To provide a detailed analysis, I need specific data from the graph you are referring to, such as coordinates, speeds at different times, and the overall shape of the graph. Nonetheless, I can guide you on how to determine the factors you're interested in based on a hypothetical graph or data.
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Determining the Rate of Deceleration: To find the rate at which the car is slowing down (in miles per hour per second), identify the speed at the point just before the car begins to slow down and the speed at which it slows down after a certain period. Subtract the initial speed from the final speed to find the change in speed. Then, determine the time taken for this change (from the point the car starts to slow down to when it comes to a stop or reaches another speed). The formula for acceleration (or deceleration in this case) is: \[ \text{Deceleration} = \frac{\text{Change in Speed}}{\text{Time Change}} \] Remember to convert speeds from miles per hour to miles per hour per second as necessary.
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Interval of Greatest Change in Speed: To find the interval of time where the automobile experiences the greatest change in speed, look for the steepest slope in the speed vs. time graph (the most pronounced decline). The change in speed is the difference between the speed at the beginning of this interval and the speed at the end.
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Constant Speed Interval: For the interval where the speed remains constant, identify the segment of the graph where the line is horizontal (indicating no change in speed). The speed during this interval is simply the value of the speed at that horizontal line.
Please provide specifics from the graph or numerical data if you would like me to calculate or explain further!