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Before You Travel List
QuizΒ by Lia Poole
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What is an official invitation letter? The companies write a letter of invitation-business when they host business visitors from abroad or from the same region or country. The business visitors can be investors; potential buyers may be conference visitors, business partners, employees of any company, or mere individuals who come for training at the companyβs facilities. If a company is inviting any visitor, a representative of that company must write the letter. Also, the firms must have some specific people who would sign the invitation letters. These letters are very much precise, only containing the necessary information. The invitation letter should state the name of the business organization they represent and their relationship to the host (e.g., distributor, regional sales reps, etc.). The letter should articulate the planned dates of travel, and must be formatted professionally. What is a personal invitation letter? A Personal invitation letter is a letter one writes to invite people to a party or a social gathering at a very personal level. It is a formal request asking for the personβs presence at the event that is going to take place. All the relevant details regarding the event like the reason, date, time and venue and the dress code, if any, must be provided in the invitation letters. This will keep the guests informed, and they will feel happy to attend the event. The style and tone of the letter would depend upon the relationship between the sender and receiver. Through the letter, you should be able to make the receiver feel that you highly value his/her presence at the party or the event. A personal invitation letter can be written to invite a person to a birthday party, wedding, conference, meeting, dinner, etc. Before writing the letter, make sure you have a list of people whom you would like to invite to the party or the event. How to Write an Invitation Letter Writing an invitation letter becomes easy and swift once you get through the tips and the format of the invitation letter provided below. Usually block, semi-block or a modified block format is used for official invitation letters. The important aspects of any invitation letters are date, time, salutations and closing. For more advice refer to the tips provided. Tips for Invitation Letter Writing β Organize the Matter β Before you draft an invitation letter ensure that you have all the required material. This material refers to a list of the people to be invited, sequential order of the events, timings of the events, special guest, official documents, photocopies and any other required item. Some items may also need to be attached along with the letter, keep them alongside. Refer to these as and when required. All the relevant documents will help you in drafting the letter. β Drafting β You donβt just write a letter straightway and post it. It has to be reviewed and finalized. One of these processes is drafting. Drafting ensures that your mistakes and their rectification arenβt passed on to the invitation itself. Make all the mistakes in the draft itself. Drafting an invitation letter is important as sometimes we may make mistakes that we are not able to see but they are visible to others. One may require a draft to be approved by seniors before it is finalized. A second opinion from a friend or peer etc. may be required as well to determine certain things. β Politeness β You donβt need to be told that you have to use polite language while writing an invitation letter, why would you be rude when sending an invitation? True, but you have to remind yourself of certain manners and etiquettes required of an invitation. Your invitation is your initiative, not the recipients so you need to be gracious. Always begin the letter with a welcome note instead of straightforward information of the invitation. Words of respect and gratitude are symbols of courtesy and politeness, always expressing your gratitude in the beginning and the end of the letter. β Positive Tone β The gesture of welcome and gratitude themselves are positive points of an invitation letter. Apart from these, gestures of appreciation and anticipation are other positive points which can persuade a guest to attend the event. When you show your appreciation and anticipation towards the recipient through your words, it is an acknowledgement of his importance and thereby a positive approach. Towards this effect two tenses are used within the invitation letter, the present and the future. The present tense conveys information about the event and the future tense conveys an anticipated presence of the guest. β Offer Assistance β An invitation being the responsibility of the sender, the assistance to the recipient by default becomes a responsibility of the host. The more facilities you provide the better the chances of someoneβs attendance. You can offer pick up and drop services, accommodation, meals, provide them contact numbers in case you are not present at the venue and other required assistance. Relevant facts like date, time and venue of the event in the beginning itself is itself assisting. These assistances encourage a positive response from the invitees. β Special Instructions β Some occasions require special instructions for the guests. These instructions can be: 1. Dress code 2. Road or route map 3. Purpose of the occasion β birthday, honor, anniversary etc. 4. Return gift 5. Response or confirmation to the invitation 6. Attire and items required for the guest to bring 7. No eatables allowed 8. Entrance only by invitation 9. 