How to Define Acceleration

How to Define Acceleration Acceleration is the rate of change of velocity as a function of time. It is a vector, meaning that it has both magnitude and direction. It is measured in meters per second squared or meters per second (the objects speed or velocity) per second. In calculus terms, acceleration is the second derivative of position concerning time or, alternately, the first derivative of the velocity concerning time. Acceleration- Change in Speed The everyday experience of acceleration is in a vehicle. You step on the accelerator, and the car speeds up as increasing force is applied to the drive train by the engine. But deceleration is also acceleration - the velocity is changing. If you take your foot off the accelerator, the force decreases and velocity is reduced over time. Acceleration, as heard in ads, follows the rule of the change of speed (miles per hour) over time, such as from zero to 60 miles per hour in seven seconds. Units of Acceleration The SI units for acceleration are m / s2(meters per second squared or  meters per second per second). The gal or galileo (Gal) is a unit of acceleration used in gravimetry but is not an SI unit. It is defined as 1 centimeter per second squared. 1 cm/s2 English units for acceleration are feet per second per second,  ft/s2 The standard acceleration due to gravity, or standard gravity  g0 is the gravitational acceleration of an object in a vacuum near the surface of the earth. It combines the effects of gravity and centrifugal acceleration from the rotation of the Earth. Converting Acceleration Units Value m/s2 1 Gal, or cm/s2 0.01 1 ft/s2 0.304800 1 g0 9.80665 Newtons Second Law- Calculating Acceleration The classical mechanics equation for acceleration comes from Newtons Second Law: The sum of the forces (F) on an object of constant mass (m) is equal to mass m multiplied by the objects acceleration (a). F am Therefore, this can be rearranged to define acceleration as: a F/m The result of this equation is that if no forces are acting on an object (F   0), it will not accelerate. Its speed will remain constant. If mass  is added to the object, the acceleration will be lower. If  mass  is removed from the object, its acceleration will be higher. Newtons Second Law is one of the three laws of motion Isaac Newton published in 1687 in  Philosophià ¦ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy).   Acceleration and Relativity While Newtons laws of motion apply at speeds we encounter in daily life, once objects are traveling near the speed of light, the rules change. Thats when Einsteins special theory of relativity is more accurate. The special theory of relativity says it takes more force to result in acceleration as an object approaches the speed of light. Eventually, acceleration becomes vanishingly small and the object never quite achieves the speed of light. Under the theory of general relativity, the principle of equivalence says that gravity and acceleration have identical effects. You dont know whether or not you are accelerating unless you can observe without any forces on you, including gravity.

Sum of Squares Formula Shortcut

Sum of Squares Formula Shortcut The calculation of a sample variance or standard deviation is typically stated as a fraction. The numerator of this fraction involves a sum of squared deviations from the mean. In statistics, the formula for this total sum of squares is ÃŽ £ (xi - xÌ„)2 Here the symbol xÌ„ refers to the sample mean, and the symbol ÃŽ £ tells us to add up the squared differences (xi - xÌ„) for all i. While this formula works for calculations, there is an equivalent, shortcut formula that does not require us to first calculate the sample mean. This shortcut formula for the sum of squares is ÃŽ £(xi2)-(ÃŽ £ xi)2/n Here the variable n refers to the number of data points in our sample. Standard Formula Example To see how this shortcut formula works, we will consider an example that is calculated using both formulas. Suppose our sample is 2, 4, 6, 8. The sample mean is (2 4 6 8)/4 20/4 5. Now we calculate the difference of each data point with the mean 5. 2 – 5 -34 – 5 -16 – 5 18 – 5 3 We now square each of these numbers and add them together. (-3)2 (-1)2 12 32 9 1 1 9 20. Shortcut Formula Example Now we will use the same set of data: 2, 4, 6, 8, with the shortcut formula to determine the sum of squares. We first square each data point and add them together: 22 42 62 82 4 16 36 64 120. The next step is to add together all of the data and square this sum: (2 4 6 8)2 400. We divide this by the number of data points to obtain 400/4 100. We now subtract this number from 120. This gives us that the sum of the squared deviations is 20. This was exactly the number that we have already found from the other formula. How Does This Work? Many people will just accept the formula at face value and do not have any idea why this formula works. By using a little bit of algebra, we can see why this shortcut formula is equivalent to the standard, traditional way of calculating the sum of squared deviations. Although there may be hundreds, if not thousands of values in a real-world data set, we will assume that there are only three data values: x1 , x2, x3. What we see here could be expanded to a data set that has thousands of points. We begin by noting that( x1 x2 x3) 3 xÌ„. The expression ÃŽ £(xi - xÌ„)2 (x1 - xÌ„)2 (x2 - xÌ„)2 (x3 - xÌ„)2. We now use the fact from basic algebra that (a b)2 a2 2ab b2. This means that (x1 - xÌ„)2 x12 -2x1 xÌ„ xÌ„2. We do this for the other two terms of our summation, and we have: x12 -2x1 xÌ„ xÌ„2 x22 -2x2 xÌ„ xÌ„2 x32 -2x3 xÌ„ xÌ„2. We rearrange this and have: x12 x22 x32 3xÌ„2 - 2xÌ„(x1 x2 x3) . By rewriting (x1 x2 x3) 3xÌ„ the above becomes: x12 x22 x32 - 3xÌ„2. Now since 3xÌ„2 (x1 x2 x3)2/3, our formula becomes: x12 x22 x32 - (x1 x2 x3)2/3 And this is a special case of the general formula that was mentioned above: ÃŽ £(xi2)-(ÃŽ £ xi)2/n Is It Really a Shortcut? It may not seem like this formula is truly a shortcut. After all, in the example above it seems that there are just as many calculations. Part of this has to do with the fact that we only looked at a sample size that was small. As we increase the size of our sample, we see that the shortcut formula reduces the number of calculations by about half. We do not need to subtract the mean from each data point and then square the result. This cuts down considerably on the total number of operations.

