Analysis of Travel Time Approximation on Trips Using Maclaurin Series

Mathematical approximation plays an important role in the analysis of travel time which is influenced by factors such as speed, distance, and acceleration. This study uses the Maclaurin series to approximate the value of travel time based on the distance traveled (x) and the number of terms in the series (n). The calculation was done manually and implemented using MATLAB for the case of distance x = 2 with the first five terms n = 5. The results of the manual calculation showed an estimated travel time of 0.9094 seconds, while the calculation using MATLAB resulted in 0.9093 seconds. The small difference between the two methods shows the accuracy of the Maclaurin series in travel time approximation. By increasing the number of terms in the sequence, the calculation results will be closer to a more precise value. This study emphasizes the benefits of the Maclaurin sequence method in simplifying mathematical analysis and improving calculation efficiency in physical and computational applications.