Stop+Light+Violations+(by+Taylor+Valentine)

= // Green means go  Yellow means slow  Red means STOP!  //**Introduction**= Running a red light is one of the worst violations a motorist can commit. Disobeying stop lights puts not only the driver and passengers at risk, but pedestrians and other motorists as well. In fact, in 2007, almost 900 deaths and 153,000 injuries occurred in the U.S. as a result of violating red lights (Insurance Institute for Highway Safety). Stop light violations are especially common with new drivers, who are often unaware of the information needed to decide whether to go through a yellow light or stop.

In response to this rising phenomenon, many cities have begun to install red light cameras at dangerous intersections. While this has reduced the number of people running red lights, it has led to an increase in rear end collisions (see Collisions Due to Heavy Traffic page), as people slam on their brakes to avoid getting a ticket (Durso). Clearly, it is important to know how much time and space is necessary and how quickly one must stop in order to safely avoid this hazard. The following information, as well as common sense, will enable a driver to avoid running a red light.

=Relation to Kinematics= In order to stop in time for a red light, a driver must consider the speed at which they are traveling (velocity), their distance from the light (displacement), and the length of the light (time). These three quantities will allow a driver to calculate the acceleration rate necessary to stop.

=Example Scenario #1:= John Smith is driving his Chevy along Route 20, at 40mph (17.9 m/s/s), during the early afternoon. Having taken his eyes off the road, he looks up to see the light in front of him has turned yellow. Because he is unaware of the kinematics involved in stopping, he is unable to slow down before entering the intersection. The following ensues: media type="youtube" key="sDhiS9feGsU" height="344" width="425"

Using kinematic principles, John Smith could have determined the acceleration that he needed to apply to his brakes in order to slow down quickly enough to avoid hitting the motorcycle.

With the formula **velocity (final)=acceleration*time+velocity (initial)** he could calculate acceleration given a final velocity of 0m/s (because he's coming to a stop), a starting velocity of 17.9m/s and a time of 2.76 (the measured length of the yellow light). In order to come to a stop in during the length of the yellow light, John Smith would have needed to slow down at a rate of **6.5 meters/second each second.** Using this information, he could have calculated the distance from the stop light that he needed to begin slowing using the formula **displacement = ½ × acceleration × time² + initial velocity × time**.
 * In order to stop in time for red light, John Smith should have begun stopping 24.6 meters from the intersection and slowed at a rate of 6.5 m/s each second.** Unfortunately, he did not and crashed into a motorcycle.

His original motion and adjusted, safe motion can be represented in multiple forms, including a data table, position vs. time, velocity vs. time, and acceleration vs. time graphs, and equations for position and velocity.



The following graph shows John Smith's __position__, based on his original motion and adjusted motion, over the course of the yellow light (2.76 seconds). The star indicates his point of impact. Since his position after the crash is unpredictable, his original motion ends there. Original equation: x=17.9 m/s(t) Adjusted equation: x= 0.5(-6.5m/s² )(t²)+17.9m/s(t)

The following graph shows John Smith's __velocity__, based on his original motion and adjusted motion, over the course of the yellow light. The star indicates his point of impact. Like his position, his velocity is also unpredictable after the crash, so his original motion ends there. Original equation: v=17.9m/s Adjusted equation: v=-6.5m/s²(t)+17.9 m/s

The following graph shows John Smith's __acceleration__, based on his original motion and adjusted motion, over the course of the yellow light. The star indicates his point of impact. His acceleration after the crash is also unpredictable, so it also ends at 1.4 seconds.

=Example Scenario #2:= Taylor is driving along Poplar St. at a steady 25mph (11.2 m/s) during rush hour. As a safe driver, she is always aware of her surroundings on the road. When she is 15 meters away from the intersection of 29th and Poplar, she sees the light turn yellow. Using kinematic principles, she is able to figure out whether to stop or proceed through the intersection.

Using the equation **displacement = ½ × acceleration × time² + initial velocity × time**, she can determine the acceleration rate necessary to get to the intersection before the light turns red: In order for Taylor to reach the intersection during the length of the yellow light, she must slow down at approximately **4.28 meters/sec each second**. In order to stop at the intersection, she must "decelerate" (accelerate in the negative direction) at an even higher rate. Since this is a quick "deceleration" for rush hour traffic, it is safer for her to maintain speed and continue through the light. This will allow her to avoid a rear end collision (see Collisions page).

