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Although motorcyclists have an inherent disadvantage when colliding with larger vehicles, their smaller mass also means that they have the ability accelerate and respond to potential collisions faster. The Kinetic Energy-Work Theorem describes some of the relationships between the mass of a moving object and the distance required for it to stop. In this theorem the stopping distance, $d$, which can be achieved with a uniform force, $F$, is determined by both the mass, $m$, and the original velocity, ${v}_{i}$, of the cycle according to $F d = \frac{1}{2} {m {v}_{i}}^{2}$.

A study was conducted to analyze driver awareness and the effects on stopping distance. In this study participants partook in two days of test sessions in which their stopping distances were recorded at various times throughout the course of the day. One of the two days was arranged to occur after a normal night of sleep and the other day was arranged to occur after a night of total sleep deprivation (TSD) as shown in Figure 1. The order of the two days of testing was randomly assigned and separated by a period of one week to allow for recovery from the night of TSD.

Figure 1

To examine the impact of ${v}_{i}$, the stopping distances which the motorcyclists were able to achieve throughout the course of a day were also examined for two initial traveling velocities. Comparisons can be made with riders who slept a normal night of sleep and those who underwent total sleep deprivation (TSD). Figure 2 shows the entire range of stopping distances for all participants as well as the average for each group.

Figure 2

Which of the following figures most accurately illustrates the theoretically determined impact of velocity on stopping distance?

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