From Amperes to Acceleration: Understanding Electric Vehicles through Math & Physics.

On the evening of November 3, 2023, the LUMS Math Circle set out on a fascinating exploration of electric vehicles under the banner "From Amperes to Acceleration: Understanding Electric Vehicles through Math & Physics.” Guiding this exciting adventure were two distinguished educators from LUMS: Dr. Hafsa Qamar, an Assistant Professor in Electrical Engineering, and Dr. Shaheen Nazir, an Associate Professor in Mathematics. LUMS Math Circle is becoming a platform for participants to evolve with experience.

The journey commenced with a deceptively simple yet thought-provoking question: "What exactly is an electric vehicle?" Participants, brimming with curiosity, responded with remarkable clarity. Dr. Hafsa then injected a sense of fun and learning with a "Fun Quiz" segment, where participants eagerly tackled entertaining multiple-choice questions centered around electric and internal combustion engine vehicles, with the delightful promise of a candy bar for those who cracked the quiz.

The intrigue deepened as Dr. Hafsa posed the central question, "Why do electric vehicles matter?" Participants shared a diverse array of compelling answers, reflecting their unique perspectives. Before delving into the heart of this matter, Dr. Hafsa took the audience on a captivating journey through the history of electric vehicles. Surprisingly, most participants believed that electric vehicles were a recent innovation, emerging only in the last 15-20 years. To their astonishment, Dr. Hafsa unveiled a captivating video documenting the existence of electric vehicles since as early as 1899. While these early electric cars faced economic challenges due to higher operating costs compared to steam or internal combustion engine vehicles, the video underscored the issue of noxious emissions from the latter, contributing to air pollution. Dr. Hafsa eloquently emphasized that thanks to advancements like lithium-ion batteries, modern electric vehicles are not only cost-effective but also environmentally friendly, producing no harmful emissions. This revelation left the students both astounded and deeply curious about the inner workings of electric vehicles, and their excitement soared as Dr. Hafsa announced, "By the end of this circle, you will be building your very own electric vehicle." Excitement reached its zenith.

The session then delved into the fundamental principles underlying the operation of electric vehicles, as well as vehicles in general, and the role of mathematics in their motion. Dr. Shaheen stepped forward to ask a thought-provoking question: "Do you understand the concept of force?" Many participants responded affirmatively, offering intriguing insights into this concept. Dr. Shaheen then explored the significance of not just the magnitude but also the direction of force, prompting a lively discussion on whether force should be classified as a scalar or a vector. The consensus, nearly unanimous, settled on "Vector." Dr. Shaheen and Dr. Hafsa proceeded to elucidate how various forces, such as friction, gravity, and acceleration, come into play as a vehicle moves. Injecting humor into the conversation, Dr. Hafsa playfully referenced TESLA, the reigning champion of electric vehicles worldwide, and emphasized the cost-effectiveness of these marvels. Dr. Shaheen added a touch of wit, saying, "But electricity isn't exactly easy on the pocket these days," eliciting laughter throughout the room.

Dr. Shaheen continued her exposition, shedding light on the concept of vectors and how they can be constructed using two points within a plane. She also introduced the idea of equivalent vectors, vector magnitude, and direction. This set the stage for engaging activities on worksheets, where participants were tasked with drawing or creating specific vectors based on predefined conditions. Dr. Shaheen then introduced the fundamental trigonometric functions and their relationship with vector direction. Soon, participants were able to discern the practical applications of Pythagoras' Theorem in determining vector magnitude. As the session progressed, Dr. Shaheen illustrated how these trigonometric functions influence the force acting on a vehicle, explaining why more power is required to ascend steep hills while vehicles naturally descend on negative slopes. The participants were visibly thrilled to connect this intuitive concept with its mathematical foundations.

For the grand finale of the session, Dr. Hafsa provided a hands-on demonstration of the basic components of an electric vehicle using a toy remote-controlled car. She then distributed disassembled toy electric car components to different groups and encouraged them to employ their imagination to assemble their own electric vehicles. In no time, all groups successfully crafted their own electric cars, radiating a sense of accomplishment and delight. As a parting thought, Dr. Hafsa remarked, "If you found this fascinating, who knows, you might consider this as a future profession."

Certificates of participation were distributed to the enthusiastic participants by our esteemed instructors, Dr. Hafsa Qamar and Dr. Shaheen Nazir, as a token of recognition for their active engagement.