Her safe and unsafe motion can be represented in multiple forms, including a data table, position vs. time, velocity vs. time, and acceleration vs. time graphs, and equations for position and velocity:



The following graph shows Taylor's __position__, based on a safe and unsafe motion, over the course of the yellow light (2.76 seconds). Safe equation: x=11.2m/s(t) Unsafe equation: x= 0.5(-4.28m/s² )(t²)+11.2m/s(t)

The following graph shows Taylor's __velocity__, based on a safe and unsafe motion, over the course of the yellow light. Safe equation: v=11.2m/s Unsafe equation: v=-4.28m/s²(t)+11.2 m/s

The following graph shows Taylor's __acceleration__, based on a safe and unsafe motion, over the course of the yellow light.

=Example Scenario #3:= After safely clearing the intersection of 29th and Poplar, Taylor approaches the corner of 28th St, only to see another yellow light. She is still traveling 11.2 meters/sec (25 mph), but is now 40 m from the light. She is able to use the same formula as before to decide whether to stop or go through the light. Having solved the equation for acceleration, Taylor realizes that in order for her to be at the light before it turns red, she would have to increase her speed at a rate of 2.39 m/s. Since she is already driving at the speed limit, increasing her speed is unsafe. Therefore, she should slow to a stop and wait for a green light, instead of rushing to make the yellow.

Using the equation **velocity (final)=acceleration*time+velocity (initial)**, she can calculate a safe "deceleration" rate. Using this number, she is also able to calculate the distance from the light that she should begin slowing down using **displacement = ½ × acceleration × time² + initial velocity × time.**
 * Taylor's safe motion consists her slowing down at a rate of 4.06 m/s each second, beginning when she is 15.45 meters away from the intersection.**

As before, her safe and unsafe motion can be represented in multiple forms, including a data table, position vs. time, velocity vs. time, and acceleration vs. time graphs, and equations for position and velocity:

The following graph shows Taylor's __position__, based on a safe and unsafe motion. Her unsafe motion ends at 2.76 seconds (the point when she reaches the intersection because it is unclear whether she would continue to speed up, continue at the same speed, slow down, or be prompt in a crash.). The safe motion continues until she has safely come to a stop. Safe equation (between 0 and 2.2 seconds): x=11.2m/s(t) Safe equation (after 2.2 seconds): x= 0.5(-4.06m/s² )(t-2.2s)²+11.2m/s(t-2.2s) Unsafe equation: x= 0.5(-4.28m/s² )(t²)+11.2m/s(t)

The following graph shows Taylor's __velocity__, based on a safe and unsafe motion. Since she begins slowing down 2.2 seconds after seeing the yellow light, her velocity starts decreasing at this point. Safe equation (between 0 and 2.2 seconds): v=11.2m/s Safe equation (after 2.2 seconds): v= -4.06m/s²(t-2.2s)+11.2m/s Unsafe equation: v=2.36m/s²(t) + 11.2/s

The following graph shows Taylor's __acceleration__, based on a safe and unsafe motion. Since she changes from a constant speed to a negatively changing speed at 2.2 second, her acceleration changes from 0m/s² to -4m/s².

= = =**Avoiding Stop Light Violations with a Better Knowledge of Kinematics:**= Using the formulas **velocity (final)=acceleration*time+velocity (initial)** and **displacement = ½ × acceleration × time² + initial velocity × time,** a driver can calculate acceleration. This number will indicate the necessary change in speed each sec to reach the beginning of the intersection before the light turns red. If the rate is a positive number, a driver must stop at the red light; it is impossible to make the light without speeding as seen in example scenario #3. However, if the acceleration rate is negative, the driver has a choice. The smaller the negative number, the less likely it is that the driver will be able to stop in time as shown in scenarios #1 and #2.

=**Conclusion:**= Running red lights can lead to fatal accidents. Using these principles of kinematics, drivers should be able to avoid this hazard. As you become familiar with these concepts, it will be easier to judge whether to stop or proceed when you see a yellow light ahead. Remember: never speed up when you see a yellow light, either slow to a stop or proceed at a constant speed. The most important thing to know is that your car has limits and it cannot be expected to defy the laws of motion. If the required negative acceleration rate is too high to safely stop, go through the light, but make sure to look left and right beforehand.

Durso Jr., F. (2006, April 6). Code red. //South Philly Review//, Retrieved from http://www.southphillyreview.com/view_article.php?id=4347
 * Sources:**

Insurance Institute for Highway Safety, Highway Loss Data Institute. (2009). //Q&as: red light cameras//. Retrieved from http://www.iihs.org/research/qanda/rlr.html

//Running a red light crash//. (2008). [Web]. Retrieved from http://www.youtube.com/watch?v=sDhiS9feGsU