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(c) The vector equation that defines average velocity during a time interval At = t - i į A (; -1) (1; -n) Explain why the relative lengths of the displacement-vector components you drew in parts (a) and (b) should be proportional to the lengths of the corresponding velocity vector components. Hint: Remember that velocity equals the change in displacement over the change in time.

(c) The vector equation that defines average velocity during a time interval At = t - i į A (; -1) (1; -n) Explain why the relative lengths of the displacement-vector components you drew in parts (a) and (b) should be proportional to the lengths of the corresponding velocity vector components. Hint: Remember that velocity equals the change in displacement over the change in time.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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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### Vector Equation for Average Velocity (c) The vector equation that defines average velocity during a time interval \( \Delta t = t_2 - t_1 \) is: \[ \langle \vec{v} \rangle_{x, y} = \frac{\Delta \vec{r}}{\Delta t} = \frac{(x_2 - x_1)i + (y_2 - y_1)j}{(t_2 - t_1)} \] ### Explanation **Explain why the relative lengths of the displacement-vector components you drew in parts (a) and (b) should be proportional to the lengths of the corresponding velocity vector components.** **Hint:** Remember that velocity equals the change in displacement over the change in time. --- This equation expresses the relationship between displacement and velocity, indicating that the velocity vector components are directly proportional to the displacement vector components over the same time interval.
Transcribed Image Text:### Vector Equation for Average Velocity (c) The vector equation that defines average velocity during a time interval \( \Delta t = t_2 - t_1 \) is: \[ \langle \vec{v} \rangle_{x, y} = \frac{\Delta \vec{r}}{\Delta t} = \frac{(x_2 - x_1)i + (y_2 - y_1)j}{(t_2 - t_1)} \] ### Explanation **Explain why the relative lengths of the displacement-vector components you drew in parts (a) and (b) should be proportional to the lengths of the corresponding velocity vector components.** **Hint:** Remember that velocity equals the change in displacement over the change in time. --- This equation expresses the relationship between displacement and velocity, indicating that the velocity vector components are directly proportional to the displacement vector components over the same time interval.
### Educational Transcription of Displacement Vector Diagram #### Diagram Explanation: The provided educational material focuses on the representation of displacement vectors and their components. #### Diagram (a): 1. **Description**: - The diagram presents a displacement vector \(\Delta \vec{r}\) originating from point \(x_1, y_1\) and terminating at point \(x_2, y_2\). - The vector is drawn as a slanted arrow in the quadrant described by the origin points. 2. **Task**: - **Draw and label the x-component**: Students are instructed to represent the x-component of the displacement vector. Label this component as \(\Delta \vec{r}_x\). - **Placement**: The tail of this x-component vector should be at \(x_1, y_1\). - **Hint**: The x-component points only in the x-direction. 3. **Graph Detail**: - The x-component would be represented as a horizontal arrow starting from \(x_1, y_1\) extending towards \(x_2, y_1\). #### Diagram (b): 1. **Description**: - Again, the displacement vector \(\Delta \vec{r}\) is shown from \(x_1, y_1\) to \(x_2, y_2\). 2. **Task**: - **Draw and label the y-component**: Students are asked to depict the y-component of the displacement vector, labeling it as \(\Delta \vec{r}_y\). - **Placement**: This time, the tail is placed at \(x_1, y_1\). - **Hints**: This component points in the y-direction only, and its length is shorter than \(\Delta \vec{r}\). 3. **Graph Detail**: - The y-component would be visualized as a vertical arrow starting from \(x_1, y_1\) extending upwards to \(x_1, y_2\). By understanding these diagrams and completing the tasks, students will learn how to decompose a vector into its horizontal and vertical components.
Transcribed Image Text:### Educational Transcription of Displacement Vector Diagram #### Diagram Explanation: The provided educational material focuses on the representation of displacement vectors and their components. #### Diagram (a): 1. **Description**: - The diagram presents a displacement vector \(\Delta \vec{r}\) originating from point \(x_1, y_1\) and terminating at point \(x_2, y_2\). - The vector is drawn as a slanted arrow in the quadrant described by the origin points. 2. **Task**: - **Draw and label the x-component**: Students are instructed to represent the x-component of the displacement vector. Label this component as \(\Delta \vec{r}_x\). - **Placement**: The tail of this x-component vector should be at \(x_1, y_1\). - **Hint**: The x-component points only in the x-direction. 3. **Graph Detail**: - The x-component would be represented as a horizontal arrow starting from \(x_1, y_1\) extending towards \(x_2, y_1\). #### Diagram (b): 1. **Description**: - Again, the displacement vector \(\Delta \vec{r}\) is shown from \(x_1, y_1\) to \(x_2, y_2\). 2. **Task**: - **Draw and label the y-component**: Students are asked to depict the y-component of the displacement vector, labeling it as \(\Delta \vec{r}_y\). - **Placement**: This time, the tail is placed at \(x_1, y_1\). - **Hints**: This component points in the y-direction only, and its length is shorter than \(\Delta \vec{r}\). 3. **Graph Detail**: - The y-component would be visualized as a vertical arrow starting from \(x_1, y_1\) extending upwards to \(x_1, y_2\). By understanding these diagrams and completing the tasks, students will learn how to decompose a vector into its horizontal and vertical components.
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