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Active Calculus - Multivariable

Activity 10.3.3. Is it a property of the driver or the road?
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.
(a)
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.
Hint.
Remember that we are not asking if the driver or road can control time. We are asking if the elapsed time is the same for all drivers at a fixed point on the racetrack or if drivers can have a different elapsed time to a particular location on the racetrack.
(b)
Is position (the location of the car on the racetrack) a property of the driver or the road? Be sure to explain your answer.
Hint.
You should make sure you understand that the measurements for different drivers must be made at the same location on the track, as stated above. Your explanation sentence may sound a little silly.
(c) Speedometer Reading.
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.
(d)
What vector calculus quantity is the speedometer reading?
Hint.
The vector calculus quantities we have covered are time, position, velocity, acceleration, speed, and arc length.
(e) Odometer 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.