The distance versus time plot for a particular object shows a quadratic relationship. Which column of distance data is possible for this situation?
Scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. The temperature of the gaseous planet varies linearly with the height of the atmosphere. The delicate instruments on board completely fail at a height of 61.5 kilometers. What is the approximate temperature at this altitude?
To determine which column of distance data is possible for a quadratic relationship, we need to understand what a quadratic relationship represents in terms of the distance versus time plot.
A quadratic relationship is represented by a parabolic curve. In the context of distance versus time, this suggests that the object's speed is changing nonlinearly. We can observe this in the graph as the slope of the curve continuously varies.
Now, let's consider the possible columns of distance data for this situation. In a distance versus time plot, the x-axis represents time, and the y-axis represents distance. The data in the distance column should be arranged according to the corresponding time values.
Possible columns of distance data for a quadratic relationship could be:
1. Distance Data Column: The distance values could be the squares of the corresponding time values. For example, if the time values are 1, 2, 3, 4, the distance values could be 1, 4, 9, 16.
2. Distance Data Column: The distance values could be multiples of the squares of the corresponding time values. For example, if the time values are 1, 2, 3, 4, the distance values could be 2, 8, 18, 32.
3. Distance Data Column: The distance values could be a combination of squared time values and a constant term. For example, if the time values are 1, 2, 3, 4, the distance values could be 2, 9, 20, 35.
In summary, possible columns of distance data for a quadratic relationship in a distance versus time plot could involve squared time values, multiples of squared time values, or a combination of squared time values and a constant term.