: - The car has a velocity vector **\(v\)** tangential to the track, indicating its direction and speed. - A yellow rectangle represents the car on the track. - **Angular Position**: The angle **\(\theta\)** is measured from the positive x-axis, representing the car's position at 122 degrees in a counter-clockwise direction. ### Problem Statement A car is traveling along a circular track with the following parameters: - **Speed**: 16.5 meters per second (m/s) - **Acceleration**: The car is accelerating at a rate of 2.7 meters per second squared (m/s²). - **Angle**: The car is positioned at an angle of \(\theta = 122\) degrees from the positive x-axis. - **Radius of the Track**: 77.5 meters #### Task Calculate the magnitude of the car's acceleration, expressed in meters per second squared (m/s²).
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