Comparing the Spanish and English Colonies in the New World free essay sample

The Spanish settlements in the American Southwest and the English colonies in New England of the seventeenth century can be contrasted in primarily two ways. First, their politics were based on entirely different ruling classes and systems of government. Second, they employed different avenues of economic development. The Spanish settlements began with Cortes and others conquering the Native Americans of South, Central, and parts of Southwestern North America. After eradicating a large portion of the Native American population, the Spanish began to intermarry into the Native American gene pool. Consequently, only portions of the population were pureblooded Spaniards. These Spaniards occupied the highest social and political status. Those from Spain were one step above those born in the New World while those of mixed or Indian heritage were at the bottom of the social ladder. Additionally, because the Spanish came as conquerors, the resulting political system was entirely autocratic and solely devoted to the furthering of the motherland. We will write a custom essay sample on Comparing the Spanish and English Colonies in the New World or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Immediately after conquering the Native Americans, the Spanish looted large amounts of gold, silver, and other valuables. This tradition continued into the seventeenth century as Spanish ships would come annually to bring gold and other valuables back to Spain. In this way, Spain viewed Spanish America as an object useful only for its mercantilist objectives. Since mercantilism was its only objective, Spain gave its colonies little self-rule. Instead, Spanish rulers dictated all the policies of its New World territories. The English, on the other hand, settled relatively peacefully into the Eastern Seaboard of North America. Englishmen migrated to the New World not as conquerors but rather because they wanted independence, political freedom, and economic opportunity. Combined with Englands tradition of partial representation, the English Colonies had a large degree of self-government. The colonies all had some form of a representative assembly that was voted in by popular support. While only white male landowners could vote, this still constituted some degree of democracy. In some colonies, even the governors were decided by popular vote. Also, many of the British colonies, such as Virginia, were established by joint stock companies or established as proprietary colonies, such as Pennsylvania. Even royal colonies were often simply colonies given a royal charter but still established by a group of people not directly affiliated

The Place I Have Visited for Holiday free essay sample

New Year would be my first one week break after entering the life of a college student. It was such a pleasant relieve because I do not think I could take another pressure after my mid-term examination. My friends from other colleges were also having their break from college so all of us decided to go for a short trip to Pulau Pinang. There were a total of nine people including myself. Originally, we planned to take the train to Pulau Pinang but they were out of tickets due to the festive celebration. So we took the bus instead. On our way there, the bus made a pit stop at Tapah. Most of my friends went down because it was just so cold on the bus but I decided to stay in. As the bus started to continue the journey to Pulau Pinang, I realised that my friends were not on the bus. We will write a custom essay sample on The Place I Have Visited for Holiday or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page And then I received a phone call from one of my friends saying that they were left behind. I quickly went to the driver to ask him to pull over so that my friends could catch up and get on the bus. Luckily, they were not too far behind. The journey took about six hours due to heavy rain. We reached Butterworth at around dawn. After that, we had to take the ferry to cross over to other side to get to Batu Ferringhi, Pulau Pinang. We were all really excited to finally arrive in Pulau Pinang but exhausted at the same time because of the long journey. So we decided to straightaway go to the guest house and check in. We spent the rest of the afternoon getting some rest before heading out to the beach which is just in front of the place we were staying at. After enjoying the view and playing some volleyball at the beach, we went for dinner at Gurney Drive. There was a wide variety of food to choose from. Each and every one of us bought different kinds of food then we exchange with each other and taste them. The food there was very delicious and tasty. We even took away some, in case we get hungry later. Then all of us went for a walk at the Ferringhi Night Market. There were so many tourists walking around too. We stopped by Sixty Nine Mansion to have some drinks before we head back to our guest house. The next day we checked out around noon and we took a train back home. We reached Kuala Lumpur safely later that night. In conclusion of our short trip to Pulau Pinang, it was truly a memorable experience. Pulau Pinang is definitely one of the most beautiful cities in Malaysia. Pulau Pinang is also an exciting place to visit because it has so many attractions to offer. There are so many things to see and so many other things to do. All in all, Pulau Pinang is surely an amazing place to go for a short trip or vacation.

