What indicates the relationship in a vertical curve rate of change?

The concept of a vertical curve in surveying, particularly in road design, involves a transition between different grades or slopes. The correct response, which is the difference in heights of starting and ending points, effectively defines the vertical curve's overall change in elevation. This difference provides the necessary information to establish the vertical curve's length and geometry, ensuring a smooth transition for vehicles between different slopes.

While change in elevation over time could provide insights into how quickly the elevation alters at specific intervals, it doesn't adequately capture the essential characteristics of the curve. The rate of slope adjustment refers to how quickly the slope changes but doesn’t specify that the overall difference between initial and final elevations is being measured. Similarly, the difference in gradients provides a measure of slope steepness but is not as comprehensive in denoting the overall vertical relationship determined by the change in heights between starting and ending points. Thus, understanding the difference in heights is vital in surveying as it directly influences the design and safety of transportation routes.