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West Region States
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West Region States and Capitals
South West Region of the United States of America
Southeast Asia, vast region of Asia situated east of the Indian subcontinent and south of China. It consists of two dissimilar portions: a continental projection (commonly called mainland Southeast Asia) and a string of archipelagoes to the south and east of the mainland (insular Southeast Asia). Extending some 700 miles (1,100 km) southward from the mainland into insular Southeast Asia is the Malay Peninsula; this peninsula structurally is part of the mainland, but it also shares many ecological and cultural affinities with the surrounding islands and thus functions as a bridge between the two regions. Mainland Southeast Asia is divided into the countries of Cambodia, Laos, Myanmar (Burma), Thailand, Vietnam, and the small city-state of Singapore at the southern tip of the Malay Peninsula; Cambodia, Laos, and Vietnam, which occupy the eastern portion of the mainland, often are collectively called the Indochinese Peninsula. Malaysia is both mainland and insular, with a western portion on the Malay Peninsula and an eastern part on the island of Borneo. Except for the small sultanate of Brunei (also on Borneo), the remainder of insular Southeast Asia consists of the archipelagic nations of Indonesia and the Philippines. Southeast Asia stretches some 4,000 miles at its greatest extent (roughly from northwest to southeast) and encompasses some 5,000,000 square miles (13,000,000 square km) of land and sea, of which about 1,736,000 square miles is land. Mount Hkakabo in northern Myanmar on the border with China, at 19,295 feet (5,881 meters), is the highest peak of mainland Southeast Asia. Although the modern nations of the region are sometimes thought of as being small, they are—with the exceptions of Singapore and Brunei—comparatively large. Indonesia, for example, is more than 3,000 miles from west to east (exceeding the west-east extent of the continental United States) and more than 1,000 miles from north to south; the area of Laos is only slightly smaller than that of the United Kingdom; and Myanmar is considerably larger than France. All of Southeast Asia falls within the tropical and subtropical climatic zones, and much of it receives considerable annual precipitation. It is subject to an extensive and regular monsoonal weather system (i.e., one in which the prevailing winds reverse direction every six months) that produces marked wet and dry periods in most of the region. Southeast Asia’s landscape is characterized by three intermingled physical elements: mountain ranges, plains and plateaus, and water in the form of both shallow seas and extensive drainage systems. Of these, the rivers probably have been of the greatest historical and cultural significance, for waterways have decisively shaped forms of settlement and agriculture, determined fundamental political and economic patterns, and helped define the nature of Southeast Asians’ worldview and distinctive cultural syncretism. It also has been of great importance that Southeast Asia, which is the most easily accessible tropical region in the world, lies strategically astride the sea passage between East Asia and the Middle Eastern–Mediterranean world. Within this broad outline, Southeast Asia is perhaps the most diverse region on Earth. The number of large and small ecological niches is more than matched by a staggering variety of economic, social, and cultural niches Southeast Asians have developed for themselves; hundreds of ethnic groups and languages have been identified. Under these circumstances, it often is difficult to keep in mind the region’s underlying unity, and it is understandable that Southeast Asia should so often be treated as a miscellaneous collection of cultures that simply do not quite fit anywhere else. Roofs of the Forbidden City, Beijing, China Britannica Quiz All About Asia Yet from ancient times Southeast Asia has been considered by its neighbors to be a region in its own right and not merely an extension of their own lands. The Chinese called it Nanyang and the Japanese Nan’yō, both names meaning “South Seas,” and South Asians used such terms as Suvarnabhūmi (Sanskrit: “Land of Gold”) to describe the area. Modern scholarship increasingly has yielded evidence of broad commonalities uniting the peoples of the region across time. Studies in historical linguistics, for example, have suggested that the vast majority of Southeast Asian languages—even many of those previously considered to have separate origins—either sprang from common roots or have been long and inseparably intertwined. Despite inevitable variation among societies, common views of gender, family structure, and social hierarchy and mobility may be discerned throughout mainland and insular Southeast Asia, and a broadly common commercial and cultural inheritance has continued to affect the entire region for several millennia. These and other commonalities have yet to produce a conscious or precise Southeast Asian identity, but they have given substance to the idea of Southeast Asia as a definable world region and have provided a framework for the comparative study of its components.
