As Chief Engineer and CEO at Steer Clear, you have done great work in transforming information from your location tracking system (LTS) into information on the position, velocity, and distance traveled by your car. In order to make the “self-driving” part of the self-driving car, you will need to compare information from the LTS (which describes how your car is moving) to GPS location data for the network of roads (which describe the paths your car should be taking). Since everyone on the road drives differently, you realize that you need to measure how quickly a stretch of road is turning in different places, which leads you to contact a friend who is a civil engineer for help understanding highway construction specifications.
Figure 10.5.2 shows a map of a section of road on your testing route for your self-driving car with points labeled \(P_0\) and \(P_1\) which are 10 meters apart (along the road). Draw a vector in the direction of travel at both \(P_0\) and \(P_1\text{.}\) Use these vectors to describe how the direction of travel is changing along the path from \(P_0\) to \(P_1\text{.}\)
Figure 10.5.3 shows a map of a section of road on your testing route for your self-driving car with points labeled \(Q_0\) and \(Q_1\) which are 10 meters apart (along the road). Draw a vector in the direction of travel at both \(Q_0\) and \(Q_1\text{.}\) Use these vectors to describe how the direction of travel is changing along the path from \(Q_0\) to \(Q_1\text{.}\)
Is the direction of travel changing faster over the path from \(P_0\) to \(P_1\) or over the path from \(Q_0\) to \(Q_1\text{.}\) Write a few sentences to explain your reasoning and connect to your arguments and plots for the first two tasks.