When I Have Fears - John Keats A Literary Analysis an Example of the Topic Literature Essays by

When I Have Fears - John Keats A Literary Analysis When I have Fears that I May Cease to Be ( 1818; 1848). This sonnet, is possibly John Keats first use of the Shakespearean form, is usually regarded as a prophecy in metaphoric form, of his early death. Shakespearean, too, in theme. He depicts a desolate shore which anticipates John Clare and Matthew Arnold in its emptiness. The sonnet is all the more poignant when we know that Keats died at the age of 25, a tragically young age, with a poetic career of even greater fulfillment in front of him. He was the Romantic poet par excellence: his continuing dedication to poetry in the knowledge that he was dying (from tuberculosis) made him a symbol for the Romantic Movement. At the time of his death, the first generation of Romantics, Wordsworth and Coleridge, could no longer write the intense poetry of their early years. He became an emblem of transience, and Shelley's visionary essay Adonais on Keats's death depicts the exquisite early flowering and then sudden death of Keats, the man and poet. Need essay sample on "When I Have Fears - John Keats A Literary Analysis" topic? We will write a custom essay sample specifically for you Proceed It is evident from this sonnet, one of his most serious, that to Keats the beauty of the marbles consists in their capacity to set the imagination into such play as to arouse anew in the spectator the vision of life the artist had originally caught and then portrayed in the plastic figures upon which he worked. This for the observer is the moment of arrival at "that trembling delicate and snail-horn perception of beauty," of which Keats writes elsewhere the moment of realization of the identity of form with content, of beauty with truth. It is the instant of the completed fabric of the creative imagination, either for the artist or for him who understands his art. That is, in looking upon a Grecian urn the creative imagination of the observer arrives at the same point as did the creative imagination of the artist a delicate, snail-horn perception of the truth the Idea expressed in the urn; hence the beauty of it. The mere external aspects of an urn would not make it beautiful, a thin g of art, to Keats. It is rather that the symbols executed there, themselves a product of mind and soul, still contain within themselves a dynamic something, itself the offspring of imaginative insight, that has the power to set aflame the mind and soul of an imaginative observer: that is true art, that, beauty; that is truth preserved in enduring form for the ages. "For soul is form and doth the body make. Students Often Tell Us:Who wants to write essay for me?Essay writer professionals recommend:Essay Help Service Writing A Paper Online How to Prepare an Assignment Write My Essay Reviews The poetry of Keats may be limited because of its very concentration, its rapt attention to detail and absorption in beauty. But never has poetry been enclosed in an atmosphere of purer enchantment. In 'When I have fears that I may cease to be', the poet imagines a dissolution of consciousness, of thought, thinking 'till thought is blind'. Indeed, in a letter to J. H. Reynolds, Keats comments on writing 'some lines' in Burns's cottage, but says that 'they are so bad I cannot transcribe them', and to Benjamin Bailey he comments that 'I had determined to write a Sonnet in the Cottage. In any poem, but perhaps especially in the compact territory of a sonnet, every word takes on full weight and significance. Metaphorical construction can provide both a method of organization and an avenue of development, as relationships multiply through the course of the poem. In a sonnet such as That time of year, the metaphorical pattern acts as the backbone, the controlling pattern of the sonnet itse lf, further reinforced by syntactic patterns and repetitions. In When I have fears that I may cease to be by John Keats (17951821), metaphor is used similarly to provide fundamental structure. In, When I have fears that I may cease to be, we can see the widening implications of the representational mode Keats learned from Edmund Kean. When I have fears presents a moment of crisis in which the speaker considers the consequences his current state of mind will have on future endeavor. Here, though, Keats is at his most "negatively capable," in the sense that the poem represents a Kean-like "instant feeling" of high uncertainty, expressed precisely from the "when" of that uncertainty's occurrence. And while the sonnet does not represent a moment of strictly cultural reception, Keats relies on the same understanding of subjective experience to convey the encounter. Keats uses the Shakespearean form for the first time in this, his thirty-sixth, sonnet, and the poem is the most compressed expression to this point of negatively capable lyricism. (The observation is supported by the fact that Keats composed When I have fears shortly after composing the Lear sonnet's Shakespearean six-like closing.) The three quatrains--beginning "When," "When," and "And when"--each represent and speak from a temporal moment, a time when, and an affective state, a sense of being as. Each relates the speaker's experience of an action unaccomplished, a potential unfulfilled. In the first quatrain the "high pil'd books, in charactry" do not "Hold like rich garners the full ripen'd grain." In the second, the "Huge cloudy symbols of a high romance" remain untraced. And in the third, the "fair creature of an hour" is never looked upon more. The double connotation of "when" as moment and as state--and its repetition in all three quatrains--gathers and suspends the effect o f each act of perception (the having of fears, the beholding of cloudy symbols, and the feeling of loss of the beloved) until the extended final couplet's expression of "instant feeling": standing alone "on the shore / Of the wide world" and thinking, without an object of thought. In When I have fears, the poet does not reflect on past achievement or consider the promise of future accomplishment; instead, he publicizes a moment of unmitigated uncertainty in which to "think" is to stand paralyzed until "love and fame to nothingness do sink." What is most "theatrical" about the poem, in the sense I have described in this essay, is what is most Shakespearean and most Kean-like about it: not Keats's removal to a "self-distancing point of view" (Rzepka, The Self as Mind 168), but his ability to represent individual subjectivity as a suspended relation between possibilities for self-realization. By naturalizing a language of feeling unmarred by narrative or explanatory context, the poet communicates his crisis as though it were contemporaneous with the reading act. "Negative capability," so often described by Keatsians as a private mode of cultural production, is more properly understood here as a public