The graph shows the velocity of a motorcycle police officer plotted as a function of time. a ) Find the instantaneous acceleration at t = 3 s, t = 7 s, 50 * 45 * 40 and t = 11 s. 35 b) How far does the officer go in the first 5 s ? The first 30 9 s? The first 13 s? c) Using the graph shown at the bottom, 25 20 draw a graph of acceleration versus time. 15 10 5 4 6 8 10 12 14

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The problem and graph pertain to the velocity of a motorcycle police officer as a function of time. The text and the graph illustrate several aspects of this motion. The task involves three parts:

5) The graph shows the velocity of a motorcycle police officer plotted as a function of time.

a) Find the instantaneous acceleration at t = 3 s, t = 7 s, and t = 11 s.

b) How far does the officer go in the first 5 s? The first 9 s? The first 13 s?

c) Using the graph shown at the bottom, draw a graph of acceleration versus time.

### Explanation of the Graph:

- **Axes:** 
  - The horizontal axis (x-axis) represents time, \( t \), in seconds (sec), ranging from 0 to 13 seconds.
  - The vertical axis (y-axis) represents velocity, \( v_x \), in meters per second (m/s), ranging from 0 to 50 m/s.

- **Data Points and Line Segments:**
  - The velocity remains constant at 20 m/s from t = 0 to t = 7 seconds.
  - There is an increase in velocity from 20 m/s at t = 7 seconds to 45 m/s at t = 9 seconds.
  - The velocity reaches a peak at 45 m/s, then sharply declines to 0 m/s by t = 13 seconds.

### Analyzing Instantaneous Acceleration:

- **Instantaneous Acceleration** is calculated as the change in velocity over the change in time. Examine the graph at \( t = 3 \), \( t = 7 \), and \( t = 11 \) seconds to determine the slope at these points.

### Calculating Distance Traveled:

- **Distance Traveled** can be inferred by finding the area under the velocity-time graph for the specified time intervals.

### Drawing the Acceleration-Time Graph:

- **Acceleration vs. Time Graph**: 
  - Use the slope changes from the velocity graph to plot acceleration over time, taking into account constant velocity periods (zero acceleration), and changes in velocity to indicate positive or negative acceleration.
Transcribed Image Text:The problem and graph pertain to the velocity of a motorcycle police officer as a function of time. The text and the graph illustrate several aspects of this motion. The task involves three parts: 5) The graph shows the velocity of a motorcycle police officer plotted as a function of time. a) Find the instantaneous acceleration at t = 3 s, t = 7 s, and t = 11 s. b) How far does the officer go in the first 5 s? The first 9 s? The first 13 s? c) Using the graph shown at the bottom, draw a graph of acceleration versus time. ### Explanation of the Graph: - **Axes:** - The horizontal axis (x-axis) represents time, \( t \), in seconds (sec), ranging from 0 to 13 seconds. - The vertical axis (y-axis) represents velocity, \( v_x \), in meters per second (m/s), ranging from 0 to 50 m/s. - **Data Points and Line Segments:** - The velocity remains constant at 20 m/s from t = 0 to t = 7 seconds. - There is an increase in velocity from 20 m/s at t = 7 seconds to 45 m/s at t = 9 seconds. - The velocity reaches a peak at 45 m/s, then sharply declines to 0 m/s by t = 13 seconds. ### Analyzing Instantaneous Acceleration: - **Instantaneous Acceleration** is calculated as the change in velocity over the change in time. Examine the graph at \( t = 3 \), \( t = 7 \), and \( t = 11 \) seconds to determine the slope at these points. ### Calculating Distance Traveled: - **Distance Traveled** can be inferred by finding the area under the velocity-time graph for the specified time intervals. ### Drawing the Acceleration-Time Graph: - **Acceleration vs. Time Graph**: - Use the slope changes from the velocity graph to plot acceleration over time, taking into account constant velocity periods (zero acceleration), and changes in velocity to indicate positive or negative acceleration.
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