Analysis Of Marketing Positioning Of Kelloggs Special K Marketing Essay

Analysis Of Marketing Positioning Of Kelloggs Special K Marketing Essay Kotler et als ideology of marketing entailing understanding consumers and their needs and designing marketing initiatives to deliver those needs (2009, p. 5) emerges in the marketing endeavors undertaken by the Kelloggs Special K (SK) cereal brand. The marketing foresight inculcated by the brand not only helped it contribute to the overall success of the Kellogg conglomerate but also helped it evolve as a strong contender in the UK cereal industry. This assignment will unravel the marketing practices followed by the SK brand by analyzing its positioning in the UK cereal market. The analyses will encompass highlighting the customer segmentation adapted by this cereal brand followed by evaluating the efficacy of its target market selection. Subsequently, it will assess the cereals positioning as compared with its competitors positioning including its usage of the marketing mix elements to sustain that positioning. Finally as an outcome of the above analysis, it will offer recommendatio ns to strengthen the brands market positioning. Assumptions Made: Barring considering the retailers as buyers for a five force analysis of the UK cereal industry, the assignment considers the end users as the consumers of the SK cereal. Whilst for a perceptual map, price  [1]  has been used to draw inferences on the product quality of the various cereal brands, Kelloggs product life cycle stage in the UK market and SKs brand share have been used to draw inferences on SKs product life cycle stage. UK Cereal Market and Kelloggs: The UK cereal market grew by 15.7% in value between 2004 and 2008 because of the perceived health benefits of and convenience in consuming cereals coupled with the declining popularity of the traditional breakfast (Worth, 2009). This growth rate indicates the attractiveness of UK cereal industry, which is also substantiated by a Porters five forces analysis of the market (represented diagrammatically in Figure 1.1). This oligopolistic market is dominated by three big brands: Kelloggs, Weetabix and Cereal Partners (Worth, 2009 and Datamonitor, 2009a) with Kelloggs leading the market (as shown in figure 1.2). Since giving the world its very first ready to eat cereal cornflakes (Emerald, 1991, p. 16), Kelloggs has become practically synonymous with breakfast cereals (Mitchell and Boustani, 1992, p. 21). With over 100 years of experience in the cereal business, it appears that Kelloggs has built its high brand value (shown in figure 1.3) on consistent pioneering innovations and incessant delivery of consumers nutritious food requirements. And keeping true to this tradition is Special K, the leading cereal brand of the Kelloggs family  [2]  . Special K and its marketing choices: Launched in the UK in 1959 (Kelloggs Special K, 2009), Special K is a nutritious low-fat, ready to eat diet cereal that owes its eminent market position to the enhanced marketing choices made by the Kellogg marketers (Kellogg Company, 2003,2004). Following section of the assignment will analyse the components of the marketing choices made by the SK brand. Market segmentation and Target Market: SK is targeted at weight conscious women, employed/homemakers, between the ages of 25-49 who desire to attain a slimmer shape either for a healthy lifestyle or for an occasion. And in pursuit of their weight goals these women will prefer to consume nutritious food substitutes including paying an above average price for the product. Alike the cereal manufacturers who use a number of variables to segment their customers (deduced from the data on consumption of cereals displayed in figure 1.4), it appears that SK also segments its customers using demographic variables such as gender, age and occupation and behavioral variables such as occasion and benefits. But unlike the other cereal manufacturers, SK utilized its customer segmentation to identify and serve a distinct market group, which proved to be attractive and profitable over catering to the entire mass market. Moreover factors that contribute to the continued success of serving this target market are: Dieting trends: Results of a consumer research carried out in 2008 revealed that women are constantly trying to lose weight, where 24.3% of the women dieted most of the time as compared to 13.9% of men (Baxter, 2009). This consumer behaviour augments SKs target market selection. Popularity of Health food: The popularity of health food is increasing as confirmed by a consumer research where 43.8% of the research pool displayed an affirmative interest in purchasing functional food. This growing trend benefits SK as women (47.3%) accounted for the majority of the preference over men (40.1%) (Taylor, 2008). UK Obesity levels: The forecasted UK obesity levels for 2010 where women (29%) are more likely to be obese then men (27%) (Gower, 2008) not only favors SKs product proposition but also provides the brand with an opportunity to expand its customer base. Grocery shopping: SK can effectively access its target market using Kelloggs existing distribution channel of grocery chains, owing to the consumer behaviour where women undertake majority of the shopping at supermarkets as compared to the men (shown in figure 1.5). Growth of UK cereal market: In addition to its current growth rate (as discussed earlier), the UK cereal market is also forecasted to prosper in the future (displayed in figure 1.6). This future growth rate, supported by an immense market potential that exists in the form of people still skipping their breakfast, enables SK to attract new customers. Whilst the above factors substantiate SKs distinctive target market selection it is also imperative to evaluate the brands positioning in this target market as compared to its competitors to gauge the success of its marketing foresight. Competitors versus Special Ks positioning: Though Porters five force analysis of the UK cereal industry reveals that competitive rivalry in this market is moderate, failure by cereal manufacturers in differentiating their products will result in increased competition. SK endures industry competition based on the category points of the parity from other health cereal brands, including the various Kellogg brands, and market competition from other slimming aids such as diets, meal replacements and appetite suppressants (represented diagrammatically in figure 1.7). Whilst the popularity of the cereals is on the rise (refer to prior discussion) the popularity of the slimming aids is on the decline due to the augmented awareness of the healthy eating habits (Baxter, 2009). Hence though the slimming aids are positioned as weight management products (Refer to figure 1.8 for the positioning of the various slimming aids in the market) also targeted at women, it can be deduced that SK has a superior market potential over these products. A perceptual mapping of SK with its industry competitors (displayed in figure 1.9) divulges that the brand is perceived as high quality premium priced product by its customers. However SKs consumer perceived value is not alone limited to its price and quality differentiation but rather is accentuated by its unique market positioning in the cereal industry. Special K is positioned as a premium shape management nutritious cereal for women The above positioning unveils that instead of imitating its competitors by using common variables such as quality, energy, taste, natural ingredients and price, SK utilizes the popular variable of body shape to differentiate its product (refer to figure 1.10). Though a number of consumer products and services use the variable of shape to differentiate their product, SK was the first cereal brand to employ this positioning making it unique in the cereal industry  [3]  . Kelloggs by using its extensive experience to develop and position the SK cereal, appears to have understood and delivered its consumer needs; where women may want to lose weight either post an occasion such pregnancy or holiday or to lead a healthy lifestyle or to improve their physical experience. The value proposition offered by SK that acts as its point of difference from the other cereal brands has also helped it minimize the risk of cannibalization from the other Kellogg cereals. Furthermore, SKs market positioning has helped convert the consumers cereal purchase decision from