mode of cultural reception. The poem both depicts (in Keats) a nd encourages (in the reader) a scene of reception rife with uncertainty and doubt, imagining a new kind of relation between the poet's private experience and the public to which he speaks. Edmund Kean played a crucial role in shaping both Keats's attitudes towards his own social rank and his ideas about the changing nature of cultural experience. Educated to an understanding of Kean by Hazlitt's theatrical criticism, Keats's attention to the actor in letters and theatrical reviews in late 1817 and early 1818 coincided with and, I will argue, occasioned his thoroughgoing revision of the poet's role as a cultural intermediary for readers. Keats's poetic figuration of cultural experience crystallizes in a new way in this poem, which bear the marks of Kean's influence first because they render the poet a creature of unapologetic uncertainty, and second because the speaker communicates to the public from within the experience of that uncertainty. As a subject encountering both material and imagined objects--Shakespeare's text, the cloudy symbols of "high romance"--Keats refuses to present himself as a cultural master, or even, like Wordsworth, as an already developed speake r reflecting back on growth that authorizes current speech. Like Kean, he is a teller of the instant feeling, in which past experience and future potentiality intersect, each without gaining dominance over the other. The readers of the poems, like the Keatsian watcher of Kean, feel that the utterer is thinking of the past and the future, while speaking of the instant. Conclusion The ability Keats begins to display in these poems--placing his speaker within the moment of affective reception "without any irritable reaching after fact & reason"--will propel his more intense reworking of poetic expression in the odes, his revision of "romance" in The Eve of St. Agnes, and his refiguration of the poet's relationship to history in The Fall of Hyperion. The "change" that "has taken place" in Keats's intellect at this historical point should not be attributed solely to the influence of Kean. But the change in his thinking about poetry's capacity to represent lower-class experience, in a time when divisions between high and mass culture were becoming increasingly pronounced, bears a striking resemblance to Kean's public embodiment of a new performing subject. Hazlitt commented that Kean's performance of Macbeth was a lesson in common humanity. Such humanity is what Keats had in mind when he expressed a desire to be of Kean's company in December of 1817. The "fashiona bles" and the "blue-stocking literary world" already had their poets, just as upper-class theatergoers had long had Kemble and his school. What Kean was in the theater Keats hoped to be in the world of poetry: a common man of uncommon imagining. Works Cited John Keats, The Letters of John Keats, ed. Hyder Edward Rollins, 2 vols. (Cambridge: Harvard UP, 1958) 1.192-93. Subsequently in the text, abbreviated as Letters. Nicholas Roe, John Keats and the Culture of Dissent (Oxford: Oxford UP, 1997) 237-39. Marjorie Levinson, Keats's Life of Allegory: The Origins of a Style (Oxford: Blackwell, 1988) Donald H. Reiman, "Keats and the Third Generation," in The Persistence of Poetry, eds. Robert M. Ryan and Ronald A. Sharp [Amherst: U of Massachusetts P, 1998] 111). Bate, "Keats's Style: Evolution Toward Qualities of Permanent Value," in The Major English Romantic Poets, eds. Clarence D. Thorpe, Carlos Baker, and Bennett Weaver (Carbondale, IL: Southern Illinois UP, 1957 William Hazlitt, The Complete Works of William Hazlitt, ed. P. P. Howe, 21 vols. (New York: AMS, 1967

Argumentative Persuasive Essay Topics

Argumentative Persuasive Essay Topics Argumentative Persuasive Essay Topics Argumentative Persuasive Essay Topics Writing an essay starts with creating a thesis statement.   Then you proceed with collecting information, evidence and premises to support your ideas. You need to understand that it is harder to write arguments then just the premises or conclusions alone. Writing an argument isn't the same as stating the conclusion. Very often students make this mistake while writing an essay. While writing argumentative essay, they present a lot of general information which they consider being an argument. It is more likely that they simply affirm that some ideas are true. They don't present the premises or inferences from which the conclusions derived while writing an essay. Sometimes it happens because they think that arguments seem so clear that they feel they need not write out the details. However, it is mistakable to think that the readers don't want to see the details in your argumentative persuasive essay. Argumentative Essay Writing Traditionally, there are two types of arguments:   deductive and inductive. Deductive arguments give final proof by presenting all the supporting evidence in the essay. The idea is that if the premises are true, then the conclusion must also be true. Deductive process assumes that the conclusion should be followed from the premises. Begin argumentative essay writing with thesis statement and then start writing conclusions. Deductive arguments may be either valid or invalid, it depends on the evidence and the reasoning which you present while writing an essay. An inductive argument is an argument in which the premises are provided to support the conclusion. The conclusions of the inductive arguments are developed by inference. Making inductive arguments writers use words and phrases like 'probably', 'improbably', 'likely' , 'unlikely' , and 'reasonable to conclude' . Inductive arguments are not valid or invalid, but they must be stronger or weaker than other arguments in the essay. Persuasive Essay Writing Persuasive essay writing, as any other kind of essay writing, has the goal to persuade the reader to take writer's point of view. It is not enough to present a valid argument which supports the thesis statement while writing argumentative persuasive essay.   You must also present a counter-argument showing why the opposition's reasoning and arguments are invalid. The counter-argument requires a deep analysis and examination of opposing premises, inferences, and conclusions. The counter-argument is very important, with its help you can convince a reader that your point of view on the subject is the best point of view. Help to Write Argumentative Persuasive Essay If you have started writing your persuasive or argumentative essay, however, you are not sure how to proceed.   If the deadline is approaching and you are stuck on any writing step.   If you are not sure whether the arguments you make are strong or valid enough to persuade the reader.   We offer you our help to write argumentative persuasive essay.   We are experienced in essay writing and we are able to help you with any type of assignments.   delivers only custom written papers!