Geography: the study of Earth’s physical and cultural features Landforms: the natural features of the land’s surface Climate: the average weather conditions in a certain area over a long period of time Environment: All the living and nonliving things that affect life in an area Region: An area with one or more features that make it different from other surrounding areas Map Key / Map Legend: box that explains the meaning of different symbols used on the map Map Scale: tool that measures the relationship between the distance of locations on the map and the distance of locations in real life Compass Rose: a circle that shows the key directions on a map Hemispheres: halves of the Earth Continent: one of seven large landmasses on Earth Oceans: large bodies of water that cover 71% of the Earth’s surface Latitude: imaginary horizontal lines that measure distance north and south of the Equator Equator: central line of latitude that is measured at 0° Longitude: imaginary vertical lines that measure distance east and west of the Prime Meridian Prime Meridian: the central line of longitude, which is measured at 0° and runs through Greenwich, United Kingdom Map: illustration of a specific area on Earth that is often portrayed on a flat surface Physical Map: a type of map that shows the natural landforms and terrain of a location Political Map: a type of map that identifies cities, states, and countries Globe: a spherical model that is the most accurate representation of Earth
Chapter 8: The Worlds of North and South Geography Geography refers to the seasons, climate, soil, and physical features of a region (mountains, rivers, etc.) The differences in geography b/t the N and S is one of the major reasons slavery b/c entrenched in the S while it died out in the N. Geography of the North The N has diverse geography and experiences four distinct seasons including long, harsh winters. The Great Plains region has some of the best farmland in the country. New England has rocky, hilly wilderness, not well suited for farming. It has hundreds of bays and harbors along its coastline. States farther S had rich soil and coastal access through rivers. The N also experienced mass deforestation b/c of the need for lumber and to make room for farms. Geography of the South Climate: the S had mild winters, and a long, hot, humid growing season. It has fertile lowlands, marshes and swamps. It's ideal for growing tobacco, sugar, rice, indigo, and cotton (cash crops). B/c of the geography of the S, their whole way of life was based on agriculture and geography is one of the major reasons why slavery took off in the S. Economies Economy basically refers to the way people make and spend money. The Northern economy was far more diversified than the Southern. Economy of the North The North experienced the Industrial Revolution—the shift from handmade goods to machine-made goods. This resulted in new jobs, increased production, and improved efficiency in agriculture. IOW, you can make things faster, easier, and cheaper. More ppl get more stuff. Factories were almost always located next to rivers. The Reaper The Indust. Rev. changed northern agriculture with Cyrus McCormick’s reaper. It could cut 28xs more grain than a single man. The Sewing Machine Elias Howe's sewing machine; At 250 stitches a minute, Howe's lockstitch mechanism out-stitched the output of five hand seamstresses with a reputation for speed, completing in one hour what took the sewers 14.5 hours. The Textile Mill Francis Cabot Lowell's textile mill: essentially the first factory in the US, Lowell set the model for all future factories. Interchangeable Parts Eli Whitney's interchangeable parts; considered the "dawning of a new age" of machinery. This concept was applied to pretty much all manufacturing. Economy of the South The South's economy was based on AGRICULTURE. Most southerners were agrarians. Most had small farms, some owned plantations. Slavery beginning to decline in late 1700s; prices went down (tobacco, indigo) and cotton was difficult. King Cotton Cotton was South’s most important crop. Earned more money than all other exports combined. The S would go on to supply 75% of the world's cotton demand. Cotton Gin Eli Whitney invented the cotton gin in 1794 and forever changed the US. The gin made cotton incredibly profitable. We start to see the effects of the cotton gin around 1820. Slavery and Cotton Southerners put all their money into slaves and land, and almost none into building factories. With the spread of cotton, demand for slaves increased. 1790 to 1850, number of slaves rose 600%. Transportation Again, the N was far more inventive in their approach to transportation than the S. Transportation in the North National Road National Road stretched from the East (the Potomac), over the Appalachians, to the West (Illinois), over 620 miles. Steamboat In 1807, Robert Fulton invented the steamboat. It traveled 150 miles UP the Hudson River at a speed of 5 mph. Erie Canal Built b/t 1817 and 1825, the canal spanned 363 miles and connected Lake Erie to the Hudson River. This connected farms in the W to cities in the E and the Atlantic Ocean. Clipper Ship Clippers were narrow w massive sails that were built for speed. They cut the time it took to cross the Atlantic in half. Locomotive The fastest and cheapest way to move goods was by steam-powered trains. The first RR was the B&O which was built in 1827. Transportation in the South Most people and goods in the South traveled by rivers in steamboats. The South had trains, but less than half the amount of railroad track than the North had. Society (The People) The people who made up the N and S could not have been more different. The S was primarily agrarian while the N was b/c urbanized. The S was holding on to the past, while the N was embracing change. Society in the South Society was organized into 3 distinct classes of people: rich plantation owners at the top; then white farmers and workers; slaves on the bottom. This rigid social class system was the result of a slave-based agricultural system. Power Structure Only 1 in 4 whites owned a slave. Plantation owners, who owned more than 20 slaves, dominated politics and the economy. Society in the North 7 of 10 Northerners still lived on farms by the 1840s (6 of 10 by 1860), but urbanization was growing fast in the N. The N relied on wage labor as opposed to slave labor, so most blacks in the N were free. N blacks were not treated equally and the N was about as racist as the S. Immigration Compared to the S, the N population was exploding, in large part bc of immigration. Between 1845 and 1860, 4 million immigrants came to the North. Most were German and Irish. Irish--a potato famine; German--a failed revolution. Ethnic neighborhoods developed as a result.