a low involvement to a moderate involvement activity by linking their purchase decision to the psychological and physical benefits that can be derived from the product. Infact the SK 2 week challenge, which is an important element of the brands positioning (refer to figure 1.10), facilitates potential increases in the product usage and brand loyalty as once consumers verify the benefits of the product they may want to extend their association with the brand. It can be argued that by targeting only one distinct consumer group, SK is limiting its profit potential but on the contrary the growth in its market share (depicted in figure 1.11) is a testament of its successful market positioning in highly profitable target market. However SKs current and future market share could be threatened if it is no more the only cereal adopting the shape positioning as revealed in a SWOT analysis displayed below. Hence the strength of its positioning depends on effective management of the marketing mix elements. Marketing Mix Elements: Product: SK by offering a series of value added benefits in addition to its core benefits (displayed below) appears to acknowledge the importance of support for its customers during the challenging process of weight loss. And by providing these benefits the brand has transitioned from a low fat consumer product to a perceived personal weight management partner for its customers. Furthermore it appears to understand variety seeking behaviour  [4]  of its consumers as it extended its product line to include other SK sub-brands failing which women might have used other tasty healthy cereals with the SK personal plan. The brands packaging while being environmentally and user friendly: easy to transport and store, also serves as an effective marketing tool. It provides product information and reinforces the brands positioning by illustrating its value proposition of shape on the box. Moreover by using the Kelloggs name and tag line: If it doesnt say Kellogg on the boxà ¢Ã¢â€š ¬Ã‚ ¦.it isnt Kellogg in the box on the packaging, it depicts its association with Kelloggs premium quality and high brand value thus discouraging potential brand switching  [5]  . Place: Kellogg distributes SK selectively through supermarkets, hypermarkets and convenience stores utilizing the below represented distribution network. Using popular supermarkets/hypermarkets, which are the leading medium for cereal distribution (shown in figure 1.13), is aligned with SKs target market selection (covered in a prior discussion) which is accentuated by the supermarkets ability to attract customers through their own high advertising budgets (displayed in figure 1.14). Promotion: SK utilizes promotional campaigns, advertising and interactive marketing to sustain its winning market positioning. The SK 2 week challenge, which is an integral element of the cereals offering, originated as a creative promotional campaign that helped the brand acquire its market growth (Kellogg Company 2003, 2004). Success of the 2 week challenge is largely attributable to the consumer perception that it is an easier challenge to take due to its shorter duration. Another successful campaign launched by the brand is the SK slimmer jeans challenge which astutely kicks-off at the start of the New Year when women would be keen on losing their post holiday weight and dropping a jeans size (Kelloggs 2009). SK uses its high media advertising expenditure, which is higher than any of its competitors (shown in figure 1.15) to effectively communicate its positioning to its target market. It creatively employs the informational appeal message style in its television advertisements to convey product information and benefits, aimed at sustaining and attracting new customers (as evident in its latest advertisement  [6]  ). On the downside, some women may not relate to the product as the brand stereotypes a womens body shape by using perfect size models in most of its advertisements which may also conflict with its brands positioning of slimmer shape (not perfect shape). SK also recognized the growing popularity of internet among UK consumers (Euromonitor International 2009a) and hence uses its website and facebook group, as forms of interactive marketing, to connect with its customers. SK by allowing consumers to access the brands value added services on its attractive website aims to engage its customers and encourage repeat visits. Price: As cited earlier, SK is priced higher than any of its industry competitors  [7]  (displayed in figure 1.16) which is in sync with its premium brand positioning. The brands high quality is buttressed by its high price. SKs growing brand share despite its higher pricing appears to support the consumer perception that a high value compensates for a high price. But as discussed in the SWOT analysis, SKs future product demand may decline if the consumers opt to purchase the cheaper private health cereals due to the economic recession (Worth, 2009). Moreover its future demand may also be impacted by the marketing tactics of supermarkets such as placing their cheaper cereals on the shelf next to the SK brands  [8]  . Marketing recommendations: From the above analysis, it is evident that SK is effectively managing its marketing mix elements to strengthen its market positioning. However since the brand is in the maturity stage of its product life cycle (represented diagrammatically in figure 1.17) it needs to defend its market share to avoid the onset of the decline stage. Hence the following recommendations have been offered: Firstly using its exposure of a high advertising budget, SK can enhance its promotional activities by aptly launching additional innovative promotional challenges. And increase consumer participation in these challenges by providing opportunities to win prizes such as designer wardrobes or free SK cereal vouchers. Secondly by using real  [9]  slimmer size women in its advertisements it will not only distinguish itself from the other product manufacturers who stereotype womens body shape but also may generate increased consumer confidence in the products market message. Alternatively by taking inspiration from its website, SK can incorporate the success stories of its consumers in its advertisements to reinforce the products effectiveness. Lastly owing to the growing popularity of health foods it can extend its product line to introduce other weight assistance products such as SK nutrition drinks which may complement rather than compete with the cereal. Such product introductions will also reflect the brands commitment to delivering the healthy weight management needs of its consumers. The above recommendations will not only augment SK existing strong market positioning but will also discourage possible brand switching due to the economic recession. Conclusion: This assignment acknowledges that the marketing choices made by Special K, quite like its name, prove to be special for the brand. Perceptive of its consumer needs and behaviour, Special K effectually segmented its customers and selected a profitable and sustainable target market in a flourishing cereal industry. This target market selection has immensely contributed to the special status acquired by this brand. However the true success of the brand lies in how it differentiated itself from its competitors by relying on the SHAPE positioning that also acts as the value proposition for its consumers. Though the brand astutely manages the product, place, promotion and price attributes of its marketing mix to support its positioning, the reality of its product life cycle stage cannot be escaped. Hence recommendations to improve SKs advertising, promotional activities and brand line extensions have been made to avoid the onset of the decline stage for the product. Appendix: Kellogg brand list: Kellogg offers a vast product line catering to the needs of different customer segments. Kellogg brands include All bran, Coco Pops, Cornflakes, Crunchy Nut, Frosties, Fruit n Fibre, Winders, Natures Pleasure, Optivita, Country Store, Honey Loops, Just Right, Ricicles, Start, Pop tarts, Rice Krispies, Frosted Wheats and Special K. Special K product variations: Special K Packaging: As shown in the above images, Special Ks packaging conveys that it is a low fat cereal and provides information on the personal plan and its benefits and cereal nutrition figures. The red color is synonymous with the Special K branding and labeling which not only shows it strong connection with the Kelloggs brand but also symbolizes confidence and excitement (Kelloggs Special K, 2009) that a consumer will enjoy after achieving the shape desired by them. The packaging supports easy and convenient usage through the cardboard box and plastic bag, which help in storage and preservation of the quality of the cereal. Special K in supermarkets: The observations on the shelf space occupied by Kelloggs Special K were made by visiting two large supermarkets, Tesco and Morrisons. A large section of the middle shelf space in the cereal section of the supermarkets was devoted to Special K cereals and its sub-brands. This shelf positioning helps attract customer attention and expedite the purchase process. Another observation made was that both Tesco and Morrisons placed their cheaper cereals next to Special K which may deter the purchase decision of a cash strapped consumer. Infact Tesco has also extended this marketing gimmick to its online shop as displayed in the below images. Links to advertisements: http://www.specialk.co.uk/special-k-news.aspx Latest advert h ttp://www.tvadmusic.co.uk/2009/06/kellogs-special-k-shape-up-for-summer/