Ethnography and the interpretation of cultures Essay

Ethnography and the interpretation of cultures - Essay Example being studied However, for a social scientist the laboratory is the culture being studied and it is impossible to manipulate parts of it without destroying the culture itself. Furthermore to gain insight into the whys of cultural practices researchers must often ingratiate themselves with the people studied. However the argument is that too much emotional attachment can affect the researcher’s objectivity and thereby call into question his research conclusions. This article traces the history of changes in anthropological approaches to ethnographic studies over the years. At first blush this is a confusing phraseology, but as I understand it from the author’s explanation, the difference is that in participant observation the researcher participates in the culture’s practices but observes for study only the culture’s symbols, status relationships, norms, values, etc. to determine their significance in relation to how the culture functions (Tedlock, B. 1991) On the other hand under â€Å"observation of participation† the researcher is also more aware of the effect his participation may have on the culture and therefore tries to broaden his observations to himself as well as the culture being studied. In other words in an effort to achieve a greater degree of scientific validity he attempts to be more aware of for example any notions of cultural superiority which might color his perceptions and make him appreciate less how the practices he observes play roles in enabling the culture studied to function effectively in the context in which it operates. The author makes the point that that the recent broadening of the pool of recruits doing ethnographies to include both genders, different races and socioeconomic levels, etc. are more likely to study cultures objectively in context in th â€Å"observation of participation† methodology than their largely male, white, upper class forerunners many of whom had the â€Å"baggage† of considering themselves as members of

A review of the literature exploring the user of NIV to treat Dissertation

A review of the literature exploring the user of NIV to treat exacerbation of COPD - Dissertation Example The main objective of this paper is to review what has been found by various studies on the survival challenges, quality of life and the compliance to NIV therapy by the users. Also, the paper will review literature on the effectiveness of the NIV treatment. Challenges on survival, Quality of life and compliance to NIV therapy According to the studies by Massimo, et al (2012, pp747), it was gathered that there are indications of early NIV positive pressure ventilation, which tend to increase the rate of survival. This was made in comparison with NIPPV. As such, NIV acts as a relief from challenges relating to survival rate in patients with high level of CO2 in their blood. A study by Pepin, et al (2008, pp360) indicates these challenges. According to the study, the challenges that these patients face are: fatigue, sleep patterns that are disturbed as well as breathlessness. The group also found out that NIV does not provide a prevention against weakening of the respiratory muscle tha t tend to progress. Acute exacerbations of a chronic Obstructive Pulmonary Disease better referred to as COPD, pose great challenge to the survival rate of a patient. In the periods that the patient is faced with worsening extremes, it adversely affects the patient’s health status. There is an escalating admission to hospitals and even rise of mortality rates (Angus, et al 2011, pp84). According to the studies by Fionnuala, et al (2007, pp60), it is approximated that the mortality rate of in-patient ranged from 4%-30%. The study goes on to indicate that patients that are admitted due to complications from acute Respiratory failure have a higher mortality rate. According to the study, the patients who are elderly and have co morbidities as well as those patients needing the ICU facilities were the most affected by the high mortality rate. According to the study by Monica, et al (2004, pp605), ventilation of the respiratory worsens to perfusion ratio and this result to a mechan ism in the hypoxemia occurrence. This happens when psychological dead space enlarges. It also occurs when there is a rise in the ventilation waste. In the study by Suzy (2012, pp61), it was identified that increased resistance of the airway as well as the need for high minute ventilation tend to result to a limitation on the expiratory flow. Still, the study found out that a dynamic hyperinflation, enlarged threshold of the aspiratory load as well as respiratory muscle dysfunction result to a feeling of fatigue in a patient. Plant and Elliott (2003) studied that a rapid pattern of breathing, which is somehow shallow, occurs. This is due to the respiratory system efforts towards maintenance of enough ventilation in the alveoli. This happens when the elastic, resistive and loads of aspiratory threshold are introduced to the weakened muscles of the respiratory system. However, irrespective of an increment in stimulus of the centers of the respiratory system as well as swings in the lar ge, negative intra-thoracic pressure, carbon dioxide is still retained and as such, acedemia occurs. Other studies by Rossi, et al (1995) and Ambrosino, et al (1997) established that severe COPD which is complicated by ARF, attain characteristics such as; right ventricular failure, encephalopathy as well as dyspnea and these pose as serious challenges to the survival of the patient. In regards to the studies by Eliott (2012, pp85), a vital intervening is advantageous to the patient with COPD is advisable. He suggested a clinical experience and this was an NIV treatment. Does NIV improve respiratory function or increase survival? A

Speed Velocity And Acceleration

