Abstract:

This project explores the mathematical modeling of impact and collision dynamics with a focus on enhancing vehicle and road safety in Papua New Guinea (PNG). Using fundamental principles from classical mechanics - particularly the impulse-momentum theorem, conservation of momentum, and kinetic energy analysis - this study demonstrates how real-world vehicle collisions can be analyzed and predicted through mathematical equations. A central scenario models a 1000 kg car decelerating from 20 m/s to rest, showing how varying the impact duration significantly changes the force experienced: a crash over 0.2 seconds results in a 100,000 N force, while extending that to 0.3 seconds reduces the force to 66,667 N. These calculations highlight how small changes in crash parameters, modeled mathematically, have major effects on safety outcomes. This mathematical framework provides a low-cost, accessible alternative to physical crash testing, making it especially valuable in PNG where safety infrastructure and testing resources are limited. The project reinforces the role of applied mathematics as a powerful tool in engineering design, public safety planning, and real-world problem-solving.