Nss Phy Book 2 Answer

1 1 2 3 C Motion I 7 (a) From 1 January 2009 to 10 January 2009, the watch runs slower than the actual time by 9 minutes. Therefore, when the actual time is 2:00 pm on 10 January 2009, the time shown on the watch should be 1:51 pm on 10 January 2009. Practice 1. 1 (p. 6) D (a) Possible percentage error 10 ? 6 = ? 100% 24 ? 3600 = 1. 16 ? 10 % 1 (b) = 1 000 000 days 10 ? 6 –9 It would take 1 000 000 days to be in error by 1 s. (b) Percentage error 9 = ? 100% 9 ? 24 ? 60 = 6. 94 ? 10–2% 4 (a) One day = 24 ? 60 ? 60 = 86 400 s Practice 1. 2 (p. 15) 1 2 3 4 5 C B D D (b) One year = 365 ? 86 400 = 31 500 000 s 5 Let t be the period of time recorded by a stop-watch. Percentage error = 0. 4 ? 100% ? 1% t t ? 40 s (a) Total distance she travels 2 ? ? 10 2 ? ? 20 2 ? ? 15 + + = 2 2 2 = 141 m (b) Magnitude of total displacement = 10 ? 2 + 20 ? 2 + 15 ? 2 = 90 m Direction: east Her total displacement is 90 m east. The minimum period of time is 40 s. 6 (a) Percentage error error due to reaction time = ? 100% time measured 0. 3 = ? 100% 10 = 3% 6 7 His total displacement is 0. With the notation in the figure below. (b) From (a), the percentage error of a short time interval (e. g. 10 s) measured by a stop-watch is very large. Since the time intervals of 110-m hurdles are very short in the Olympic Games, stop-watches are not used to avoid large percentage errors. Since ZX = ZY = 1 m, ? = ? = 60 °. Therefore, XY = ZX = ZY = 1 m The magnitude of the displacement of the ball is 1 m.  © 8 (a) The distance travelled by the ball will be longer if it takes a curved path. 7 (a) Length of the path = 0. 8 ? 120 = 96 m (b) No matter which path the ball takes, its displacement remains the same. (b) Length of AB along the dotted line 96 = 30. 6 m = (c) Magnitude of Jack’s average velocity 30. 6 ? 2 = = 0. 51 m s–1 120 Practice 1. 3 (p. 23) 1 B Total time 5000 5000 = + = 9821 s 1. 4 0. 8 5000 + 5000 = 1. 02 m s–1 Average speed = 9821 Practice 1. 4 (p. 31) 1 2 C B Final speed = 1. 5 ? 1 – 0. 2 ? 1 = 1. 3 m s–1 2 C Total time = 9821 + 10 ? 60 =10 421 s 5000 + 5000 Average speed = = 0. 96 m s–1 10 421 3 A By a = 3 D When the spacecraft had just finished 1 revolution, the spacecraft returned to its starting point. Therefore, its displacement was zero and its average velocity was also zero. v ? u , t v = u + at 36 = + ( ? 1. 5) ? 2 3. 6 = 7 m s–1 = 7 ? 3. 6 km h–1 = 25. 2 km h–1 Its speed after 2 s is 25. 2 km h–1. 4 5 D (a) Average speed 100 = = 10. m s–1 9. 69 (b) Yes. This is because the magnitude of the displacement is equal to the distance in this case. 4 B Take the direction of the original path as positive. Average acceleration of the ball ? 10 ? 17 = 0. 8 = –33. 8 m s–2 The magnitude of the average acceleration of the ball is 33. 8 m s– 2. v ? u By a = , t 100 ? 0 v ? u 3. 6 t= = = 4. 27 s a 6. 5 6 (a) Two cars move with the same speed, e. g. 50 km h–1, but in opposite directions. (b) A man runs around a 400-m playground. When we calculate his average speed, we can take 400 m as the distance and his average speed is non-zero. But since his displacement is zero (he returns to his starting point), his average velocity is zero. 5 The shortest time it takes is 4. 27 s.  © 6 Time / s –1 4 0 2 4 6 17 8 22 D Average speed 80 + 60 = 5 = 28 km h–1 Average velocity = Speed / m s 2 7 12 v ? u 22 ? 2 a= = 2. 5 m s–2 = t 8 The acceleration of the car is 2. 5 m s–2. 7 (a) I will choose ‘towards the left’ as the positive direction. 80 2 + 60 2 5 (b) 5 = 20 km h–1 C Total time 10 10 = + 2 3 = 8. 33 s v ? u , t u = v ? at = 9 ? (? 2) ? 3 = 15 m s–1 –1 (c) By a = Average speed 20 = 8. 33 = 2. 4 m s–1 Her average speed for the whole trip is 2. m s–1. The initial velocity of the skater is 15 m s . 8 (a) The object initially moves towards the left and accelerates towards the left. It will speed up. 6 7 8 9 10 C C C B A Magnitude of displacement = 2000 2 + 6000 2 = 6324. 6 m Magnitude of average velocity 6324. 6 = 4 ? 3600 = 0. 439 m s–1 6000 tan ? = 2000 ? = 71. 6 ° His average velocity is 0. 439 m s–1 (S 71. 6 ° E). (b) The object initially moves towards the right and accelerates towards the left. It will slow down. Its velocity will be zero and then increases in the negative direction (moves towards the left). Revision exercise 1 Multiple-choice (p. 5) 1 2 3 C D B  © 11 C Total time = 13 min = 780 s 840 ? 2 = 2. 15 m s ? 1 Average speed = 780 (b) Displacement from Sheung Shui to Lok Ma Chau 1000 = ? 6. 3 1 = 6300 m Magnitude of average velocity 6300 = 359 = 17. 5 m s–1 (1M) (1A) (1M) (1A) 12 13 D (HKCEE 2003 Paper II Q3) Conventional (p. 37) 1 Total time left for the two players = 4 ? 60 + 9 + 5 ? 60 + 16 = 565 s Total time they have been playing = 2 ? 60 ? 60 ? 565 = 6635 s (= 110 min 35 s = 1 h 50 min 35 s) (1A) 5 (a) Total distance = 1500 + 40 ? 1000 + 10 ? 1000 = 51 500 m Total time = 2 ? 3600 + 3 ? 60 + 8 = 7388 s Average speed 51 500 = 7388 = 6. 7 m s–1 (1M) (1A) 2 (a) 50 m (1A) (b) Ma gnitude of average velocity of Kitty 50 = (1M) 1? 60 + 15 = 0. 667 m s ? 1 (1A) (1M) (1A) (c) Average speed of the coach 5 + 50 + 5 = 1? 60 + 15 = 0. 8 m s ? 1 (b) Swimming: Average speed 1500 = 21 ? 60 + 28 = 1. 16 m s–1 Cycling: Average speed 40 000 = 1 ? 3600 + 1 ? 60 + 53 = 10. 8 m s–1 Running: Average speed 10 000 = 39 ? 60 + 47 = 4. 19 m s–1 (1M) His average speed was the highest in cycling. (1A) 3 (a) Since she measures the time interval based on 1 cycle of the pendulum, the error (0. 3 s) in measuring the cycle of the pendulum accumulates. is from 8 to 14 s. 1A) (1A) The range of the time interval (10 cycles) (b) When finding the time for one pendulum cycle, Jenny should time more pendulum cycles (e. g. 20) with the stop-watch and divide the time by the number of cycles. (1A) 4 (a) Time required 7. 4 ? 1000 = 20. 6 = 359 s (5 min 59 s) (1M) (1A)  © (c) Yes. Since the time interval of this competition is quite long, (1A) using stop-watch will not result in large percentage error as the reaction time for an average person is only 0. 2 s. (1A) (1M) (c) Total time = 5 min 45 s ? 1 min 58 s = 3 min 47 s = 3 ? 60 + 47 = 227 s v? u a= (1M) t 431 ? 0 = 3. = 0. 527 m s–2 (1A) 227 The average acceleration of the train is 0. 527 m s–2. 6 (a) v = u + at =0+6? 4 = 24 m s–1 = 86. 4 km h 86. 4 km h . –1 –1 (1A) The maximum speed of the car is 8 (1M) (a) Total distance = 8000 + 4000 + 5000 = 17 000 m Total time = 1 ? 3600 + 30 ? 60 + 45 ? 60 (b) v = u + at = 24 + (–4) ? 2 = 16 m s –1 –1 = 57. 6 km h (1A) –1 = 8100 s Average speed 17 000 = 8100 = 2. 10 m s–1 (1M) (1A) (c) The final speed of the car is 57. 6 km h . v? u a= (1M) t 16 ? 0 = 6 = 2. 67 m s–2 2. 67 m s–2. (1A) The average acceleration of the car is (b) 7 (a) Average speed 30 000 = 8 ? 60 = 62. m s–1 The average speed of the train is 62. 5 m s–1. (1M) (1A) (b) Maximum speed 430 = = 119. 4 m s? 1 > average speed 3. 6 (1A) The average speed must be smaller than the maximum speed because the train needs to speed up from start and slows down to stop during the trip. (1A) Magnitude of displacement = 3000 2 + 4000 2 = 5000 m Magnitude of average velocity 5000 = = 0. 617 m s–1 8100 4000 tan ? = 3000 (1A) ? = 53. 1 ° His average velocity is 0. 617 m s (N 53. 1 ° E).  © –1 (1A) 9 (a) Distance travelled = 10. 5 ? 3 ? 