2 people per pass 10. No weapons allowed β Length of the Matter β A simple invitation letter will only contain only the relevant facts. A simple invitation letter features an introduction which allows the sender to introduce themselves and or the organization they represent. A simple background of the individual or company is enough. Though invitations are meant to be concise and straightforward, it isnβt necessary. You can vary the length as per your need and requirement. Wedding and party invitation letters are not lengthy as compared to visit and certain personal invitation letters. β Using Letterhead β As a rule official Invitation letters require a letterhead. Letterhead represents the sender and its inclusion is authority established. If you have a pre printed letterhead then use that. Personal Invitation letters donβt require letterheads and one can use it as per oneβs desire. β Gesture of Appreciation β Next, the appreciation for the guest to attend an activity or event must be shown. This can be completed with a formal note, stating that you look forward to seeing the individual at the event. β Donβt forget the Enclosure β Some requests require certain documents to be attached; these can be the photocopies of documents like agreements, hard copies of email received, earlier correspondence, receipts, warranty etc. Keep original copies of all your letters, faxes, e-mails, and other related documents. β Closing the Letter β Start the letter with Gratitude and end it with the same. It is a professional and social courtesy. At the end of your last paragraph is written, a complimentary close of the likes of βSincerelyβ, βThank youβ, βTrulyβ is essential. Close the letter by restating your appreciation and gratitude. β Proofreading β Check for - awkward phrases, grammatical errors, incomplete sentences and spelling mistakes. Fix them with appropriate punctuation and remove dull or lifeless sentences and replace them with clever phrasing, poetry or a themed approach. This is the final step; the draft will be reviewed and revised before it acquires a proper form. Read it aloud to yourself to figure out mistakes which are missed out in writing. β Inform in Advance β Invitation letters need to be sent in advance. Try to send the invitation letter two weeks or more in advance. The recipient needs to know in advance so that they can adjust their schedules, book tickets or make other arrangements which are essential.
Present Continuous Tense Quiz Multiple Choice Questions Which sentence is in the present continuous tense? A) She sings beautifully. B) They are eating dinner now. C) He played the piano. D) I have finished my homework. Correct Answer: B Fill in the blank: "They __________ (to watch) a movie tonight." A) watches B) watched C) are watching D) is watching Correct Answer: C What does the present continuous tense usually express? A) General truths B) Habits C) Actions happening right now D) Completed actions Correct Answer: C Which sentence is NOT in the present continuous tense? A) I am meeting my friends later. B) She is studying for her exams. C) He reads a book every night. D) We are visiting our grandparents this weekend. Correct Answer: C Choose the correctly formed question in the present continuous tense. A) Do you going to the party? B) Are you go to the party? C) Are you going to the party? D) Is you going to the party? Correct Answer: C Fill-in-the-Blanks I __________ (to listen) to music right now. Answer: am listening She __________ (to not study) at the moment; she's watching TV. Answer: is not studying __________ (to be) they __________ (to play) soccer in the park? Answers: Are; playing The dog __________ (to bark) because it's hungry. Answer: is barking We __________ (to plan) our holiday; we can talk later. Answer: are planning Present Perfect Tense Quiz Multiple Choice Questions Which sentence is in the present perfect tense? A) They go to Spain every summer. B) She is going to the supermarket. C) I have seen that movie before. D) He reads the newspaper. Correct Answer: C Fill in the blank: "She __________ (to never, eat) sushi before." A) has never eaten B) is never eating C) never eats D) have never eaten Correct Answer: A What does the present perfect tense usually express? A) Actions happening right now B) Actions that have a connection with the present C) Regular habits D) Future plans Correct Answer: B Which sentence is NOT in the present perfect tense? A) I have just finished my homework. B) They have lived here for ten years. C) We are watching a new film. D) She has written three books. Correct Answer: C Choose the correctly formed question in the present perfect tense. A) Have you ever been to Italy? B) Do you ever been to Italy? C) Are you ever been to Italy? D) Is you ever been to Italy? Correct Answer: A Fill-in-the-Blanks They __________ (to not, see) the Eiffel Tower yet. Answer: have not seen I __________ (to read) three books this month. Answer: have read How many times __________ you __________ (to be) to London? Answers: have; been She __________ (to not, decide) on her major yet. Answer: has not decided We __________ (to travel) to three different countries since last year. Answer: have traveled