Speed Velocity And Acceleration In this chapter we will look at the concepts of speed, acceleration, and velocity. As we all know gravity is a large factor in the acceleration of an object. For the purposes of this chapter we will differentiate between linear and vertical acceleration as being objects that move linearly or horizontally i.e. linear acceleration, versus objects that fall, fly, or are thrown etc. i.e. vertical acceleration. Vertical acceleration is much more governed by the force of gravity and is covered in greater detail in chapter 12 Newtons Laws. A short section at the end of the chapter addressing vertical acceleration is however included to put the area into context. You may have heard the old adage Speed kills. And you know whether you are driving your car or playing sport its a dangerous variable. Fast athletes are very difficult to handle, as are fast cars. However, having speed is of vital importance in sports. In this chapter well look at speed, velocity and acceleration and the factors that influence them. Speed, acceleration and velocity are all different. If you have ever watched a 100 meter race, you will notice that some athletes start faster than others, so their acceleration is different. Athletes finish the race at different times so their speed is different and athletes reach top speed at different stages so their velocity is different. The key terms to be covered in this chapter are speed, acceleration, velocity, distance, displacement, vertical and horizontal acceleration and velocity. The variables of speed, acceleration, displacement, etc. are about linear kinematics. Kinematics is a general term related to describing motion. Kinematics is also a branch of mechanics (specifically dynamics) that evaluates moving objects. In order to accurately describe kinematics there are certain terms that we must fully understand. They include the terms mentioned above (speed, acceleration, and displacement) and distance, velocity and position. Accurate understanding of these terms will allow us to accurately describe the movement of any object. There is often a lot of confusion about the terms acceleration, speed, and velocity. We often use the term speed in everyday language to imply all three terms and the word fast is an even more general term. Consider the following: A person can be moving fast and not be accelerating. A person can accelerate fast and not have a high velocity or high speed. A nice sporting example was the great Boston Celtics player Larry Bird. Larry Bird was very quick to accelerate over three or four steps, was not very fast at his top speed. So while Larry was very quick and dangerous over 3-4 steps, he would not make a good sprinter because his top end speed was not high. So if an object is accelerating, it is changing its velocity. Acceleration has to do with the change in how fast an object is moving. Therefore, if an object is not changing its velocity, it is not accelerating. We know that distance and displacement have different meanings. The same is true for speed and velocity. Speed can be considered as the rate at which an object covers a certain distance. Objects that move slowly cover distances in long periods of time, i.e., low speed. An object moving quickly covers distance in shorter amounts of time, i.e., high speed. If an object is not moving at all it has zero speed, zero velocity and zero acceleration. Let us consider some of these simple terms in more detail. Position: Position is simply the location of an object in space. You could consider it using coordinates on a map for example, or on a field, or gymnasium. Displacement: Displacement is simply the straight line distance an object has travelled. Distance: Distance is how far an object has travelled in any direction. It is also viewed as the total amount of displacement (regardless of ending position). Look at this simple example. Lets say a basketball court from baseline to baseline is 25m. If a player runs baseline to baseline and back what is his displacement and distance? Distance. This is the easy one since he ran up and down the court so that is 25m + 25m = 50m. Displacement. Since the player ran down the court and back again he ended up in the same place he started. So even though he covered a distance of 50m his displacement is actually zero, since he is back where he started. Lets say the player now runs up and down the court twice. His distance covered would be 25m + 25m + 25m +25m = 100m. Since he ended up back where he started his displacement is still zero. Finally, lets say the player runs from one baseline to the other and stops. In this case both his displacement and distance are the same at 25m. For the most part we use distance rather than displacement to describe movements as it is difficult to correctly measure displacement as we make a lot of turns when we travel. You say displacement is really like the old saying as the crow flies which means straight line. For example, the distance you travel in a car from New York City to Boston might be 250 miles (but your displacement is only 175 miles). When you drive in a car you get on the highway and follow the roads around the coast, over bridges, around hills, around towns etc. However, when you fly the plane flies right over everything in a straight line and you end up only travelling 175 miles (your displacement). Speed Speed is a very general term. Speed is a scalar quantity and is described as Distance divided by time (D/T, where D=distance and T=time). Scalar implies that speed has magnitude but not necessarily any direction, for example temperature or volume. People often use speed and velocity interchangeably but they are different. Speed relates to the distance an object has traveled, while velocity refers to the displacement that has taken place. So, the speed of an object tells us how far an object has traveled in a given amount of time but doesnt tell us anything about the direction in which it traveled. It all sounds a little heavy on the definitions but these are important. Therefore: Average speed = Distance traveled (m) Time (s) Now there are also different types of speed. We refer to them as average speed versus instantaneous speed. When an object is moving it often changes its speed (or direction) during its motion. When there is a change in speed we can alter our definitions. Instantaneous speed is the speed at any given instant, while average speed is the average of all the instantaneous speeds. For example, lets say a runner runs 400m in 60 seconds and crosses the line at 18 kmh or 5 m/s. This means his average speed over the 400m was 6.66 m/s even though he crossed the line at 5 m/s which is his instantaneous speed at the finish line. In other words, he was slowing down as he was getting to the end. If you have ever ran a 