60 = 1890 m (1M) (1A) 10 (a) Total distance = (120 + 50) ? 1000 = 170 000 m (1M) (1A) b) Circumference of the track =2 r = 2 (400) = 2513 m The distance travelled by Marilyn is 3 1890 m which is about of the 4 circumference. (1A) (b) N ?XYZ is a right-angled triangle. Z ? 50 km 30 ° Y 60 ° X ? ? 120 km Magnitude of displacement (from town X to town Z) = 120 000 2 + 50 000 2 = 130 000 m 120 tan ? = 50 ? = 67. 4 ° Magnitude of displacement AB = 400 2 + 400 2 (1A) (1A) ? = 90 ° ? 67. 4 ° = 22. 6 ° ? = 60 ° ? 22. 6 ° = 37. 4 ° The total displacement of the car is 130 000 m (N 37. 4 ° E). = 566 m Magnitude of average velocity 566 = 3 ? 60 = 3. 14 m s 400 tan ? = 400 ? = 45 ° (S 45 ° E). –1 (c) (1A) Total time 170 000 = = 10 200 s 60 3. 6 Magnitude of average velocity 130 000 = 10 200 = 12. 7 m s–1 Its average velocity is 12. 7 m s (N 37. 4 ° E). –1 (1A) (1A) (1M) (1A) Her average velocity is 3. 14 m s–1  © 11 (a) AC = 60 2 + 80 2 = 100 m 80 tan ? = ? = 53. 1 ° 60 (1M) The total displacement of the athlete is 100 m (S53. 1 °W). (1A) 13 (Correct label of velocity with correct direction (towards the left). ) (Correct label of acceleration with correct direction (towards the right). ) (1A) (1A) (a) The coin moves in the following sequence: B A C C A Therefore, it is at A finally. Displacement of the coin = 15 cm (1A) (1M) (1A) (1M) b) Distance travelled by the coin = 15 + 30 + 30 = 75 cm (b) Time / s v / m s–1 0 –6 1 –4 2 –2 3 0 4 +2 5 +4 6 +6 (1A) (1A) (c) (i) Total time = 2 s ? 4 = 8 s Average velocity 15 ? 10 ? 2 = 8 = 0. 0188 m s? 1 (0. 5A ? 6) (1M) (1A) (c) The car will slow down and its speed will drop to zero. After th at the car will move towards the right with increasing speed (uniform acceleration). (1A) (1M) (1A) (1M) (1A) (1M) (1A) A (ii) Average speed 75 ? 10 ? 2 = 8 = 0. 0938 m s? 1 (1M) (1A) 12 (a) Total distance travelled = 60 + 80 + 80 + 60 = 280 m (d) (i) The coin moves in the following sequence: B A C C A B B b) Magnitude of total displacement = 80 + 80 = 160 m 160 m (west). The total displacement of the athlete is Therefore, it is at B finally. zero. the coin is also zero. (1A) (1M) (1A) (1M) (1A) (1M) (1A) (ii) The displacement of the coin is Therefore the average velocity of (c) Total distance travelled = 280 + 60 + 80 = 420 m 14 (a) Total distance = ? r = 5? ? 60 m C = 15. 7 m Total displacement =5+5 = 10 m 80 m  © The total displacement travelled by her is 10 m. (b) Jane’s statement is incorrect. (1A) Since both girls start at X and meet at Y, they have the same displacement. (1A) Betty’s statement is incorrect. 1A) Since both girls return to their starting point, their displacements are zero. (1A) Physics in articles (p. 40) (a) From 19 January 2006 to 28 February 2007, (1A) It takes New Horizons spacecraft a total of 406 days to travel from the Earth to Jupiter. (1A) (b) (i) Average speed total distance travelled = total time of travel (1M) = 8 ? 108 406 ? 24 (1A) (1M) = 8. 21 ? 104 km h? 1 (ii) Average acceleration change in velocity = total time of travel = (8. 23 ? 5. 79)? 10 4 406 ? 24 = 2. 50 ? 104 km h? 2 (1A) (1A) (c) July 2015  © 2 1 2 3 4 5 Motion II 10 (a) The object moves with a constant elocity. Practice 2. 1 (p. 61) D B D D B 30 ? 10 = 10 m s–1 v= 2 (b) The object moves with a uniform acceleration from rest. (c) The object moves with a uniform deceleration, starting with a certain initial velocity. Its velocity becomes zero finally. The velocity of the car at t = 2 s is 10 m s–1. 6 7 C (d) The object first moves with a uniform acceleration from rest, then at a constant velocity, and finally moves with a smaller uniform acceleration again. (a) Total displacement = 4 ? 5 + (? 5) ? (7 ? 5) = 10 m The total displacement from the staircase to her classroom is 10 m. (e) The object moves at a constant velocity and then suddenly moves at constant velocity of same magnitude in the opposite direction. (b) Classroom C 8 (f) The object moves with uniform deceleration from an initial velocity to rest, and continue to move with the uniform acceleration of the same magnitude in opposite direction. 9 (a) The object accelerates. (b) The object first moves with a constant velocity. Then it becomes stationary and finally moves with a higher constant velocity again. 11 (a) The object moves with zero acceleration (with constant velocity of 50 m s–1). (b) The object moves with a uniform cceleration of 5 m s–2. (c) 12 The object moves with uniform deceleration of 5 m s–2. (c) The object decelerates to rest, and then accelerates in opposite direction to return to its starting point. (a) It moves away from the sensor. (d) The object moves with uniform velocity towards the origin (the zero displacement position), passes the origin, and continues to move away from the origin with the same uniform velocity.  © (b) (c) The greatest rate of change in speed 0 ? 3. 5 = 2 = –1. 75 m s–2 (d) Total distance travelled = area under the graph 3. 5 ? 2 2 ? 6 = + 2 2 = 9. 5 m Practice 2. 2 (p. 71) 1 C By v2 = u2 + 2as, 290 3. 6 2 13 (a) =0+2? 1? s s = 3240 m = 3. 24 km < 3. 5 km The minimum length of the runway is 3. 5 km. 2 B Cyclist X is moving at constant speed. Time for cyclist X to reach finish line displacement 150 = = = 30 s time 5 For cyclist Y: u = 5 m s–1, s = 250 m, (b) Total distance travelled = area under the graph (12 + 6) ? 3 = 2 = 27 m a = 2 m s–2 By s = ut + 1 2 at , 2 1 250 = 5 ? t + ? 2 ? t2 2 (c) Average speed total distance travelled = time taken 27 = 3 t = 13. 5 s or t = ? 18. 5 s (rejected) Y needs 13. 5 s to reach finish line. Therefore, cyclist Y will win the race. 3 B Since the bullet start decelerates after fired into the wall, we could just consider the displacement of the bullet in the wall. To prevent the bullet from penetrating the wall, the bullet must stop in the wall. = 9 m s–1 14 (a) She moves towards the motion sensor. (b) The highest speed of the girl in the journey is 3. 5 m s–1.  © By v2 = u2 + 2as, 0 = 500 + 2 ? (? 800 000) ? s 2 8 By v = u + at, 14 = u + 2 ? 5 u = 4 m s–1 s = 0. 156 m = 15. 6 cm < 15. 8 cm The minimum thickness of the wall is 15. 8 m. By v2 = u2 + 2as, 142 = 42 + 2 ? 2 ? s s = 45 m 4 C When the dog catches the thief at t = 5 s, its total displacement is 30 m. The dog is sitting initially, so u = 0. 1 By s = ut + at2, 2 1 30 = 0 + a(5)2 2 The displacement of the girl is 45 m. 9 (a) v = u + at = 0 + 20 ? 0. 3 = 6 m s? 1 The horizontal speed of the ball travelling towards the goalkeeper is 6 m s? 1. a = 2. 4 m s–2 Its acceleration is 2. 4 m s–2. (b) By v2 = u2 + 2as, 02 ? 62 a= = –22. 5 m s? 2 2 ? 0. 8 The deceleration of the football should be 22. 5 m s? 2. 5 6 D 90 36 ? v? u = 3. 6 3. 6 = 1. 5 m s–2 a= t 10 By v = u + 2as, 2 2 10 (a) The reaction time of the cyclist is 0. 5 s. s= v ? u = 2a 2 2 90 3. 6 36 3. 6 2 ? 1. 5 ? 2 2 = 175 m (b) Braking distance (2. ? 0. 5)? 15 = 11. 25 m = 2 Thinking distance = 15 ? 0. 5 = 7. 5 m Stopping distance = 11. 25 + 7. 5 = 18. 75 m child. 20 m The distance travelled by the motorcycle is 175 m and its acceleration is 1. 5 m s . –2 7 (a) Thinking distance = speed ? reaction time 108 = ? 0. 8 = 24 m 3. 6 Therefore, the bicycle would not hit the (b) Since the car decelerates uniformly, braking distance v+u = ? t 2 108 +0 = 3. 6 ? (3 ? 0. 8) 2 = 33 m 11 By v = u2 + 2as, 0 = 32 + 2 ? (–0. 5) ? s s=9m 8m Therefore, the golf ball can reach the hole. 2 12 (a) (i) By v = u + at, 0 = u + (–4)(4. 75) u = 19 m s–1 The initial velocity of the car is 19 m s–1. (c) Stopping distance = thinking distance + braking distance = 24 + 33 = 57 m  © (ii) By v2 = u2 + 2as, 0 = 19 + 2 ? (–4) ? s s = 45. 1 m 2 3 C For option A, apply equation v2 = u2 – 2gs and take s = 0 (the ball returns to the second floor), v = –u = –10 m s–1 (vertically downwards) The displacement of the car before it stops in front of the traffic light is 45. 1 m. This is the same velocity as the initial velocity of option B. Therefore, in both ways the ball has the same vertical speed when it reaches the ground. (b) By v = u + 2as, 17 = 0 + 2 ? 3 ? s s = 48. 2 m 2 2 2 The displacement of the car between starting from rest and moving at 17 m s is 48. 2 m. –1 4 B Take the upward direction as positive. 1 By s = ut + at2, 2 1 0 = u ? 30 + ? (? 10) ? 302 2 u = 150 m s–1 13 (a) By v2 = u2 + 2as, v2 = 0 + 2 ? 0. 1 ? 500 v = 10 m s–1 His speed is 10 m s . –1 (b) Consider the first section. By v = u + at, v? u t= a 10 ? 0 = 0. 1 = 100 s Consider the second section. 1 By s = ut + at2, 2 1 800 = 10t + ? 0. 