A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in the figure below. The length of the arc ABC is 248 m, and the car completes the turn in 38.0 s.   (a) Determine the car's speed.  m/s (b) What is the magnitude and direction of the acceleration when the car is at point B?

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in the figure below. The length of the arc ABC is 248 m, and the car completes the turn in 38.0 s.

 
(a) Determine the car's speed.
 m/s

(b) What is the magnitude and direction of the acceleration when the car is at point B?
magnitude       m/s2
direction  ° counterclockwise from the +x-axis
### Vector Addition Using the Parallelogram Law
Vector addition can be visualized and computed using the parallelogram law. Here, we present an illustrative example of vector addition on a Cartesian plane.

In the given diagram, we have two vectors originating from point \( O \) (the origin). The first vector, \( \vec{OA} \), is represented by the arrow pointing towards point \( A \) along the negative x-axis. The second vector, \( \vec{OB} \), makes an angle of \( 35.0^\circ \) with the x-axis and extends toward point \( B \).

To add these vectors graphically:
1. **Translate vector** \( \vec{OB} \) **to point** \( A \) **forming** \( \vec{AC} \) **keeping the direction and magnitude unchanged.**
2. **Draw a vector** \( \vec{OC} \) **from the origin** \( O \) **to point** \( C \), **which is the endpoint of** \( \vec{AC} \).

The result of adding vectors \( \vec{OA} \) and \( \vec{OB} \) is the diagonal vector \( \vec{OC} \). This is confirmed by the parallelogram formed by \( \vec{OA}, \vec{AC}, \vec{OB} \), and \( \vec{OC} \).

**Key Points:**
- The angle between \( \vec{OA} \) and \( \vec{OB} \) is \( 35.0^\circ \).
- Vectors have both magnitude and direction, represented by the length and arrowhead orientation, respectively.
- The resultant vector \( \vec{OC} \) is the vector sum of \( \vec{OA} \) and \( \vec{OB} \).

This diagram and explanation illustrate the geometric method of vector addition using the parallelogram law, providing a clear visual understanding of combining vectors in a two-dimensional plane.
Transcribed Image Text:### Vector Addition Using the Parallelogram Law Vector addition can be visualized and computed using the parallelogram law. Here, we present an illustrative example of vector addition on a Cartesian plane. In the given diagram, we have two vectors originating from point \( O \) (the origin). The first vector, \( \vec{OA} \), is represented by the arrow pointing towards point \( A \) along the negative x-axis. The second vector, \( \vec{OB} \), makes an angle of \( 35.0^\circ \) with the x-axis and extends toward point \( B \). To add these vectors graphically: 1. **Translate vector** \( \vec{OB} \) **to point** \( A \) **forming** \( \vec{AC} \) **keeping the direction and magnitude unchanged.** 2. **Draw a vector** \( \vec{OC} \) **from the origin** \( O \) **to point** \( C \), **which is the endpoint of** \( \vec{AC} \). The result of adding vectors \( \vec{OA} \) and \( \vec{OB} \) is the diagonal vector \( \vec{OC} \). This is confirmed by the parallelogram formed by \( \vec{OA}, \vec{AC}, \vec{OB} \), and \( \vec{OC} \). **Key Points:** - The angle between \( \vec{OA} \) and \( \vec{OB} \) is \( 35.0^\circ \). - Vectors have both magnitude and direction, represented by the length and arrowhead orientation, respectively. - The resultant vector \( \vec{OC} \) is the vector sum of \( \vec{OA} \) and \( \vec{OB} \). This diagram and explanation illustrate the geometric method of vector addition using the parallelogram law, providing a clear visual understanding of combining vectors in a two-dimensional plane.
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