How is the rate of change for a vertical curve expressed mathematically?

The rate of change for a vertical curve is calculated to understand how the slope transitions from one grade to another. In this context, G1 represents the initial grade, while G2 represents the final grade of the curve.

The formula for the rate of change is determined by the difference in grades, represented as the change in grade from G1 to G2, which is G2 - G1. To find the average rate of change over the length of the curve, this difference should be divided by 2 since the rate is usually assessed across the entire length of the vertical curve.

Thus, the correct formula for expressing the rate of change mathematically is (G2 - G1) / 2. This calculation reflects the average change in grade over the curve, rather than just the immediate change between the two grades, which is useful for engineers and surveyors in design assessments and roadway planning.

The other options do not accurately represent this average rate of change. For instance, simply subtracting G1 from G2 does not account for the average effect over the curve's length, and adding G1 or dividing incorrectly does not provide a representation of the average slope between the two grades.