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x(t) (Position) Time (s) v(t) (Velocity) Time (s)

x(t) (Position) Time (s) v(t) (Velocity) Time (s)

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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Sketch the velocity vs time graph from the position vs time graph
### Analyzing Motion: Position and Velocity Graphs The image presents two distinct graphs that illustrate the concepts of position and velocity as functions of time. #### Graph 1: Position vs. Time - **Axes:** - Horizontal Axis (X-axis): Time (s). This axis measures the passage of time in seconds. - Vertical Axis (Y-axis): \( x(t) \) (Position). This axis measures the position of the object over time. - **Description:** - The graph starts from the top left, indicating a positive value for the initial position at \( t=0 \). - Initially, the position decreases as time progresses, dipping below the zero mark (the x-axis), which indicates a negative position. - The curve then rises, passes through the origin, and increases steeply, indicating an increase in position over time. #### Graph 2: Velocity vs. Time - **Axes:** - Horizontal Axis (X-axis): Time (s). This axis measures the passage of time in seconds. - Vertical Axis (Y-axis): \( v(t) \) (Velocity). This axis measures the velocity of the object over time. - **Description:** - The graph currently shows an empty framework with labeled axes, implying that detailed velocity data corresponding to the position graph might be plotted here. - Once filled, this graph should illustrate how the object's velocity changes over the same time period depicted in the position graph. ### Educational Summary: These graphs are pivotal in understanding the motion of objects. The first graph offers insight into how the position of an object evolves with time. When coupled with the velocity graph, students can interpret the speed and direction (positive or negative) of the object's movement. Understanding the relationship between these two graphs is crucial for mastering kinematic concepts in physics.
Transcribed Image Text:### Analyzing Motion: Position and Velocity Graphs The image presents two distinct graphs that illustrate the concepts of position and velocity as functions of time. #### Graph 1: Position vs. Time - **Axes:** - Horizontal Axis (X-axis): Time (s). This axis measures the passage of time in seconds. - Vertical Axis (Y-axis): \( x(t) \) (Position). This axis measures the position of the object over time. - **Description:** - The graph starts from the top left, indicating a positive value for the initial position at \( t=0 \). - Initially, the position decreases as time progresses, dipping below the zero mark (the x-axis), which indicates a negative position. - The curve then rises, passes through the origin, and increases steeply, indicating an increase in position over time. #### Graph 2: Velocity vs. Time - **Axes:** - Horizontal Axis (X-axis): Time (s). This axis measures the passage of time in seconds. - Vertical Axis (Y-axis): \( v(t) \) (Velocity). This axis measures the velocity of the object over time. - **Description:** - The graph currently shows an empty framework with labeled axes, implying that detailed velocity data corresponding to the position graph might be plotted here. - Once filled, this graph should illustrate how the object's velocity changes over the same time period depicted in the position graph. ### Educational Summary: These graphs are pivotal in understanding the motion of objects. The first graph offers insight into how the position of an object evolves with time. When coupled with the velocity graph, students can interpret the speed and direction (positive or negative) of the object's movement. Understanding the relationship between these two graphs is crucial for mastering kinematic concepts in physics.
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