5t2 2 t = 40 s or t = –80 s (rejected) The speed of the bullet is 150 m s–1 when it is fired. 5 Speed of stone Equation used t=1s t=2s t=3s t=4s v = u + at Distance travelled by the stone 1 s = ut + at 2 2 m 20 m 45 m 80 m 10 m s–1 20 m s 30 m s –1 –1 40 m s–1 Total time taken = 100 + 40 = 140 s It takes 140 s for Jason to travel downhill. 6 1 By s = ut + at2, 2 1 10 = 0 + (10) t2 2 t = 1. 41 s v = u + at Practice 2. 3 (p. 83) 1 2 D D = 0 + 10(1. 41) = 14. 1 m s–1 It takes 1. 41 s for a diver to drop from a 10-m platform. His speed is 14. 1 m s–1 when he enters the water.  © 7 Take the upward direction as positive. By v = u + 2as, 4 = 0 + (2)(–10)s s = 0. 8 m 2 2 2 Besides, since Y spends a shorter time to reach its highest point, it should be fired after X. 10 (a) By s = ut + The highest position reached by the puppy is 0. m above the ground. 8 (a) Consider the boy’s downward journey. Take the downward direction as positive. 1 By s = ut + at2, 2 1 0. 5 = 0 + (10) t2 2 t = 0. 316 s 1 2 at , 2 1 120 = 8t + ? 10 ? t2 2 t = 4. 16 s or t = ? 5. 76 s (rejected) It takes 4. 16 s to reach the ground. (b) v = u + at = 8 + 10 ? 4. 16 = 49. 6 m s–1 Its speed on hitting the ground is 49. 6 m s–1. 11 (a) Distance between the ceiling and her hands = 6 – 2 – 1. 2 = 2. 8 m Hang-time of the boy = 0. 316 ? 2 = 0. 632 s (b) Let s be her vertical displacement when she jumps. As the maximum jumping speed is 8 m s–1, i. e . u = 8 m s–1. By v2 = u2 + 2as, v2 ? 2 s= 2a 2 0 ? 82 = (upwards is positive) 2 ? (? 10) s = 3. 2 m > 2. 8 m Therefore, the indoor playground is not safe for playing trampoline. 1 (a) By s = ut + at2, 2 1 132 = 0 ? t + ? 10 ? t2 2 t = 5. 14 s The vehicle can experience a free fall in the Zero-G facility for 5. 14 s. (b) Take the upward direction as positive. By v = u + 2as, 0 = u + 2 ? (–10) ? 0. 5 u = 3. 16 m s–1 2 2 2 The jumping speed of the boy is 3. 16 m s–1. 9 Take the upward direction as positive. (a) By v2 = u2 + 2as, 0 = u2 + 2(–10)(200) u = 63. 2 m s–1 The velocity of the firework X is 63. 2 m s–1 when it is fired. 12 (b) By v = u + at, = 63. 2 + (–10)t t = 6. 32 s It takes 6. 32 s for the firework X to reach that height. (c) From (a) and (b), for firework Y to explode at 130 m above the ground, the speed of Y should be smaller than that of X. Therefore, Y should be fired at a (b) By v2 = u2 + 2as, v2 = 02 + 2 ? 10 ? 132 v = 51. 4 m s? 1 The speed of the vehicle before it comes to a stop is 51. 4 m s? 1.  © lower speed. (c) Take the upward direction as positive. By v = u + at, –v = v – gt 2v = gt If the stone is projected with a speed of 2v, let the new time of travel be t?. (–2v) = (2v) – gt? v t? = 4 ( ) g = 2t Its new time of travel is 2t. 6 B Take the upward direction as positive. 1 s = ut + at2 2 1 = (10)(4) + (–10)(4)2 2 = –40 m The distance between the sandbag and the ground is 40 m when it leaves the balloon. Revision exercise 2 Multiple-choice (p. 87) 1 D By v2 = u2 + 2as, 0 = 102 + 2a(25 – 10 ? 0. 2) a = –2. 17 m s–2 His minimum deceleration is 2. 17 m s–2. 2 3 D B Consider the rock released from the 2nd floor. By v2 = u2 + 2as, v2 = 2as floor. Note that s2 = 3. 5s. (v2)2 = 2as2 = 3. 5(2as) = 3. 5v2 v2 = 1. 87v (as u = 0) Then consider the rock released from the 7th 7 8 D C Take the downward direction as positive. u = 200 m s–1, v = 5 m s–1, a = ? 0 m s–2 By v = u + at, 5 = 200 + (? 20)t t = 9. 75 s The rockets should be fired for at least 9. 75 s. Both C and D satisfy this requirement. But for D, after firing for 10. 2 s, v = u + at = 200 + (–20)(10. 2) = –4 m s–1 i. e. it flies away from the Moon with 4 m s–1 upwards. It c annot land on the Moon. Therefore, the correct answer is C. 4 5 A C The stone returns to the ground with the same speed (but in opposite direction). 9 10 D D  © 11 12 13 (HKCEE 2006 Paper II Q1) (HKCEE 2007 Paper II Q2) (HKCEE 2007 Paper II Q33) (b) (i) Conventional (p. 89) 1 (a) The reaction time of the driver is 0. 6 s. (b) v a= t = 0 ? 12 3. 6 ? . 6 (1A) (Correct axes with label) from t = 1. 20 s to 1. 25 s) from t = 1. 45 s to 1. 50 s) (1A) (1A) (1A) (A straight line with slope = 0. 35 m s–1 (A straight line with slope = –0. 35 m s–1 (1A) (1M) = –4 m s–2 The acceleration of the car is –4 m s–2. (c) The stopping distance of the car is the area under graph. Stopping distance 12 ? (3. 6 ? 0. 6) =12 ? 0. 6 + 2 = 25. 2 m The stopping distance of the car is shorter than 27 m. The driver will not be charged with driving past a red light. (1A) (1A) (1M) (ii) 2 (a) The object moves away from the motion sensor with uniform velocity at 0. 35 m s–1 from t = 1. 20 s to 1. 25 s. 1A) From t = 1. 25 s to 1. 45 s, the object moves with negative acceleration. (1A) Then, from t = 1. 45 s to 1. 50 s, the object changes its moving direction and moves towards the motion sensor again with a uniform velocity of –0. 35 m s–1. (1A) (Correct axes with labels) (1A) (Correct graph with the acceleration of ? 0. 35 ? 0. 35 about 1. 40 ? 1. 30 = –7 m s–2 at t = 1. 30 s to 1. 40 s) (1A) !  © 3 (a) (b) Total displacement of the car = area bound by the v? t graph and the time axis 1 1 = (5 ? 5) ? (20 ? 3) 2 2 = ? 17. 5 m (1M) (1A) (c) Yes, the car moves 12. 5 m forwards from t = 0 to t = 5 s. Therefore, it hits the roadblock. 1A) 5 Take the upward direction as positive. (a) From point A to the highest point: (Correct axes with labels) (Correct shape of minibus’ graph) (Correct shape of sports car’s graph) (Correct values) (1A) (1A) (1A) (1A) By v2 = u2 + 2as, 0 = 42 + 2 (–10) s s = 0 . 8 m By v = u + at, 0 = 4 + (–10)t t = 0. 4 s (1M) From the highest point to the trampoline: 1 s = ut + at2 (1M) 2 1 = 0 + (–10)(1. 2 – 0. 4)2 2 = –3. 2 m (1A) 3. 2 m above the trampoline. (1A) The maximum height reached by him is (1M) (b) From the graph in (a), the two vehicles have the same velocity at t ? 2. 3 s after passing the traffic light. (1A) (1M) (c) The area under graph is the displacement of the cars. Consider their displacements at t = 3 s, For the sports car: 1 s = ? 15 ? 3 = 22. 5 m 2 For the minibus: 1 s = ? (7 + 13) ? 3 = 30 m 2 The minibus will take the lead 3 s after passing the traffic light. (1A) (b) Height of point A above the trampoline (1A) = 3. 2 – 0. 8 = 2. 4 m (1M) (1A) 6 (a) Initial velocity v = 90 km h–1 90 = m s–1 3. 6 = 25 m s–1 Thinking distance =v? t = 25 ? 0. 2 =5m The thinking distance is 5 m. (1A) (1M) 4 (a) The car moves forward with uniform acceleration at ? 1 m s? 2 from t = 0 s to t = 5 s. (1A) (1A) Then the car changes its moving direction. From t = 5 s to t = 8 s, it moves backwards with a uniform acceleration of ? 6. 67 m s . ?2 Its instantaneous velocity is 0 at t = 5 s. (1A) †  © (b) By v2 = u2 + 2as, v2 ? u2 a= 2s 2 0 ? 25 2 = 2 ? (80 ? 5) = ? 4. 17 m s–2 4. 17 m s–2. (1M) (c) The slope of the graph is the magnitude of the acceleration of the apple. speed / m s? 1 7. 75 (1A) (1A) Hence, the deceleration of the car is (c) By v2 = u2 + 2as, s= v ? u 2a 0 2 ? 25 2 = 2 ? ( ? 4. 17 ? 2) 2 2 (1M) 0 0. 775 time / s (Correct labelled axes) (2A) (1A) (Straight line with a slope of 10 m s? 2) = 37. 5 m Braking distance = 37. 5 m Stopping distance = 37. 5 + 5 = 42. m (1M) (d) The two graphs have no difference. (1A) (1A) 8 (a) Take the downward direction as positive. By v2 = u2 + 2gs, v = u + 2 gs 2 The driver could not stop before the traffic light. Therefore, his claim is incorrect. (1A) (1M) 7 (a) Take the downward direction as positive. 1 By s = ut + gt2, 2 1 3 = 0 ? t + ? 10 ? t2 2 3? 2 t= = 0. 775 s 10 (1M) = 0 2 + 2 ? 10 ? (40 ? 3) = 27. 2 m s–1 cushion is 27. 2 m s? 1. 1 (b) (i) By s = ut + gt2, 2 1 40 – 3 = 0 + ? 10 ? t2 2 t = 2. 72 s (1A) The speed of the residents landing on the (1M) (1A) The apple travels in air for 0. 775 s. (1A) (b) By v2 = u2 + 2as, v = 2 ? 10 ? 3 (1M) 1A) –1 = 7. 75 m s? 1 The speed of the apple is 7. 75 m s when the apple just reaches the ground. The time of travel in air is 2. 72 s. u+v (ii) By s = t, (1M) 2 2s t= u+v 2? 3 = t 27. 2 + 0 = 0. 221 s (1A) The time of contact is 0. 221 s.  © (c) (b) Slope of the graph from t = 0 to t = 0. 28 s 2. 3 ? 0 = 0. 28 ? 0 = 8. 21 m s–2 The acceleration of the ball due to gravity is 8. 21 m s–2. (1M) (1A) (c) (Correct labeled axes) (Correct shape) (Correct values) (1A) (1A) (1A) (i) 9 (a) t = 2 s: Displacement of the trolley = 0. 7 ? 0. 15 = 0. 55 m t = 3. 4 s: (1A) Displacement of the trolley = 1. 175 ? 0. 15 = 1. 025 m t = 4. 9 s: 1A) Displacement of the trolley = 0. 6 ? 0 . 15 = 0. 45 m (1A) (b) It moves away from the motion sensor with a changing speed from t = 2 s to t = 3. 