To the Lakota, and other indigenous people on North America's Great Plains, the bison was an essential part of their culture ( expressed in the quote on the previous page). The bison provided meat for nutrition, a hide for clothing and shelter, bones for tools, and fat for soap. The bison was also central to their religious beliefs. So, when European settlers hunted the bison nearly to extinction, Lakota culture suffered. Culture is central to a society and the identity of its people, as well as its continued existence. Therefore, geographers study culture as a way to understand similarities and differences among societies across the world, and in some cases, to help preserve these societies. Analyzing Culture All of a group's learned behaviors, actions, beliefs, and objects are a part of culture. It is a visible force seen in a group's actions, possessions, and influence on the landscape. For example, in a large city you can see people working in offices, factories, and stores, and living in high-rise apartments or suburban homes. You might observe them attending movies, concerts, or sporting events. Culture is also an invisible force guiding people through shared belief systems, customs, and traditions. Culture is learned, in that it develops through experiences, and not merely transmitted through genetics. For example, many people in the United States have developed a strong sense of competitiveness in school and business, and believe that hard work is a key to success. These types of elements, visible and invisible, are cultural traits. A series of interrelated traits make up a cultural complex, such as the process of steps and acceptable behaviors related to greeting a person in different cultures. A single cultural artifact, such as an automobile, may represent many different values, beliefs, behaviors and traditions and be representative of a cultural complex. Since culture is learned there are many ways that one generation passes its culture to the next. Children and adults learn traits three ways: β’ imitation, as when learning a language by repeating sounds or behaviors from a person or television β’ informal instruction, as when a parent reminds a child to say "please" β’ formal instruction, as when students learn history in school 132 HUMAN GEOGRAPHY: AP" EDITION CULTURAL COMPLEX OF THE AUTOMOBILE The automobile provides much more than just transportation, as it reflects many values that are central to American culture. Origins of Culture The area in which a unique culture or a specific trait develops is a culture hearth. Classical Greece was a culture hearth for democracy more than 2,000 years ago. New York City was a culture hearth for rap music in the 1970s. Geographers study how cultures develop in hearths and diffuse-or spread-to other places. Geographers also study taboos, behaviors heavily discouraged by a culture. For example, many cultures have taboos against eating certain foods, such as pork or insects. What is considered taboo changes over time. In the United States, marriages between Protestants and Catholics were once taboo, but they are not widely opposed now. Traditional, Folk, and Indigenous Cultures With the beginning of the Industrial Revolution in the late 18th century, modern transportation and communication connected people as never before and led to extensive cultural mixing, especially as cities have grown. The world prior to this time was very different; however, remnants of the past are still evident in our modern cultures. Traditional, folk, and indigenous cultures share some important characteristics and are often grouped together, but they do have some subtle differences. Traditional Culture Recently, the meanings of traditional, folk, and indigenous culture have begun to merge, causing geographers to debate when each should be used. Increasingly, the term traditional culture is used to encompass all three cultural designations. All three types share the function of passing down long-held beliefs, values, and practices and are generally resistant to rapid changes in their culture. Folk Culture The beliefs and practices of small, homogenous groups of people, often living in rural areas that are relatively isolated and slow to change, are known as folk cultures. Like all cultures, they demonstrate the diverse ways that people have adapted to a physical environment. For example, people around the world learned to make shelters out of available resources, whether 3.1: INTRODUCTION TO CULTURE 133 it was snow or mud bricks or wood. However, people used similar resources such as wood differently. In Scandinavia, people used trees to build cabins. In the American Midwest, people processed trees into boards, built a frame, and attached the boards to it. Many traits of folk culture continue today. Corn was first grown in Mexico around 10,000 years ago, and it is still grown there today. While many elements of folk culture exist side by side with modern culture, there are people whose societies have changed little, if at all, from long ago. These people practice traditional