Answer
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Step 1:: Determine the distance needed to stop the car within the amber duration.
d_{decel} = \frac{(37 \frac{miles}{hour} * \frac{1 hour}{3600 \frac{seconds}{hour}})^2}{2 * 10 \frac{feet}{second^2} * \frac{4.5 seconds - 1.5 seconds}{1 second}} = 67.72 feet
The driver has a perception/reaction time of 1.5 seconds, during which they will continue at their initial speed. After this time, they will begin decelerating until they stop. First, calculate the distance traveled during the perception/reaction time: where Substituting the given values: Next, calculate the distance needed to stop the car during the amber duration: where Substituting the given values:
Step 2:: Calculate the total stopping distance.
d_{total} = d_{reaction} + d_{decel} = 8.17 feet + 67.72 feet = 75.89 feet
Add the distance traveled during the reaction time and the distance needed to stop the car during deceleration:
Step 3:: Compare the total stopping distance to the intersection width.
d_{total} = 75.89 feet < 50 feet
If the total stopping distance is greater than or equal to the intersection width, the driver should have been able to stop before crossing the intersection.
Step 4:: Determine if the driver is innocent.
t_{amber\_remaining} = t_{amber} - t_{reaction} - 0.33 seconds = 4.5 seconds - 1.5 seconds - 0.33 seconds = 2.67 seconds
Since the total stopping distance is less than the intersection width, the driver was not able to stop before crossing the intersection. However, the driver crossed the intersection 0.33 seconds into the red light. If the amber duration was 4.5 seconds, the amber light was on for 4.17 seconds before the driver crossed the intersection. The driver did not cross the intersection during the amber duration, so they are not innocent.
Final Answer
The driver is not innocent, as they crossed the intersection 0.33 seconds after the amber light turned red.
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