4 s. (Correct sign) (Correct shape) (1A) (1A) (1A) (1A) (1A) (ii) The method does not work Then it rests momentarily at t = 3. 4 s. After that, it moves towards the motion since ultrasound will be reflected by the transparent plastic plate. (1A) (c) sensor with a changing speed. 1 By s = ut + at2, 2 1 ? 0. 1 = 0. 7 ? 2. 9 + ? a ? (2. 9)2 2 a = ? 0. 507 m s? 2 (1A) (1M) 11 (a) (i) The ball is held 0. 15 m from sensor before being released. The ball hits the ground which is 1. m from the sensor. (1A) (1A) Therefore, the ball drops a height of 0. 95 m. which are 0. 45 m, 0. 65 m and 0. 775 m from the sensor in its first 3 rebounds. (1A) The acceleration of the trolley is ? 0. 507 m s? 2. (ii) The ball rebounds to the positions 10 (a) The motion sensor is protruded outside the table to avoid the reflection of ultrasonic signal from table. (1A)  © At the 1st rebound, the ball rises up (1. 1 ? 0. 45) = 0. 65 m. nd The average acceleration is 66. 6 m s–2. (1A) (1A) (1A) (c) v / m s? 1 6. 32 At the 2 rebound, the ball rises up (1. 1 ? 0. 65) = 0. 45 m. rd At the 3 rebound, the ball rises up (1. 1 ? 0. 75) = 0. 325 m. (b) (i) The ball hits the ground with velocities of 3. 9 m s , 3. 25 m s and 2. 75 m s–1 in its first 3 rebounds. (3A) 3. 9 (1M) 0. 95 ? 0. 55 (1A) –1 –1 t3 t1 t2 t4 t5 t/s (ii) Acceleration = slope of graph = = 9. 75 m s–2 ?6. 32 (3 straight lines) (Correct slopes) (1A) (1A) 12 Take the downward direction as positive. 1 (a) By s = ut + gt2, (1M) 2 1 2 = 0 ? t + ? 10 ? t2 2 2? 2 t= = 0. 632 s (1A) 10 It takes 0. 632 s from t1 to t2. (Correct labels of time and velocity)(1A) 13 (a) Speed v = 70 km h–1 70 = m s–1 3. 6 = 19. 4 m s–1 d Reaction time = v 6 = 19. 4 = 0. 309 s The reaction time of the man was 0. 09 s. (1M) (b) At t2, v = u + at (1A) = 0 + 10 ? 0. 632 = 6. 32 m s –1 –1 (1 M) Shirley’s speed is 6. 32 m s when she lands on the trampoline at t2. At t4, she leaves the trampoline at the same speed. Therefore, from t3 to t4, by v2 = u2 + 2as, a= v2 ? u2 2s (? 6. 32) 2 ? 0 2 = 2 ? 0. 3 (b) By v2 = u2 + 2as, v2 ? u2 a= 2s 2 0 ? 19. 4 2 = 2 ? 48 = –3. 92 m s–2 3. 92 m s–2. (1M) (1M) (1A) The average deceleration of the car was (c) (1A) Speed v = 80 km h–1 80 = m s–1 3. 6 = 22. 2 m s–1 = 66. 6 m s–2  © Thinking distance = vt = 22. 2 ? 0. 309 = 6. 86 m By v = u + 2as, braking distance s v2 ? u2 = 2a 2 0 ? 22. 2 2 = 2 ? ? 3. 92) 2 2 (1A) Take the upward direction as positive. 1 s = ut + at2 (1M) 2 1 = 7 ? 1. 75 + ? (–10) ? 1. 752 2 = –3. 06 m (negative means the water is below the spring board) The spring board is 3. 06 m above the water. Alternative method: (1A) = 62. 9 m Therefore, the stopping distance = 6. 86 + 62. 9 = 69. 8 m (1A) Consider the upward motion and downward motion separatel y. For the upward motion, she takes 0. 7 s to reach the highest point from the spring board. Take the upward direction as positive. 1 By s = ut + at2, (1M) 2 1 s1 = 7 ? 0. 7 + ? (–10) ? 0. 72 2 = 2. 45 m For the downward motion, she takes 1. 5 s from the highest point to enter water. Take the downward direction as positive. By s = ut + 1 2 gt , 2 1 s2 = 0 + ? 10 ? 1. 052 = 5. 51 m 2 (1A) This stopping distance is greater than the initial distance between the car and the boy. (1A) Therefore, the car would have knocked down the boy if the car had travelled at 80 km h? 1 or faster. (d) A drunk has a longer reaction time. (1A) This means that the thinking distance, and thus the stopping distance (sum of thinking distance and braking distance), increases. (1A) (1M) (1A) 14 (a) Take the upward direction as positive. By v = u + at, u = 0 ? (? 10) ? 0. 7 = 7 m s–1 board is 7 m s . 1 Therefore the height of the spring board above the water = s2 – s1 = 5. 51 – 2. 4 5 = 3. 06 m (1A) (1M) (1A) The speed of Belinda leaving the spring (b) Total time taken from the spring board to the water = 0. 7 + 1. 05 = 1. 75 s (c) v = u + at = 0 + (? 10) ? 1. 05 = ? 10. 5 m s–1 is 10. 5 m s–1.  © The speed of the diver entering the water (d) Deceleration of car Y = slope of the graph during 0. 5 s? 8. 5 s = 0 ? 19. 4 = –2. 43 m s–2 8. 5 ? 0. 5 (1A) The deceleration of car Y is 2. 43 m s–2. (c) Thinking distance = area under the graph during 0? 0. 5 s = 19. 4 ? 0. 5 = 9. 7 m (1A) (Correct shape) (Correct times) (Correct velocities) 1A) (1A) (1A) Braking distance = area under the graph during 0. 5 s? 8. 5 s 1 = ? 19. 4 ? (8. 5 – 0. 5) 2 = 77. 6 m distance are 9. 7 m and 77. 6 m respectively. (1A) The thinking distance and the braking (e) (See the figure in (d). ) (Correct slope – parallel to that in (d). ) (1A) (Correct position – above that in (d). ) (1A) 15 (a) Speed 70 km h–1 70 = m s–1 3 . 6 = 19. 4 m s –1 (d) The coloured area is equal to the difference in the stopping distances travelled by cars X and Y. (1A) (e) (1M) Stopping distance of car X = area under the graph during 0? 5 s 1 = ? 19. 4 ? 5 = 48. 5 m 2 Coloured area = 9. 7 + 77. 6 – 48. = 38. 8 m < 50 m Since the difference in stopping distances of the cars is smaller than the initial separation of the cars, the two cars do not collide with each other before they stop. (1A) (1M) (1M) Distance travelled by car Y in 2 s = vt = 19. 4 ? 2 = 38. 8 m < 50 m Since the distance between the cars is greater than the distance that car Y can travel in 2 s, the driver of car Y obeys the rule. corresponding v–t graph. Deceleration of car X = slope of the graph during 0? 5 s (1A) (1M) (b) Deceleration of a car is the slope of their 0 ? 19. 4 = 5? 0 = –3. 88 m s–2 The deceleration of car X is 3. 88 m s–2. (1A) 16 a) From t = 0 s to t = 5 s, the car moves with a uniform acceleration of 17 ? 0 = 3. 4 m s–2. 5 (1A)  © From t = 5 s to t = 20 s, the car moves with a constant velocity of 17 m s–1. (1A) From t = 20 s to t = 28 s, the car moves with a uniform acceleration of 0 ? 17 = ? 2. 125 m s–2. 28 ? 20 at rest. (1A) (b) s = ut + 1 2 at 2 1 = 0 + ? 17. 5 ? (8 ? 60)2 2 = 2 016 000 m (2016 km) (1M) (1A) The Shuttle travels 2 016 000 m (2016 km) in the first 8 minutes. From t = 28 s to t = 30 s, the car remains (1A) 19 (a) (i) The cyclist is using first gear when the acceleration is greatest before braking. shortest time. (1A) (1A) (1M) (1M) (1A) b) (ii) The cyclist uses second gear for the (b) Distance travelled = area under straight line PQ (8 + 6) ? 2 = 2 = 14 m The cyclist travels 14 m in second gear. (c) The acceleration during t = 18 s? 20 s 0? 9 = (1M) 20 ? 18 = ? 4. 5 m s–2 The deceleration is 4. 5 m s . –2 (1A) (Correct shape) (Correct time instants) (Correct accelerations) (1A) (1A) (1A) (1A) (1A) 20 21 (c) Yes. (HKCEE 2 005 Paper I Q1) 1 (a) s = ut + at2 2 1 = 0 + ? 10 ? (500 ? 10? 3)2 2 = 1. 25 m Therefore the minimum height the (1M) The car changes direction at t = 30 s. Its velocity changes from positive to negative, showing a change in its travelling direction. 1A) (1M) (1A) (1A) laptop must fall for it to be ‘saved’ is 1. 25 m. (b) v = u + at = 0 + 10 ? (500 ? 10 ) = 5 m s? 1 the ground is 5 m s–1. ?3 (1M) (1A) 17 18 (HKCEE 2002 Paper I Q8) (a) v = u + at = 0 + 17. 5 ? 8 ? 60 = 8400 m s–1 minutes is 8400 m s–1. The speed of the computer when it hits The speed of the Shuttle after the first 8  © (c) Most falls are likely to be from below this height, effect. (1A) (1A) (1A) so the protection will not have taken Physics in articles (p. 96) (a) 2. 45 m (b) (i) By v2 = u2 + 2as, u = v ? 2as u2 = 0 ? 2(? 10)(2. 45 + 0. 07 ? 1. 09) u = 5. 35 m s? 1 2 2 (1A) (1M) Take the upward direction as positive. 22 (a) Any one from: Rate of change of displacement Displacement per unit time (1A) (b) The velocity of a braking car is decreasing (with time) (1A) so the car has negative acceleration. (1A) Its displacement is (still) increasing with time, so its velocity is (still) positive In this case, the acceleration and velocity are in opposite directions. (1A) (1A) (1A) The vertical speed of Javier Sotomayor is 5. 35 m s? 1 when he leaves the ground. (ii) Take the upward direction as positive. Consider the upward journey. By v = u + at, v ? u 0 ? 5. 35 t= = = 0. 54 s a ? 10 (1M) (c) i) Consider the downward journey. 1 By s = ut + at2, (1M) 2 1 ? (2. 45 + 0. 07 ? 0. 71) = 0 + (? 10) t2 2 t = 0. 60 s The time that he stays in the air = (0. 54 + 0. 60) = 1. 14 s Alternative method: (1A) (Correct graph) (1A) Take the upward direction as positive. 1 By s = ut + at2, (1M) 2 (0. 71 ? 1. 09) = 5. 35t + 1 (? 10)t 2 (1M) 2 t = 1. 14 s or t = ? 0. 07 s (rejected) (ii) Vertical distance travelled = area under the graph from 4. 0 s to 10. 0 s (70 + 130)? 