Human behavior Essay Example | Topics and Well Written Essays - 2000 words

Human behavior - Essay Example Thus individuals’ omissions either willfully or accidentally in their actions have contributed to devastating occurrences. Common place accidents such as leaving an iron box on, a dropped cigarette or an electric heater left too close to flammable material have been reported to be major cause of fire fatalities in private residences (Grosse and Malvern, 2004). Consequently, most cigarettes’ related fires begin as a result of the smoker’s carelessness. Similarly, electricity is another commonly reported cause of fire in residential places due to human errors. This has been explained by (Grosse and Malvern, 2004) as emanating from either blown fuses or over warming of hot plugs and sockets. Faulty electrical wiring with exposed naked wires in the wall due to poor workmanship has also been reported to result in short circuiting, consequently starting a fire. Moreover, numerous reports have variously faulted the habit of leaving appliances like lamps, ovens and even baby monitors unplugged for over 24 hours a day. Grosse and Malvern (2004) explain that these implements have occasionally shorted out starting a fire. In the same vein, leaving fireplaces and heating devices such as pots, burners, stoves and lighted candles unattended in rooms have frequently resulted in devastating consequences according to the views of Duncan (2005). Research findings have associated majority of these causes to particular rooms in private residences. Duncan (2005), Elaine (2000) and Grosse and Malvern (2004) have variously demonstrated that the kitchen is the number one cause of domestic fires since it contains numerous hazardous items like the frying pans that can cause fire easily. Furthermore, majority of the mentioned risky items are probably stored in the kitchen. Overloading extension cords in the bedroom with electrical devices such as electric blankets or warmers and heaters with no lab-approval have significantly increased fire risks in the bedroom