400m race then you will now how tired you are at the end and are definitely slowing down. How did we do these calculations? Average speed = Distance/time 400m/60 seconds 6.66 m/s The instantaneous speed recording of 5 m/s would have been measured with a radar or timing device. You could also look at various split times for different portions of the race. Many coaches do in fact do this, so a 400m coach might look at each 100m split and look at both the acceleration and deceleration patterns and average speeds during each of the four separate 100 meters. Here is another problem for you to try. Can you calculate the average speed of a swimmer that completes the 200m butterfly in 2.15 seconds? Answer: 2.15 seconds = 135 seconds. So 200m/135 seconds = 1.48 m/s A 400m freestyler swims the race in 4.10 seconds. The 200m split was 2.02 seconds. Can you calculate the following? a. What was the swimmers average speed for the race? b. What was the difference in speed for the first 200m versus the second 200m? Answer: a. 400m/250 seconds = 1.6 m/s b. First 200m split = 1.64 m/s Second 200m split 1.56 m/s As you can see, the swimmer slowed down over the second 200m. Velocity Velocity is somewhat similar to speed but velocity involves both direction and speed. So, whereas speed is a scalar quantity, velocity is a vector quantity, that is, it has both magnitude and direction. Velocity also uses displacement as opposed to distance. Remember displacement is measured as the straight line distance an object travels from starting to ending position. Velocity is direction sensitive since it is dependent upon displacement. Therefore, when you calculate velocity, you must also keep track of direction. Therefore, if you say an airplane has a velocity of 600 kmh, you would actually be a little vague. You should really say the airplane has a velocity of 600 kmh North. So, speed doesnt worry about direction, velocity does. Velocity is a positive number as we dont have negative velocity. So to summarize, a airplane traveling at 600 kmh as a speed of 600 kmh. The same airplane has a velocity of 600 kmh, North. Finally, the same airplane probably had little acceleration in the middle of its trip as it would only need positive acceleration and negative acceleration during take off and landing. Here is an interesting and challenging little problem for you to solve. Can you fill in the following table with acceleration, speed, and velocity data? We know the following, the direction of travel is south and acceleration doubles every second. If youre feeling confident you can also try and calculate the total distance that was covered over the 6 seconds. Hint! You can use the velocity for each second to help you. Time Vel.m/s Accel. m/s2 *Speed.m/s 0s 1 1 1 1s 2 2s 7 3s 8 4s 31 5s 3 6s 64 Answers Time Vel.m/s Accel. m/s2 *Speed.m/s 0s 1 1 1 1s 3 2 1.5 2s 7 4 3.5 3s 15 8 5.0 4s 31 16 7.75 5s 63 32 12.6 6s 127 64 21.16 *Average speed through that time period So: Average velocity = Displacement Time Let try some additional calculation examples: For example, if an athlete runs around a 400 meter track in 50 seconds we can calculate numerous factors. What was the distance traveled? What was the displacement? What was the average speed? What was the average velocity? 1. What was the distance traveled? Answer: Easy enough = 400 meters 2. What was the displacement? Answer: Since the athlete ended up in the same place as they started, displacement is equal to zero. 3. What was the average speed? Answer: Speed = Distance/Time = 400 m/60 seconds = 6.66 m/sec 4. What was the average velocity? Answer: Velocity = Displacement/Time = 0/60 seconds. In this case we end up with a value of zero and in this scenario average speed is a better indicator of overall performance. In many situations we actually calculate average velocity as speed because we cant gather the correct information to calculate speed. For example, if a punt returner catches the ball on the 20 yard line and then avoids a few tackles to ultimately score a touchdown twelve seconds later, we assume the punt returner ran 80 yards. In fact, they may have run 100 yards with all the turning and weaving but we cant accurately calculate the true distance traveled and instead use displacement. For our purposes in sports, thats okay. You try the following problem. Review Problems Can you accurately calculate average speed, velocity, distance and displacement for each of the following situations? Hint: You may not be able to calculate them all accurately. Problem: 1. A punt returner catches the ball on his own 40 yard line and scores a touchdown nine seconds later. 2. A 100 meter sprinter runs the 100 meter in 10.0 seconds flat. Acceleration The law of acceleration is Newtons second law and basically states The change of motion of an object is proportional to the force impressed and occurs in the direction in which the force is impressed. So far we have talked about speed and velocity and performed some calculations. However, while speed and velocity are valuable components, they tend to provide us with summary information and very little about specific detail. For example, if we consider the data for a 200 meter race run in 20 seconds we know that average speed was 10 m/sec. However, we would not know any information about who accelerated the fastest or who was leading after 100 meters. This information is also important as it helps with identifying strength and weaknesses in athletes and in developing training programs for particular athletes. The measurement of acceleration is important. Acceleration is the rate of change in velocity. Therefore, when acceleration is zero, velocity is constant. So when an object changes speed either by slowing up or down, or changes direction, it is accelerating (or decelerating). We can calculate acceleration by measuring the difference in velocity over the time it took for that ch ange in velocity to occur. Consider this: If you were to watch a 100M race the person leading at the 50M mark doesnt always win the race. The reason for this is that runners have different acceleration and deceleration rates, in other words their speed changes. Athletes vary dramatically in their acceleration. Some athletes are very fast over 40M but not over 100M and vice versa. So: Acceleration (a) = Velocity2 Velocity1 Where V2 is velocity at T2 Tim Where V1 is