6 = 2 (1M) (1A) The time that he stays in the air is 1. 14 s. = 600 m (1A) The vertical distance travelled by the rocket between t = 4. 0 s and t = 10. s is 600 m.  © 3 1 2 3 4 C C Force and Motion 6 (a) The MTR train is accelerating in the forward direction. The man tends to move at his original speed (smaller speed), so he would move backwards relative to the MTR train. (b) The MTR train is slowing down. The man tends to move at his original speed (greater speed), so he would move forwards relative to the MTR train. (c) The MTR train is moving forwards at constant velocity. The man moves forwards with the same constant velocity, so he would remain at rest relative to the MTR train. (d) The MTR train is turning a corner. The Practice 3. 1 (p. 104) (b), (e), (f) 5 a) Stretching a rubber band (b) Standing on the floor (c) Walking time (e) (f) A compass A rubbed plastic ruler attracts small bi ts of paper (d) Exists in every object on the earth at any 7 man tends to move at his original direction, so he would move outwards relative to the MTR train. In space, the gravitational force acts on the spaceship is negligible. When the rockets are shut down, they do not exert a force on the spaceship. Therefore, no net force acts on the spaceship. By Newton’s first law, the spaceship is in uniform motion and can travel far out in space. 8 Joan moves on the ice surface with a constant velocity. Practice 3. 2 (p. 111) 1 2 3 4 5 C C D C (a) No. Athletes would hit the wall of the stadium if it is too close to the finishing line. (b) The mat is used to protect the athletes if they hit the wall after passing the finishing line. Practice 3. 3 (p. 122) 1 2 3 4 5 D A B A D  © 6 (a) 7 (a) Horizontal component = 40 + 30 cos 30 ° = 66. 0 N Vertical component = 30 sin 30 ° = 15 N Resultant = 66 2 + 15 2 = 67. 7 N Let ? be the angle between the resultant Resultant’s magnitude is 67 N and the angle between the resultant and the horizontal is 13 °. (b) and the horizontal. 15 tan = ? = 12. 8 ° 66 Resultant’s magnitude is 67. N and the angle between the resultant and the horizontal is 12. 8 °. (b) Horizontal component = 40 + 30 cos 45 ° = 61. 2 N Vertical component = 30 sin 45 ° = 21. 2 N Resultant’s magnitude is 65 N and the angle between the resultant and the horizontal is 19 °. (c) Resultant = 61. 2 2 + 21. 2 2 = 64. 8 N Let ? be the angle between t he resultant and the horizontal. 21. 2 tan = ? = 19. 1 ° 61. 2 Resultant’s magnitude is 64. 8 N and the angle between the resultant and the horizontal is 19. 1 °. (c) Resultant’s magnitude is 60 N and the angle between the resultant and the horizontal is 25 °. (d) Horizontal component = 40 + 30 cos 60 ° = 55 N Vertical component = 30 sin 60 ° = 26. 0 N Resultant = 55 2 + 26. 0 2 = 60. 8 N Let ? be the angle between the resultant and the horizontal. 26. 0 ? = 25. 3 ° tan = 55 Resultant’s magnitude is 60. 8 N and the angle between the resultant and the Resultant’s magnitude is 50 N and the angle between the resultant and the horizontal is 37 °. horizontal is 25. 3 °.  © (d) Resultant = 40 2 + 30 2 = 50 N Let ? be the angle between the resultant and the horizontal. 30 tan = ? = 36. 9 ° 40 Resultant’s magnitude is 50 N and the angle between the resultant and the horizontal is 36. 9 °. Hence, the angle between the two 5-N forces is 120 °. Alternative method: By tip-to-tail method, the two 5-N forces and the resultant 5-N force form an equilateral triangle. It is known that each angle of an equilateral triangle is 60 °. Therefore, the angle between the two 5-N forces is 120 °. 8 (a) 10 (b) Resultant force = 2 ? 400 = 800 N The resultant force provided by the cable is 800 N. 11 For the 2-kg mass: (c) 9 R = weight ? cos ? = 20 cos 30 ° = 17. 3 N Suppose the two forces act in the direction as shown. T = 20 N Therefore we have: Vertical component Fx = 5 sin ? Horizontal component Fy = 5 ? 5 cos ? = 5 ? 1 ? cos ? ) (magnitude of the resultant)2 = Fx2 + Fy 2 52 = (5 sin ? )2 + [5 ? (1 ? cos ? )]2 1 = sin ? + 1 ? 2 cos ? + cos ? 2 2 2T cos 45 ° = W 2 ? 20 ? cos 45 ° = W cos ? = 0. 5 W = 28. 3 N ? = 60 °  © 12 (a) 2T sin 10 ° = 500 T = 1440 N The tension of the string is 1440 N. 3 4 5 6 B C A Net force = ma = 40 ? 0. 5 = 20 N C By v2 – u2 = 2as, 0 à ¢â‚¬â€œ u2 = 2a(20) ? u2 = 40a u2 a=? 40 Resistance = ma = 12 ? ? u2 = –0. 03u2 40 (b) Component of force = T cos 10 ° = 1440 ? cos 10 ° = 1420 N The component of the force that pulls the car is 1420 N. 13 (a) 7 8 ‘A bag of sugar weighs 10 N. ’ or ‘A bag of sugar has a mass of 1 kg. By F = ma, F 800 000 a= = = 2 m s–2 m 4 ? 10 5 (b) As the mass is stationary, the net force acting on it is zero. When it flies horizontally, its acceleration is 2 m s–2. 100 ( )? 0 v? u (a) a = = 3. 6 = 4. 63 m s–2 t 6 The acceleration of the car is 4. 63 m s–2. (c) (i) y-component of F1 = weight of mass = 10 N 9 y-component of F1 = F1 sin 30 ° F1 sin 30 ° = 10 N F1 = 20 N x-component of F1 = F1 cos 30 ° = 20 cos 30 ° = 17. 3 N (b) F = ma = 1500 ? 4. 63 = 6945 N The force provided by the car engine is 6945 N. 10 (a) (ii) y-component of F2 = 0 x-component of F2 = x-component of F1 = 17. 3 N

The Troubled American Education System

In an enlightening article by writer April Shenandoah, on March 20, 2002, the reality that Americas' education system is in real trouble becomes clearly evident. The writer feels that when a child in America attends school, he is, in fact, more at risk than if he did not attempt to attend. This is because, of late, it has become obvious that most negative influences that children are faced with are being increasingly found in the public schools that they attend, and it is during the past few decades that the situation has worsened even further. In a simple comparison between the situation in public schools today and that during the 1940's, it is indeed amazing that punishments were given for ‘offences' such as, for example, running in the corridor, chewing gum, talking in the class, and at times, unfinished homework, whereas today the top offences are drunkenness, drug abuse, assault, rape, and many other similar crimes, including murder. (Shenandoah, 2002) What has made the system even worse is that not only does the child have to cope with drugs and the immorality that is generally associated with them, but he would also be forced to study in the ‘second rate' education system of today. This is evident in the fact that from the year 1963 onwards, the scores for the ‘Scholastic Aptitude Tests' have been constantly dropping. This has developed into yet another problem, and this is that since the grade have been dropping, students are not able to cope with the existing syllabus, and today, newer textbooks have to be written for students at a lower grade level, so that they may cope better. It is the truth that today's newspapers and magazines are written for people at about a sixth grade level, and this is the standard of the average American citizen. What is even worse is the fact that many students are not at all aware of how little they are actually learning, and when they apply for University education elsewhere, it is then that they are forced to accept the fact that they have not received a good and solid education. (Shenandoah, 2002) An extract from a speech made in the Senate on January 23, 1990, shows that the author believes that the American education system is in deep trouble. One reason for this may be that everyone, politicians, educators, and numerous others who are involved in the system seem to have forgotten one important aspect of public education: the child. No one really seems to care for the child; more concern is being shown towards racial balance, effective teaching methods, an improvement of the curriculum, and so on and so forth, but the student, the child has become lost is all this. For example, in a school in North Carolina, importance is given to ‘racial balance', wherein school children belonging to all types of races are put into the bus two hours before the start of school, and dropped off an hour before school is supposed to begin, and the children are quite worn out and tired even before school has started. (American Education in Trouble) In a similar manner, teachers are being trained into becoming more ‘effective' teachers, and this would entail that they follow a set pattern of behaviors within the classroom so that they may be able to secure a better score with the administration. What about the children? Who cares about them? They are not allowed to interrupt, or