Marketing Principles Essay Example | Topics and Well Written Essays - 2750 words

Marketing Principles - Essay Example The main competitor has however been Pepsi Company. The latter for instance has a market share of about 75% in the Asian market. This is compared to 25% of the coca cola company in the same market. One of the main concerns in the company has been the sharp drop in the consumption of the sugary soft drinks. The drop has been witnessed in the United States, which offers the largest market, and the United Kingdom. The major cause of drop has been health concerns. For instance, majority of people with diabetes cannot drink the normal soft drinks. In addition to that, the increased lifestyle diseases have prompted majority of people to seek more healthy drinks. To achieve this, most consumers have shifted to sugarless drinks and fresh juices. This has put the coca cola company in an awkward situation with no option than begin production of sugar free products to maintain its growth and market control. Despite this, there have been allegations that some of the chemicals used as ingredients in the manufacture of coke may cause people to get cancer. It is this fear that has led to a sharp drop in consumptions. In India for instance, there was a sharp drop of about 11% in 2003 after the ministry of health raised health concern issues (Crowley 2000, p.98). To overcome the above challenges, there is need for the company to produce a new product will address the gap in the market. The main challenge has been the need to produce healthy drinks. Although the Diet Coke has been produced to address the problem, it is only found in few markets such as the United States and United Kingdom (Elcock 2000, p.90). The drink contains fewer calories compared with the normal drinks. However, the introduction of the new product does not mean that the company should stop the production of the present products. It is important to note that different consumers have different tastes and preferences. For that reason, the new product is aimed at addressing the gap and the new demand in the mar ket. This is imperative for gaining a competitive edge, in a market that is dominated by other companies such as Pepsi. The latter company has attracted a large pool of clients because it produces some of the most health drinks. In order to facilitate the production of a new product, the coca cola company needs to have an objective strategy. Apart from carrying out a marketing research to collect important information, the 7Ps of marketing mix and new product development process will be considered. This will assist the company make informed decision before making any decision. Task 1 Marketing is a wide concept that involves a number of processes. Firstly, the business communicates to the customers directly through an avenue. The customers get the knowledge of what is being produced in a market. Secondly, marketing is also a strategy employed by a company to gain a competitive edge over its clients. The Coca Cola Company has been using the marking strategy to attract more clients an d retain the current ones. The process involves advertisement and different forms of communications meant to reach the clients. Marketing concepts refer to the process through which the management seeks to fulfil both the identified and unidentified needs of the society. To achieve this though, different marketing orientations such as branding, business and industrial marketing and society

Communication Reflection Essay -- Business

Introduction On Monday, November 14, 2011, Terry Burnham, Shawn Carlson, Roger Chikamura, Heidi Davidson and Natasha DeJesus were assigned membership of Team 1 for a virtual team project. The purpose of the project was to conduct a leadership analysis of a world-renowned leader, to be presented in the form of a narrated PowerPoint presentation. Areas of organizational behavior to be analyzed include: leadership of diversity practices; leadership values, personality and decision-making; leadership of organizational culture; leadership of follower motivation; and overall success as a leader. Team 1, by mutual consent, chose to use e-mail as the primary means of communication. Although, the planning and execution of the project, was carried out efficiently and considered a success by all members of the team, there are still a number of lessons that were learnt for future projects. Virtual Teams According to Kurland and Bailey (1999) a virtual team â€Å"consists of team members who are geographically dispersed and who come together by way of telecommunications technology. Each team member may be located in a traditional office setting, but the offices are not proximate to one another† (p. 56). This definition is supported by Berry (2011) who adds that the two main differences between virtual and regular teams are that the members of virtual teams may be dispersed geographically and rely predominately on computer-mediated communication. As stated by Robbins and Judge (2011) virtual teams face a number of particular challenges. Members experience very little social interaction and do not feel the benefit of the usual give-and-take experienced by teams. They tend to be more task-orientated and members often report less satisfactio... ...n be taken away from this project is that virtual teams work well when members are motivated and focused. But, had one, or more, members been uncommunicative, unreliable, or comfortable with the use of email as a primary means of communication, the team may have struggled to reach its goal. Other means of communication would have been required, and a more authoritarian form of leadership needed to keep the whole team focused. â€Æ' References Berry, G. R. (2011). Enhancing Effectiveness on Virtual Teams. Journal Of Business Communication, 48(2), 186-206. doi:10.1177/0021943610397270 Kurland, N.B., & Bailey, D.E. (1999). Telework: The advantages and challenges of working here, there, anywhere, and anytime. Organizational Dynamics, Autumn, 53-68. Robbins, S.P., & Judge, T.A. (2011). Organizational behavior (14th ed.). Upper Saddle River: Pearson Prentice Hall

