Which graph best represents the relationship between the mag- nitude of the centripetal acceleration and the speed of an object moving in a circle of constant radius? Speed Speed Speed Speed (1) (2) (3) Centripetal Acceleration Centripetal Acceleration Centripetal Acceleration Centripetal Acceleration
Which graph best represents the relationship between the mag- nitude of the centripetal acceleration and the speed of an object moving in a circle of constant radius? Speed Speed Speed Speed (1) (2) (3) Centripetal Acceleration Centripetal Acceleration Centripetal Acceleration Centripetal Acceleration
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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When speed goes up what happens to velocity
![### Question:
Which graph best represents the relationship between the magnitude of the centripetal acceleration and the speed of an object moving in a circle of constant radius?
### Graph Descriptions:
1. **Graph 1:** A straight line starting from the origin and increasing linearly, depicting a direct proportionality between centripetal acceleration and speed.
2. **Graph 2:** A curve starting from the origin with a sharp increase, representing an exponential relationship between centripetal acceleration and speed.
3. **Graph 3:** A curve starting from a high point on the y-axis and decreasing towards the x-axis, indicating an inverse relationship between centripetal acceleration and speed.
4. **Graph 4:** A horizontal line, indicating that centripetal acceleration remains constant regardless of the speed.
### Explanation:
The centripetal acceleration (\(a_c\)) of an object moving in a circle is given by the formula:
\[ a_c = \frac{v^2}{r} \]
where \(v\) is the speed of the object, and \(r\) is the constant radius of the circle. According to the formula, centripetal acceleration is directly proportional to the square of the speed. Therefore, the most accurate representation would be Graph 2, where centripetal acceleration increases exponentially with speed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cfece43-f1db-4e28-a37f-2540c2511499%2F27174231-7cc7-46a5-aec3-fab7c79e7885%2Fa5mbac_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question:
Which graph best represents the relationship between the magnitude of the centripetal acceleration and the speed of an object moving in a circle of constant radius?
### Graph Descriptions:
1. **Graph 1:** A straight line starting from the origin and increasing linearly, depicting a direct proportionality between centripetal acceleration and speed.
2. **Graph 2:** A curve starting from the origin with a sharp increase, representing an exponential relationship between centripetal acceleration and speed.
3. **Graph 3:** A curve starting from a high point on the y-axis and decreasing towards the x-axis, indicating an inverse relationship between centripetal acceleration and speed.
4. **Graph 4:** A horizontal line, indicating that centripetal acceleration remains constant regardless of the speed.
### Explanation:
The centripetal acceleration (\(a_c\)) of an object moving in a circle is given by the formula:
\[ a_c = \frac{v^2}{r} \]
where \(v\) is the speed of the object, and \(r\) is the constant radius of the circle. According to the formula, centripetal acceleration is directly proportional to the square of the speed. Therefore, the most accurate representation would be Graph 2, where centripetal acceleration increases exponentially with speed.
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