velocity at T1 Sometimes you will see this presented as the change in velocity (Delta sign à ¢Ã‹â€ Ã¢â‚¬  ) or the change in time (à ¢Ã‹â€ Ã¢â‚¬  T) A = à ¢Ã‹â€ Ã¢â‚¬  V à ¢Ã‹â€ Ã¢â‚¬  T Look at the following acceleration example. Question: A sprinter leaves the starting block at 2.5 m/s. One second later they are traveling at 5.5 m/s. What is the acceleration rate? Answer: V2 V1 = 5.5 m/s 2.5 m/s = 3 m/s squared T 1 You will note that we end up with meters per second squared as our answer would really be presented as 3 m/s/s. Heres another problem to try. Question: A punt returner catches the ball standing still and begins to return. Two seconds later his velocity was 5 m/s. What was his average acceleration over the first two seconds? Answer: V2 V1 = 5 m/s 0 m/s = 3.5 m/s squared T 2 So far we have looked at relatively straightforward examples of speed, acceleration and velocity in that they have all been examples of horizontal movement. Now let us discuss the vertical components of projectile acceleration, speed and velocity. Factors Affecting Acceleration Linear acceleration is affected by many factors and you will recall from chapter ? that the mass of an object is a very important one. Heavier objects accelerate more slowly with a given force. This has to do with both inertia and mass. Heavier objects are harder to both accelerate and decelerate. Think about how easy it is to throw a basketball versus a medicine ball. There are some other points to consider when looking at acceleration, speed, and velocity. First, we now know the units for velocity are meters per second (m/s) and meters per second squared for acceleration (m/s/s). For speed they are also m/s. Since acceleration (like velocity) is a vector quantity, it also has direction associated with it. The direction of acceleration depends on two factors: a. Whether the object is speeding up or slowing down b. Whether the object is moving in a negative (upwards) or positive (downward) direction We can simplify this by saying that if an object is slowing down then its acceleration is in opposite direction of its motion. If it is speeding up then its acceleration is in the same direction as its motion. Therefore: Acceleration (m/s2) = mass (kg)/force (newtons) Vertical speed, acceleration and velocity If you were to throw a ball up in the air and then catch it again at the same height as you released it, how would the ending velocity be? Would it be greater, less, or the same as the release speed? If you guessed the same you would be correct. You see, all objects, whether traveling vertically or horizontally, are subjected to the constant force of gravity (9.81 m/s2). This means that as soon as the ball left your hands it started to negatively (de)accelerate at 9.81 m/s2 until it had no more velocity. Then, it started to positively re-accelerate over the same distance (and time) at a rate of 9.81 m/s2 until you caught it again. This is a very neat relationship as it allows us to make many calculations based on this constant acceleration force. Projectiles are subjected to both vertical and horizontal components in their motion. The horizontal components are affected by the mass of the object and the acceleration force as previously mentioned. The vertical components are also affected by these two factors plus gravity. Consider this statement: A ball shot horizontally (at zero degrees) has the same vertical component as a ball that is simply dropped with no horizontal velocity. What this means is that if you were to throw a pass from your chest and it hit the ground 15 meters away 1.5 seconds later, and at the same time drop a second ball straight down from the same height, they would both hit the ground at the exact same time. What this is showing us is that the force of gravity component is acting consistently regardless of whether the ball has a horizontal component or not. In other words adding a horizon tal acceleration component does not affect in any way the force of gravity. Remember also that gravitational acceleration is a vector quantity comprising both magnitude and direction and acceleration is a squared variable to the magnitude of the force of gravity. This means that for every second an object is in free fall it will accelerate by ad additional 9.81m/s2. Thus the total distance travelled is directly proportional to the square of the time. Or we could say that if an object travels twice the time it will travel four times the distance. If an object travels for three seconds it will cover nine times the distance, for four seconds it is sixteen times the distance travelled in the first second. Look at the following. A coin is dropped from a cliff. The table shows how fast it is travelling at different time points. Time Speed m/s 1 sec 9.81 2sec 19.62 3 sec 29.43 4 sec 39.24 5 sec 49.05 6 sec 58.86 7 sec 96.23 Consider this simple math problem: Question: A boy drops a ball from a balcony and records a time of 3 seconds for the ball to hit the ground. At what velocity did the ball hit the ground? Answer: 29.43 m/s How do we get this answer? Well, remember that gravity acts as a constant 9.81 m/s2. What this means is that for each second the ball is in flight it accelerates an additional 9.81 m/s. So: Insert schematic to demonstrate after 1 second = 9.81 m/s after 2 seconds = 9.81 m/s + 9.81 m/s = 19.62 m/s after 3 seconds + 19.62 m/s + 9.81 m/s = 29.43 m/s This is a simple illustration of the concept. Next question, what velocity would the ball have to be released at ground height for the boy to catch it on the balcony? Answer: A minimum of 29.43 m/s. The answer is the same because gravity and acceleration (or deceleration) is working to the same effect when the ball is moving upwards. This is sometimes referred to a negative acceleration. Question. A boy is standing on a balcony and is curious about how high the balcony is from the ground. The boy drops a ball and records the time it takes to hit the ground. It took 3.2 seconds for the ball to hit the ground. The boy concludes that the balcony is 66.7m high. How did he work it out? Well at the end of the first second the ball was travelling 9.81m/s, at the end of the second the ball was travelling 19.62m/s, at the end of the third second the ball was travelling 29.43m/s. If you add these three distances together you get 58.86 meters travelled after three seconds. If