Activity 10.6.4. The Driver or the Road?
In this activity, you will determine if the measurements related to the splitting of acceleration are properties of the driver or properties of the road. This is a continuation of Activity 10.3.3. As a reminder, a measurement is a property of the driver if the value 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 when different drivers must have the same value(s) when measured at the same location on the racetrack.
(a)
Pedal Usage: We measure the pedal usage as \(+\text{,}\) \(-\text{,}\) or \(0\) in the following way:
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\(+\) if the gas pedal is being used
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\(-\) if the brake pedal is being used
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\(0\) if no pedal is being used
Since our drivers are safety minded, they do not use more than one pedal at a time. Note that this measurement is a sign rather than a numerical value. Which vector calculus quantity’s sign corresponds to the pedal usage? Write a sentence to explain your answer.
Hint.
The vector calculus quantities related to the motion along a curve we have covered are time, position, velocity, acceleration, speed, arc length, unit tangent vector, unit normal vector, binormal vector, tangential acceleration component, normal acceleration component, curvature, and osculating circle.
(b)
Describe how the value of \(a_{\vec{N}}\) would be felt by the driver in our analogy.
(c)
In terms of the race car analogy, explain why \(a_{\vec{N}}\) can’t be negative.
(d)
Write a few sentences about whether \(a_{\vT}\) is a property of the driver or a property of the road.
(e)
Write a few sentences about whether \(a_{\vN}\) is a property of the driver or a property of the road.