cultures, those which have not been affected by modern technology or influences. They often live in remote regions, such as some small tribes in the Amazon rainforest, and have scant knowledge of the outside world. As the lines continue blurring between cultural designations, the Amish of Pennsylvania are often referenced as both folk and traditional culture. Indigenous Culture When members of an ethnic group reside in their ancestral lands, and typically possess unique cultural traits, such as speaking their own exclusive language, they are considered an indigenous culture. Some indigenous peoples have been displaced from their native lands, but still practice their indigenous culture. Native Americans in the United States, such as the Navajo, have kept indigenous cultural practices. First Nations of Canada, such as the Inuit, have also retained their indigenous culture. Globalization and Popular Culture As a result of the Industrial Revolution, improvements in transportation and communication have shortened the time required for movement, trade, or other forms of interaction between two places. This development, known as space-time compression (see Topics 1.4 and 3.6), has accelerated culture change around the world. In 1817, a freight shipment from Cincinnati needed 52 days to reach New York City. By 1850, because of canals and railroads, it took half that long. And by 1852, it took only 7 days. Today, an airplane flight takes only a few hours, and digital information takes seconds or less. Similar change has occurred on the global scale. People travel freely across the world in a matter of hours, and communication has advanced to a point where people share information instantaneously across the globe. The increased global interaction has had a profound impact on cultures, from spreading English across the world to instant sharing of news, events and music. Globalization specifically refers to the increased integration of the world economy since the 1970s. The process of intensified interaction among peoples, governments, and companies of different countries around the globe has had profound impacts on culture. The culture of the United States is intertwined with globalization. Through the influence of its corporations, Hollywood movies, and government, the United States exerts widespread influence in other countries. But other countries also shape American culture. For example, in 2019, the National Basketball Association included players from 38 countries or territories. When cultural traits- such as clothing, music, movies, and types of 134 HUMAN GEOGRAPHY: AP. EDITION businesses-spread quickly over a large area and are adopted by various groups, they become part of popular culture. Elements of popular culture often begin in urban areas and diffuse quickly through globalization processes such as the media and Internet. These elements can quickly be adopted worldwide, making them part of global culture. People around the world follow European soccer, Indian Bollywood movies, and Japanese animation known as anime. With people in many nations wearing similar clothes, listening to similar music, and eating similar food, popular cultural traits often promote uniformity in beliefs, values, and the cultural landscape across many places The cultural landscape, also known as the built environment (see Topic 3.2), is the modification of the environment by a group and is a visible reflection of that group's cultural beliefs and values. Traditional Culture to Popular Culture Popular culture emphasizes trying what is new rather than preserving what is traditional. Many people, especially older generations or those who follow a folk culture, openly resist the adoption of popular cultural traits. They do this by preserving traditional languages, religions, values, and foods. While older generations often resist the adoption of popular culture, they seldom are successful in keeping their traditional cultures from changing, especially among the young people of their society. One clash between popular and traditional culture is occurring in Brazil. As the population expands to the interior of the rain forest, many indigenous cultures, like the Yanamamo tribe, have more contact with outside groups. Remaining isolated by the forest is becoming increasingly difficult as many young people from the indigenous cultures become exposed to popular culture and begin to integrate into the larger Brazilian society. As the young people leave their communities, they are more likely to accept popular culture at the expense of their indigenous cultural heritage, which threatens the very existence of their folk culture. Traditional culture typically exhibits horizontal diversity, meaning each traditional culture has its own customs and language that makes it distinct from other culture groups. Yet, people people within each group are usually homogeneous, or very similar to each other. By contrast, popular culture typically exhibits vertical diversity, meaning that modern urban societies are usually heterogeneous, or exhibiting differences, within the society and usually contain numerous multiethnic neighborhoods. However, on a global scale popular cultures are relatively similar with the same type of malls, shops, fast food, and clothing. Urban global culture centers are not identical, yet, global cities often do not have as much horizontal diversity across space as folk cultures. 