In this activity, we want to determine if the different measurements we have described are a property of the driver or the road. A measurement is a property of the driver provided that the values of that measurement can be different for different drivers when measured at the same location on the racetrack. A measurement is a property of the road provided that different drivers must have the same values when measured at the same location on the racetrack.
Let's start by looking at a couple of easy measurements. Is the time elapsed a property of the driver or the road? Be sure to explain your answer.
Is position (the location of the car on the racetrack) a property of the driver or the road? Be sure to explain your answer.
Now that we are warmed up, let's look at some more interesting measurements. The car's speedometer reading measures how fast (as a scalar) the car is moving. Is the car's speedometer reading a property of the driver or the road? Be sure to explain your answer.
What vector calculus quantity is the speedometer reading?
The racecar's odometer measures the distance traveled by the car. Every car's odometer is set to be zero at the start of the race. Is the car's odometer reading a property of the driver or the road? Be sure to explain your answer.
Long, Keller & Schlicker, Active Calculus Multivariable, §10.4 Arc Length, Activity 10.4.3