the ball travelled another full second it would travel another 39.24m, but it only travelled in this zone for 0.2 sec. So, 39.24m x 0.2sec =7.84m. Now we add the 58.86m + 7.84m = 66.7m, and thats our answer. There are some other factors to consider with vertical projectiles. The pattern of change in vertical velocity is symmetrical about the apex of the trajectory. So not only does the object land at the same speed it was released, it also follows the reverse flight path on the way down. Using these constant parameters we can now extend our calculations into more complex situations. For example, lets say you are watching a volleyball game in a high school gym with a 10 meter high ceiling. An opponent spikes the ball over the net and a player digs the ball at ground level at which time the ball has a velocity of 15 m/s. The question is will the ball hit the ceiling? To solve for this we can use an equation that combines several variables we talked about already. Where: V2 = velocity at time 2 V1 = velocity at time 1 a = acceleration t = time In order to answer this question we need to look at what we know and what we want to know. Well, we want to know the distance (d) the ball travels. We already know a = 9.81 m/s2 and we know V1 = 15 m/s. We also know that at the apex the velocity is zero, so V2 can be set to zero. So now our formula looks like this: 1. 0 = V1 squared + 2ad 2. 0 = (15 m/s) squared + 2 (-9.81 m/s squared) x d Now if we rearrange to solve for d our formula looks like: = (19.62 m/s squared) x d = 225 m/s squared = d = 11.47 m The answer is yes! The ball will hit the ceiling as it will travel 11.47 m. Heres another similar problem: A ball is deflected vertically at 18 m/s and the ceiling height is 11 meters. Will the ball hit the ceiling? Factors affecting projectile motion We have discussed several factors that affect the movement (or acceleration) of an object. The factors that affect vertical acceleration are the mass of the object, the force (speed) of release and gravity. Horizontal acceleration is affected only by mass and force of release (application). Gravity is of course a factor but not in determining its horizontal component. But sometimes we want to throw objects e.g. discus, hammer, etc. and while these projectiles are influenced by force and mass, there are other factors that influence how far the projectile will travel. We generally recognize three other factors that influence how far a projectile will travel when a constant force is applied. They are: 1. Angle at which projectile is released. 2. The speed of release. 3. The height of release. The optimum angle of release to increase horizontal displacement is 45 °. Projectiles released at over or below this angle will not reach their greatest distance. Look at Table 1 to see how distance traveled varies with changing angles of release. You will see from table 1 that the optimum angle of release is 45 ° and after that the decrease in distance traveled is symmetrical as height compromises distance (I.e. follows the same pattern as increasing angle of release up to 45 °). The greater the speed of release the greater the distance a projectile will travel. This holds true simply because there is a greater acceleration force applied in the first place. Simply put, if you want to throw a ball further you need also to throw it harder. The greater the height of release the greater the distance a projectile will travel. If you consider field sports in athletics you will notice that most successful hammer, discus and javelin throwers are taller, giving the mecha nical advantage over shorter competitors in that event. If you were to throw a ball from the top of a building it would strike the ground much further away than it would if you were to throw it from standing on the ground. Table 1: Distance a Projectile travels at a constant speed and height of release with change in angle of release. (need the reference) Speed of release Release angle Distance Travelled 10m/s 10 3.49m 10m/s 20 6.55m 10m/s 30 8.83m 10m/s 40 10.04m 10m/s 45 10.19m 10m/s 50 1.04m If you have watched a discuss competition or a hammer throw you might notice that these athletes are quite tall (often over 1.9m). The reason for this is that these athletes have an advantage over their shorter counterparts as their angle of release is already several centimeters higher. Summary This chapter has provided a basic introduction to the concepts of speed, acceleration and velocity. We have also looked at how differentiating between these variables is important and sometimes difficult. Using some known constants, such as the accelerating force of gravity (9.81 m/s2) allows us to calculate and even predict the speeds, velocities and flight paths of selected projectiles. We have also discussed other factors that affect projectile motion such as height and speed of release. While this information is very important, it is a basic introduction as there are many other more complex factors affecting speed, acceleration and velocity. We did not talk about shape or design or, indeed materials which also play a role in the way particular objects react to forces. The factors are extremely important but for now are beyond the scope of this text. Following this section are additional problems for you to solve and practice. Review Problems Can you provide a one sentence definition for each of the follow terms? Distance Displacement Acceleration Velocity Speed Position Scalar Vector A ball rolls with an acceleration of -.5 m/s 2. If it stops after 7 seconds, what was its initial speed? A wheelchair marathoner has a speed of 5m/s after rolling down a small hill in 1.5sec. If the wheelchair underwent a constant acceleration of 3 m/s 2 during the descent, what was the marathoners speed at the top of the hill? A runner completes 6.5 laps of a 400m track in 12 mins (720 secs). He starts half way around the bend. Can you calculate the following? a. Distance covered: b. Displacement after 12 minutes: c. Runners average speed: d. Runners average pace: min/mile = A soccer ball is rolling across a field. At T = 0, the ball has an instantaneous velocity of 4 m/s. If acceleration occurs at a constant -0.3 m/s2 how long will it take to stop? A batter strikes a ground ball with an instantaneous velocity of 18m/s. If acceleration occurs at -0.7m/s2 how long will it take to stop?