3.1: INTRODUCTION TO CULTURE 135 COMPARING TRADITIONAL AND POPULAR CULTURE Trait Traditional Culture Popular or Global Culture Society β’ Rural and isolated location β’ Urban and connected location β’ Homogeneous and β’ Diverse and multiethnic indigenous population population β’ Most people speak an β’ Many people speak a global indigenous or ethnic local language such as English or language Arabic β’ Horizontal diversity β’ Vertical diversity Social β’ Emphasis on community and β’ Emphasis on individualism and Structure conformity making choices β’ Families live close to each β’ Dispersed families other β’ Weakly defined gender roles β’ Well-defined gender roles Diffusion β’ Relatively slow and limited β’ Relatively rapid and extensive β’ Primarily through relocation β’ Often hierarchical β’ Oral traditions and stories β’ Social media and mass media Buildings and β’ Materials produced locally, β’ Materials produced in distant Housing such as stone or grass factories, such as steel or glass β’ Built by community or owner β’ Built by a business β’ Similar style for community β’ Variety of architectural styles β’ Different between cultures β’ Similar between cities β’ Traditional architecture β’ Postmodern / contemporary architecture Food β’ Locally produced β’ Often imported β’ Choices limited by tradition β’ Wide range of choice β’ Prepared by the family or β’ Purchased in restaurants community Spatial Focus β’ Local and regional β’ National and global Artifacts, Mentifacts, and Sociofacts Whether a cultural attribute is considered traditional, folk, indigenous, or popular in nature, it is valuable to differentiate between elements of culture that can be seen and those that can not. There are artifacts that comprise the material culture, which consists of tangible things, or those that can be experienced by the senses. Art, clothing, food, music, sports, and housing types are all tangible elements of culture. Another element of the study of artifacts is understanding the techniques to use or build a specific artifact. Artifacts can be unique to a particular culture, or can be shared. For example, people of all cultures need to communicate through language, yet there are many groups that possess languages unique to their culture. The ability to read, write and understand the English language is an artifact of importance for much of popular global culture. 136 HUMAN GEOGRAPHY: AP" EDITION Mentifacts comprise a group's nonmaterial culture and consist ofintangible concepts, or those not having a physical presence. Beliefs, values, practices, and aesthetics (pleasing in appearance) determine what a cultural group views as acceptable and desirable. Mentifacts can also be unique or shared. People of many cultures possess an belief in one or many deities, and often the deities are unique to that culture. The belief in a god is a mentifact-the religious building or symbols are artifacts. Cultural groups also possess sociofacts, which are the ways people organize their society and relate to one another. Taken altogether, people tend to see the whole of their culture as greater than the sum of its individual parts. Sociofacts are embodied through families, governments, sports teams, religious organizations, education systems, and other social constructs. As with artifacts and mentifacts, sociofacts may also be unique or similar to other societies. Families are the foundations of most societies, yet what constitutes the structure of a family may vary widely between cultural groups. For example, Western cultures tend to view the nuclear family, consisting of the parents and their children as the basic family unit. By contrast, in many Western African cultures the norm is the extended family, consisting of several generations and other family members such as cousins living under one roof.
Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: β’ Free-falling objects do not encounter air resistance. β’ All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs β’ Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 β’ a β’ d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 β’ (-8.00 m/s2) β’ d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) β’ d (16.0 m/s2) β’ d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi β’ t + Β½ β’ a β’ t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) β’ (4.1 s) + Β½ β’ (6.00 m/s2) β’ (4.10 s)2 d = (0 m) + Β½ β’ (6.00 m/s2) β’ (16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: β’ An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. β’ If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. β’ If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. β’ If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi β’ t + Β½ β’ a β’ t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) β’ (t) + Β½ β’ (-9.8 m/s2) β’ (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) β’ (t)2 -8.52 m = (-4.9 m/s2) β’ (t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 β’ a β’ d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 β’(-9.8m/s2) β’d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) β’d (-19.6 m/s2) β’ d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) β’ d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.