Beautiful Boy Application Essay

He kept experimenting with more drugs and finally Crystal Meth. To be honest I think that he may have never developed the full capacity for formal reasoning. He also had a lot of different environmental and cultural influences that had a huge impact on him. Certain things would lead him towards the path of drugs, and he couldn’t reason to himself differently. â€Å"Now I am in my own program to recover from my addiction to [Nic’s addiction]† (p. 305). I feel like that is a good example of how â€Å"logical† his reasoning really is. 2. Apply the concepts of Erikson Theory to Nic’s Development. At age 4 Nic’s parents got divorced. That was during the Preschool stage, where the conflict is Initiative vs. Guilt. In this stage children need to begin asserting control and power over their environment. Nic was doing well in this stage and the school age stage as well. His grades well good, he had friends and was active and involved in sports. His father thought that Nic was coping well because he was doing so well in school and playing sports. â€Å"Nic was excelling in school and I could have been happier. (30) However related to Preschool stage – Nic was able to control his grades, and his activities therefore he was about to successfully show his power. However, at age 12 Nic’s father found pot in Nic’s back pack. This is the adolescence stage where the conflict is Identity vs. Role Confusion. This is where teens need to develop a sense of self and personal identity. Success leads t o an ability to stay true to yourself, while failure leads to role confusion and a weak sense of self. Well Nic was not successful and true to himself because by the age 18 he had experimented with many other drugs and was on looking towards Crystal Meth. At this point, he has lost his true identity and is going off track. Going into his Young Adulthood he was already strong on Meth. He became more and more into the drug; everyday losing more of himself and hurting his family. The vicious cycle never seemed to end. 3. Apply Family Systems theory to the Sheff family. What concepts are evident in their interactions? â€Å"We are dysfunctional†¦I’m not sure if I know any ‘functional’ families, if functional means a family without difficult times and members who don’t have a full range of problems. (14) The Sheff family was dysfunctional, but also considering all the challenged and obstacles they went through with Nic that can cause a strain, which would certainly not result in normal functional family. And I would have to agree with David – I don’t know if I know any â€Å"functional families. † Nic certainly was the most difficult member in the family. Calls to the hospitals and long nights wondering if Nic was OK are things his dad became very familiar with. When Nic was on the street, his dad would drive around looking for him, hoping to find him and get him help. That would cause strain on any family. His father tried to instill family roles and family rules and boundaries; however Nic would always end up on his own path –Crystal Meth. The family roles were very unclear. Did anybody even really know the real Nic? (probably not) Also, there was really never any consistency in the family. I mean the father would try his best but things always would get off track when it came to Nic and Meth. What was consistent was the â€Å"typical behaviors† and â€Å"the way it is† that the family became accustom too. Nic’s lie, stealing, and using. To me it seemed like the family was slowly disconnecting. Families are systems of interconnected and interdependent individuals; none can be understood when isolated from the family. â€Å"(pp) 4. What characteristics of resilience do you see in Nic? * He valued learning and he had excelled at writing. * I believe that he did have positive relationships with caring adults when he was in the right state of mind. * He also d id have problem solving skills. â€Å"Now I am in my own program to recover from my addiction to [Nic’s addiction]† (p. 305). He did not always make the best choice but when not on meth he could. * He did like to help others – especially his family when he was on the right path.

The Sexism Of Women And Women s Power, Possibilities, And...

The sexism in Shakespearean time against women limited the women s power, possibilities, and fair treatment. The play Hamlet written by William Shakespeare illustrated the gender inequality and the affects it has on the two female characters in the play Ophelia and Gertrude. The social and legal roles and rules for women mere a major impact on how the women lived and what was expected of them. Religion has limited women in regards to their position to men, making them inferior. As mentioned in the Social History of England By Horrox, Rosemary, and W. M. Ormrod. A: Legal Treatise Henry of Bracton in the thirteenth century said Women differ from men in many respects for their position is inferior to men. This has†¦show more content†¦Women were not allowed to have professions, therefore limiting their work abilities. Women were expected to stay home, cook, take care of the house and raise kids. Women also did not go to school, some were taught by men and only high class women were able to have education. All these factors limited women’s independence, making them dependent on men. (Tim Lambert, Life for women in the 16th century, 2016) Marriages were often arranged, and even in the cases where they weren’t men still attempted to control it. For example, women were allowed to gain inheritance if their father or husband passed away without a male figure to pass the belongings to. However according to Rosemary Horrox, Social history of England, - lords were keen to control the marriage and remarriage. Those anxious to limit the impact of female inheritance upon the descent of land began to use entail to ensure that land would pass only in the male line, although this was a strategy that could generate major legal disputes This means that men would also attempt to marry women, in which case they would gain their inheritance. Women in the Elizabethan era were discriminated against socially and legally, and were inferior to men. Shakespeare s play Hamlet which is set in Elizabethan era discovers these inequalities from point of view of two characters Ophelia and Gertrude. Gertrude’s limited power had a negative effect on her relationships with Hamlet andShow MoreRelatedA Brief Analysis on Sexism in English5522 Words   |  23 PagesA Brief Analysis on Sexism in English Abstract Sexism is engrained in the language people speak all over the world. English, one of the most popular languages in the world is no exception. The phenomenon of sexism is not only a linguistic one, but basically, a social issue that is far more notice-worthy than the public would have thought. Demonstrations of Sexism in English are too numerous to be totally covered. 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