The slope of a distance-time graph represents the speed or rate of change of an object's motion.
In a distance-time graph, distance is plotted on the vertical axis (y-axis), and time is plotted on the horizontal axis (x-axis). The slope of the graph is determined by the steepness of the line connecting the data points.
Mathematically, the slope is calculated by dividing the change in distance (vertical change) by the change in time (horizontal change) between two points on the graph. It represents the ratio of how much the distance changes with respect to the corresponding change in time.
If the slope of the graph is steeper, it indicates a higher speed or faster rate of change in distance over time. Conversely, a flatter slope suggests a slower speed or a slower rate of change in distance over time.
For example, a steeper positive slope on a distance-time graph indicates a higher speed, while a negative slope represents motion in the opposite direction. A horizontal line with a slope of zero indicates that the object is not moving (at rest), as there is no change in distance over time.
In summary, the slope of a distance-time graph provides information about the object's speed or rate of change of distance with respect to time.