Influence of China and India China ChinaChina under the Han emperor Wudi (c. 100 bce) and (inset) at the end of the Chunqiu (Spring and Autumn) Period (c. 500 bce). Between approximately 150 bce and 150 ce, most of Southeast Asia was first influenced by the more mature cultures of its neighbours to the north and west. Thus began a process that lasted for the better part of a millennium and fundamentally changed Southeast Asia. In some ways the circumstances were very different. China, concerned about increasingly powerful chiefdoms in Vietnam disturbing its trade, encroached into the region and by the end of the 1st century bce had incorporated it as a remote province of the Han empire. For generations, the Vietnamese opposed Chinese rule, but they were unable to gain their independence until 939 ce. From India, however, there is no evidence of conquests, colonization, or even extensive migration. Indians came to Southeast Asia, but they did not come to rule, and no Indian power appears to have pursued an interest in controlling a Southeast Asian power from afar, a factor that may help to explain why only the Vietnamese accepted the Chinese model. Yet, in other ways the processes of Indianization and Sinicization were remarkably similar. Southeast Asia already was socially and culturally diverse, making accommodation easy. Furthermore, indigenous peoples shaped the adaption and adoption of outside influences and, indeed, seem to have sought out concepts and practices that enhanced rather than redirected changes already underway in their own societies. They also rejected some components: for example, some of the vocabulary and general theories related to the Indian notions of social hierarchy were borrowed but much of the specific practices were not, and neither Indian nor Chinese views of women as socially and legally inferior were accepted. In the later stages of the assimilation process—particularly in the Indianized areas—local syncretism often produced exuberant variations, which, despite familiar appearances, were expressions of local genius rather than just inspired borrowings. Get Unlimited Access Try Britannica Premium for free and discover more. Sculptures at Borobudur, central Java, Indonesia. 1 of 2 Sculptures at Borobudur, central Java, Indonesia. Pagan, Myanmar 2 of 2 Pagan, MyanmarRuins of ancient Buddhist shrines and pagodas, Pagan, Myanmar. Still, Chinese and Indian influences were anything but superficial. They provided writing systems and literature, systems of statecraft, and concepts of social hierarchy and religious belief, all of which were both of intrinsic interest and pragmatic significance to Southeast Asians of the day. For elites seeking to gain and retain control over larger and more complex populations, the applications of these ideas were obvious, but it would also seem that the sheer beauty and symbolic power of Hindu and Buddhist arts tapped a responsive vein in the Southeast Asian soul. The result was an imposing array of architectural and other cultural wonders, at first very much in the Indian image and hewing close to current styles and later in more original, indigenous interpretations. The seriousness and profundity with which all this activity was undertaken is unmistakable. By the 7th century ce, Palembang in southern Sumatra was being visited by Chinese and other Buddhist devotees from throughout Asia, who came to study doctrine and to copy manuscripts in institutions that rivaled in importance those in India itself. Later, beginning in the 8th century, temple and court complexes of surpassing grandeur and beauty were constructed in central Java, Myanmar, and Cambodia; the Borobudur of the Śailendra dynasty in Java, the myriad temples of the Burman dynastic capital of Pagan, and the monuments constructed at Angkor during the Khmer empire in Cambodia rank without question among the glories of the ancient world.
