Stop+Light+Violations

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An Introduction

 * Stop lights, from their creation, have been one of the most beneficial additions to roadways since the dividing lines placed in the middle of most streets. The stop light allows drivers and pedestrians to coexist in a pleasant fashion that guarantees each party the opportunity to get exactly where they need. However, when people, whether driver or pedestrian, violate a stoplight the pleasant equilibrium is thrown into disarray. Sadly these days we find this neglect of our friendly stop lights happening all too often. This page will offer an example of how and why it happens as well as how it can be avoided, while endowing you with instructions on how you can use these same methods to solve similar problems. **

News Articles and Statistics
**Here are two articles discussing Philadelphia's plans for dealing with the rampant stop light violations.**

"Stop for the camera: Fines begin Tuesday for red light violations around City Hall in Phila." //Philadelphia Business Journal//. 8 December 2009. Philadelphia News, Web. 11 Dec 2009. <[]>.

"City Hall Red-Light Cameras Go Online." //My Fox Philly//. Fox News, Web. 11 Dec 2009. <[|http://www.myfoxphilly.com/dpp/news/local_news/120809_City_Hall_Red_Light_Camera.]

How Kinematics Applies

 * Kinematics applies in several ways here. You see it when drivers try to hastily speed through traffic lights under the impression that they can accelerate at a quick enough rate to avoid oncoming traffic or when they attempt this same stunt but do not consider how much time the brakes need to stop the car. Kinematics in this case allow us to the gain an understanding on the effects that seemingly nominal actions can have on you and the world around you. A driver increases his velocity to make the light thinking that his brake will be able to stop him immediately yet finds that brakes do not immediately stop motion but rather steadily decrease it. Kinematics will help explain and calculate all the little interactions that are behind the simple actions we choose, ones that can prove fatal if we are not careful. **

Example Scenario
**A young man is driving home early in the morning after having driven all night, leaving him weary and slow to react. He comes to a stop at a stop light behind several cars, feeling sluggish he takes a small nap at the light. When he awakes he finds all the cars once in front of him have already gone and he, assuming the light is still green without actually checking, tries to quickly catch up. He applies much too much pressure to the gas pedal and takes off at an acceleration of 5.7m/s/s. Five seconds after he started he is hit by a car, traveling at 20.1m/s, crossing the same intersection due to the fact that the light for the young man had in fact turned red, meaning he ran the light. Assume that at second zero he was at position zero.**

How To Solve
**First we are going to identify what we know…** -His acceleration was 5.7m/s/s -His starting point and time was 0 -He traveled for 5 seconds before being hit -The car that hit him was traveling at a constant velocity of 20.1m/s

**Now that we figured out the velocities we can now solve for each position. We know that position was zero at zero seconds. We also know that at one second the position will be 5.7. For the rest of the amounts we had two portions to the equations and need to solve for the rest. The equation for velocity is as follows....
 * Next we interpreted our information, we know that the velocity would have to increase by 5.7m/s each second due to the acceleration being a constant 5.7m/s/s. This is due to the fact that acceleration is change in velocity over time. Knowing this we were able to deduce that in order to determine the velocity of the next second you simply needed to add 5.7 to your previous velocity. (0+5.7, 5.7+5.7, etc.) We put this information in the table below. **
 * ** Time(s) ** || ** Velocity(m/s) ** ||
 * ** 1 ** || ** 5.7 ** ||
 * ** 2 ** || ** 11.4 ** ||
 * ** 3 ** || ** 17.1 ** ||
 * **4** || **22.8** ||
 * **5** || **28.5** ||

We know that the time is going to be done one second at a time, as shown below, so we do not need to worry about any bothersome division, leaving an unknown position-(a position we do know)=velocity. Below we have provided an example since the phrasing may be confusing.

We proceeded to subtract the time from the time before, ensuring it remains one, and the position from before in order to solve in accordance with the velocity. The lovely T-Chart shows what we did.**
 * **Time(s)** || **Velocity (m/s)** || **Equation** || **Position(m)** ||
 * **0** || **0** || **x-0=0 --> x=0** || **0** ||
 * **1** || **5.7** || **X-0=5.7 --> x=5.7** || **5.7** ||
 * **2** || **11.4** || **X-5.7=11.4 --> x=(11.4+5.7)** || **17.1** ||
 * **3** || **17.1** || **X-17.1=17.1 --> x=(17.1+17.1)** || **34.2** ||
 * **4** || **22.8** || **X-34.2=22.8 --> x=(22.8+34.2)** || **57** ||
 * **5** || **28.5** || **X-57=28.5 --> x=(28.5+57)** || **85.5** ||

**The graphs below show the information in the aforementioned T-Chart. Notice that in the position vs. time chart, the graph forms a parabola.** **This means that the slope is not constant, showing that the car accelerated. The velocity chart, however, shows that though the velocity was not the same each time it increased by a constant amount.

In this graph, the acceleration vs. time graph, you can see that the acceleration stayed the same through out the problem. We did not really need to make a graph for this particular section due to the fact that the directions told us what the acceleration was but it never hurts.** **In order to find the positions of the second car we simply need work backwards from second 5, where we know both cars are located.****(****Collision point.) We know that the car was traveling in a negative direction when it hit the young man's vehicle, meaning the position for the other car will be larger at earlier time intervals as adequately shown below.** **We have now dissected this accident to, hopefully, understand exactly what occurred.**
 * Now that we have addressed the young male driver's car we can start to look into the accident itself. In order to understand the circumstances that led to this accident we also need to look at the driver of the other car. What we need to know in order to solve this problem is the velocity at which the car was moving, a position, and the time interval with which we are concerned. Luckily for us we have just hose things! **
 * **Time(s)** || **Velocity(m/s)** || **Equation** || **Position(x)** ||
 * **5** || **20.1** || **85.5 (given)** || **85.5** ||
 * **4** || **20.1** || **85.5+20.1** || **105.6** ||
 * **3** || **20.1** || **105.6+20.1** || **125.7** ||
 * **2** || **20.1** || **125.7+20.1** || **145.8** ||
 * **1** || **20.1** || **145.8+20.1** || **165.9** ||
 * **0** || **20.1** || **165.9+20.1** || **186** ||

How To Avoid This Hazard

 * As the work above shows, these accidents happen almost instantaneously and are often hard to maneuver out of quickly. These particular events are ones best prevented with a bit of forethought. This means that when you approach a light and it is already yellow to not try to speed through it. However, if you find yourself approaching a light consider the amount of time it would take for you to both slow down and stop. The idea of guessing whether or not you are capable of making a light solely on gut instinct is dangerous and the principals discussed here can easily be applied. If you know the distance from the light, the velocity you are traveling, and the length of the light you can easily calculate the likelihood of you making the light. Be sure to recall the importance of using these concepts when you find yourself in this situation, we can guarantee it will help .**

Conclusion
**When trying to decide if taking the light is for you,** **bear in mind the things addressed here and consider all factors at work.** **You need to consider the length of the light, how quickly your car can accelerate, the amount of time it takes to brake, topped off by the fact that you have no idea how other drivers will react. Each of things is sensationally important in making the decision on whether or not to take the light, each of more consequence than we ever seem to acknowledge. This site has given you the tools to be able to understand the logistics behind making the right decisions but all of this comes to naught if you rely solely on gut instinct. From those us who have calculated the aspects to car accidents and have experienced driving ourselves, be careful and think first.**