even to become involved with the lesson being taught, because this may interfere with the ‘mandated' behaviors that the effective teacher is set to follow, and lower his rating. Today, most states are becoming aware of the fact that this system is doing absolutely no good for the children, and are therefore trying to eliminate it. Another is the ‘merit pay' system. This may be a credible concept and linked to the evaluation of teachers, but the problem here is that even today, the evaluation is carried out under the ‘effective teacher' plan and not under the merit pay system, and therefore, this is not at all valid. The textbook system in public education in America today has, in fact, become more of an ‘absurdity' than anything else. Textbooks today are not only becoming more and more expensive, but the content of the textbooks is also going down in its standard. Today, it is a fact that more and more textbooks are being written by the so called ‘experts' in the field, and the curriculum as such is dictated by either the current educational ‘fad' of the time, or by the special interests that the expert may have in the entire episode. It must be remembered that almost all educational fads last for a maximum period of ten years, and it is a sad fact indeed that by the time the teacher becomes accustomed to the content and the information contained within the textbooks, they have already become obsolete, and it is time to change them yet again. In addition, it is a fact that the textbook industry is a huge and lucrative one, and all the smaller schools and the smaller states find that they are completely at the mercy of the textbook selectors in the states, where they are the largest spenders. One example is the influence that a large state like California has had on the textbook industry. In recent times, California had rejected all the science textbooks because it felt that the subject matter of evolution had not been given enough importance and the information was much too scanty, and today, all science textbooks are full of assertions that want to prove that the unproven theory of evolution is indeed a fact. At the same time, religion was banished from textbooks, especially during the 1980's, because of the separation of the church and the state and the controversy surrounding the issue. Teachers are also scapegoats in the education system in America, for who really cares for them? At the outset, they are extremely overworked, in fact, more than any other worker. They are forgotten too, just like their students, in the long run. At the same time, they are expected to care for the forgotten students, and they are also expected to teach more and more, despite the fact that they are not given more and more time in which to teach. Neither extra time nor money would be able to solve all these problems. And teachers may be asked to teach the basics of mathematics, English, science, a foreign language, and social studies instead. They must also be asked to teach those children who are well rested and well fed, and not exhausted after long bus rides and longer waits in the cafeteria. They may be evaluated by those persons who have a valid teaching certificate in their possession, and who have been active in the classroom for at least a minimum period of one year. In addition, if they were not given any extra duties, and if the administration was willing to share in any extra duties, then the teacher would be able to fare much better in the classroom, and care for her children in a way never done before. It is the opinion of Michael L Berger in his book entitled ‘The Public Education System' that there are six important controversies that generally appear in American public education systems, and these are: the budget that has been allocated for the educational system, the various auxiliary services that are needed, the facilities and the equipment needed in schools, the basic curriculum of education, the various personnel involved in teaching, and finally, the administrative rules and regulations that have to be followed by the schools. In the book ‘Critical Social Issues in American Education: Democracy and Meaning in a Globalizing World', the authors feel that it is the various interrelationships between different educational institutions, public education in particular, that is very important in the American public education system. Public education is in general, subject to a vast number of influences, like for example, community pressure, and community concerns. Schools also tend to interact with other schools, and therefore, leave an impact on each other; in other words, it can be said that there is a wide interaction between various aspects of the educational system, and when cultural and religious and other beliefs interact with budgetary concerns, and demographic concerns as well as politics and ideological debates come into the picture, the educational system has to keep all these considerations in mind so that it may be a good and an effective one. It is when it does not happen that the educational system suffers a setback. (Purpel; Shapiro, 2004) It must be remembered, however, that teachers are a very important part of the public education system anywhere in the world, and especially in the United States of America, and when taken from an economic point of view, it is the so-called ‘teacher unions' that are not only producers of representative services, but are also consumers of such representative services in the educational system. From the time when unionization took place for teachers, during the 1960's, the National Educational Association' and the ‘American Federation of Teachers' have been monopolizing the market in terms of representative services. This type of monopoly does indeed have its adverse effects, and these are that the costs have skyrocketed, and at the same time, the service has become vastly inferior to what it was before. (Leiberman, 2003). Finding the best possible schooling for a child in the present circumstances has indeed become an uphill task today, especially for minorities, like African- American children. Perhaps this may be because of the large number of options available to children today, what with the educational system being bombarded by ‘magnet programs', charter schools', and manifold other public school options. Parents today have to be choosier than ever before, and at times, this can very well be overwhelming. (Lord, 2005) Recently, when two important economists were asked the question about what was America's greatest challenge today, the reply was that it was the education system. The problems can be seen as being from both outside and also from within the school and perhaps one of the most important reasons is the breakdown of the ‘family unit'. As parents today find less time to spend with their children, the school is expected to compensate. In addition, the decline of values in society is a major contributing factor, and this leads to a lack of basic discipline, a lack of attention, and so on. Another important factor is the worsening health of American children, and while some are exhausted and tired, some more are hungry, and some others are diagnosed with learning disabilities of some kind. The teaching system is also at fault, because children are forced to learn according to the teacher's convenience and not to theirs'. The lack of emphasis on spiritual development can also be taken as a major factor contributing to the lackluster American public education system, and along with various other factors, this can become a major drawback. What can be done to change the educational system? Redesigning the public education system is a daunting task, but it must be undertaken for the betterment of American children and eventually the society. Long standing practices have to be reconsidered, high quality learning opportunities must be provided to American children even before kindergarten, and perhaps the existing method of promoting a child from one class to the next can be eliminated so that children may be allowed to learn and to progress at their own pace. More teachers must be brought in, and the quality of teaching must be improved. If at least some of these measures were to be adopted for a start, then changes can indeed be brought in to the declining public education system in the United States of America (Guillory, 2001).

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