Early society and accomplishments Origins Knowledge of the early prehistory of Southeast Asia has undergone exceptionally rapid change as a result of archaeological discoveries made since the 1960s, although the interpretation of these findings has remained the subject of extensive debate. Nevertheless, it seems clear that the region has been inhabited from the earliest times. Hominid fossil remains date from approximately 1,500,000 years ago and those of Homo sapiens from approximately 40,000 years ago. Furthermore, until about 7000 bce the seas were some 150 feet (50 metres) lower than they are now, and the area west of Makassar Strait consisted of a web of watered plains that sometimes is called Sundaland. These land connections perhaps account for the coherence of early human development observed in the Hoabinhian culture, which lasted from about 13,000 to 5000 or 4000 bce. The stone tools used by hunting and gathering societies across Southeast Asia during this period show a remarkable degree of similarity in design and development. When the sea level rose to approximately its present level about 6000 bce, conditions were created for a more variegated environment and, therefore, for more extensive differentiation in human development. While migration from outside the region may have taken place, it did not do so in a massive or clearly punctuated fashion; local evolutionary processes and the circulation of peoples were far more powerful forces in shaping the region’s cultural landscape. Technological developments and population expansion Perhaps because of a particular combination of geophysical and climatic factors, early Southeast Asia did not develop uniformly in the direction of increasingly complex societies. Not only have significant hunting and gathering populations continued to exist into the 21st century, but the familiar cultural sequences triggered by such events as the discovery of agriculture or metallurgy do not seem to apply. This is not to say that the technological capabilities of early Southeast Asian peoples were negligible, for sophisticated metalworking (bronze) and agriculture (rice) were being practiced by the end of the 3rd millennium bce in northeastern Thailand and northern Vietnam, and sailing vessels of advanced design and sophisticated navigational skills were spread over a wider area by the same time or earlier. Significantly, these technologies do not appear to have been borrowed from elsewhere but were indigenous and distinctive in character. Austronesian languages Austronesian languagesMajor divisions of the Austronesian languages. These technological changes may partially account for two crucial developments in Southeast Asia’s later prehistory. The first is the extraordinary seaborne expansion of speakers of Proto-Austronesian languages and their descendants, speakers of Austronesian (or Malayo-Polynesian) languages, which occurred over a period of 5,000 years or more and came to encompass a vast area and to stretch nearly half the circumference of Earth at the Equator. This outward movement of people and culture was evolutionary rather than revolutionary, the result of societal preference for small groups and a tendency of groups to hive off once a certain population size had been reached. It began as early as 4000 bce, when Taiwan was populated from the Asian mainland, and subsequently it continued southward through the northern Philippines (3rd millennium bce), central Indonesia (2nd millennium bce), and western and eastern Indonesia (2nd and 1st millennia bce). From approximately 1000 bce on the expansion continued both eastward into the Pacific, where that immense region was populated in a process continuing to about 1000 ce as voyagers reached the Hawaiian Islands and New Zealand, and westward, where Malay peoples reached and settled the island of Madagascar sometime between 500 and 700 ce, bringing with them (among other things) bananas, which are native to Southeast Asia. Thus, for a considerable period of time, the Southeast Asian region contributed to world cultural history, rather than merely accepting outside influences, as frequently has been suggested. The second development, which began possibly as early as 1000 bce, centred on the production of fine bronze and the fashioning of bronze-and-iron objects, particularly as they have been found at the site in northern Vietnam known as Dong Son. The earliest objects consisted of socketed plowshares and axes, shaft-hole sickles, spearheads, and such small items as fishhooks and personal ornaments. By about 500 bce the Dong Son culture had begun producing the bronze drums for which it is known. The drums are large objects (some weigh more than 150 pounds [70 kg]), and they were produced by the difficult lost-wax casting process and decorated with fine geometric shapes and depictions of animals and humans. This metal industry was not derived from similar industries in China or India. Rather, the Dong Son period offers one of the most powerful—though not necessarily the only or earliest—examples of Southeast Asian societies transforming themselves into more densely populated, hierarchical, and centralized communities. Since typical drums, either originals or local renditions, have been found throughout Southeast Asia and since they are associated with a rich trade in exotics and other goods, the Dong Son culture also suggests that the region as a whole consisted not of isolated, primitive niches of human settlement but of a variety of societies and cultures tied together by broad and long-extant trading patterns. Although none of these societies possessed writing, some displayed considerable sophistication and technological skill, and, although none appears to have constituted a territorial centralized state, new and more complex polities were forming.
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: • Free-falling objects do not encounter air resistance. • 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 • 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 • a • 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 • (-8.00 m/s2) • d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) • d (16.0 m/s2) • 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 • t + ½ • a • 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) • (4.1 s) + ½ • (6.00 m/s2) • (4.10 s)2 d = (0 m) + ½ • (6.00 m/s2) • (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: • 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. • 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. • 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. • 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 • t + ½ • a • 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) • (t) + ½ • (-9.8 m/s2) • (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) • (t)2 -8.52 m = (-4.9 m/s2) • (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 • a • 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 •(-9.8m/s2) •d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) •d (-19.6 m/s2) • d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) • 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.