Question

1 what do the axes in distance - time graphs represent? 2 how do you find the speed in a distance - time graph? 3 what does a flat, horizontal line in a distance - time graph mean?

Explanation:

1. In a distance - time graph, by convention, the horizontal axis (x - axis) represents time and the vertical axis (y - axis) represents distance.
2. The speed in a distance - time graph is found by calculating the slope of the line. The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). In the context of distance - time graph, if \(y\) represents distance \(d\) and \(x\) represents time \(t\), then speed \(v=\frac{d_2 - d_1}{t_2 - t_1}\) (average speed for a non - linear graph, instantaneous speed for a linear graph).
3. A flat, horizontal line in a distance - time graph means that the distance \(d\) is not changing with respect to time \(t\). According to the formula \(v = \frac{\Delta d}{\Delta t}\), if \(\Delta d=0\) (no change in distance), then \(v = 0\). So it means the object is at rest.

Answer:

1. The horizontal axis represents time and the vertical axis represents distance.
2. Calculate the slope of the line (using the formula \(v=\frac{d_2 - d_1}{t_2 - t_1}\)).
3. The object is at rest (speed \(v = 0\)).