Before you travel FIB
Before you Travel Scramble
How to Stop Avalanchesnow with explosives, or by erecting snow fences. Explosives Explosives are primarily used to prevent avalanches, especially at ski resorts where other methods are often impractical. Maintenance staff from the ski resort travel to potential avalanche areas and areas with steep slopes. First, they measure the depth of the snow and its quality. They want to check for hard, loose, wet or icy snow layers. If an area is considered dangerous, small explosives are fired into the side of the steep terrain. The explosion loosens the top layer of snow, which tumbles harmlessly down the mountainside. But using explosives is costly and dangerous. Some researchers are currently experimenting with the cheaper and safer method of using ultrasonic sound waves that shock the snow into falling, averting an avalanche and saving lives. Snow Fences It is very common to put up snow nets or snow fences. These nylon nets or wooden and steel fences are placed at the top of slopes. They prevent the buildup of snow on the downwind side, thereby lessening the chance of a slab avalanche. Beacons and Radio Devices Fortunately, there are companies that specialize in making rescue beacons. These are small electronic devices that send out a radio signal to search and rescue crews. Most people who venture into the backcountry carry some sort of beacon or GPS device. They can help locate a buried victim up to 80 meters away. However, these beacons and GPS devices only send out a signal if the victim turns it on. Often, the victim is too injured to think clearly and press the 'on button.' If search and rescue crews do not quickly reach the victims, the skiers will not be discovered in time. Surviving an Avalanche If you are ever caught in an avalanche, the chances are slim that you will survive. If you are not killed instantly, you only have a short time (15~35 minutes) before your oxygen runs out. Take off your ski, boots and poles. Use a swimming motion to claw your way to the surface. Often people do not know which way is up or down. The effect of this is disorientation. It is not uncommon for avalanche victims to dig in the wrong direction. With proper precautions, both skiers and ski resorts can avoid the tragedy of an avalanche.
How to Stop Avalanches ToB A major concern of ski resorts is avalanche control. Most avalanches occur outside the boundaries of the regular groomed ski runs. But each year, skiers and trekkers on snowshoes go into these remote areas where most avalanches occur. There are two primary ways to prevent avalanches-by blasting the snow with explosives, or by erecting snow fences. Explosives Explosives are primarily used to prevent avalanches, especially at ski resorts where other methods are often impractical. Maintenance staff from the ski resort travel to potential avalanche areas and areas with steep slopes. First, they measure the depth of the snow and its quality. They want to check for hard, loose, wet or icy snow layers. If an area is considered dangerous, small explosives are fired into the side of the steep terrain. The explosion loosens the top layer of snow, which tumbles harmlessly down the mountainside. But using explosives is costly and dangerous. Some researchers are currently experimenting with the cheaper and safer method of using ultrasonic sound waves that shock the snow into falling, averting an avalanche and saving lives. Snow Fences It is very common to put up snow nets or snow fences. These nylon nets or wooden and steel fences are placed at the top of slopes. They prevent the buildup of snow on the downwind side, thereby lessening the chance of a slab avalanche. Beacons and Radio Devices Fortunately, there are companies that specialize in making rescue beacons. These are small electronic devices that send out a radio signal to search and rescue crews. Most people who venture into the backcountry carry some sort of beacon or GPS device. They can help locate a buried victim up to 80 meters away. However, these beacons and GPS devices only send out a signal if the victim turns it on. Often, the victim is too injured to think clearly and press the 'on button.' If search and rescue crews do not quickly reach the victims, the skiers will not be discovered in time. Surviving an Avalanche If you are ever caught in an avalanche, the chances are slim that you will survive. If you are not killed instantly, you only have a short time (15~35 minutes) before your oxygen runs out. Take off your ski, boots and poles. Use a swimming motion to claw your way to the surface. Often people do not know which way is up or down. The effect of this is disorientation. It is not uncommon for avalanche victims to dig in the wrong direction. With proper precautions, both skiers and ski resorts can avoid the tragedy of an avalanche.