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Lesson: This is Me !
Quiz by Camila Sånchez G
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'Create a quiz based on this lesson: . Tenali Rama was known for his sense of humour. In fact, King Krishnadevaraya used to enjoy his witty remarks even when they were targeted at him. Here is one such story. Scene 1 One day, an Arab horse trader visited the court of King Krishnadevaraya. He had a fine horse for the king. The (Greek/Chinese/Arab/ British) trader visited the court of King Krishnadevaraya King: All of you know that I am very fond of horses. The horses in my stable are the finest indeed! Send the trader in! I always want some rare breeds of horses from across the world to add to my man collection. Trader: Good day, Your Majesty! I have brought one of the finest horses from ArabiaI request you to see the horse. I am sure you will want him for your royal stable. King: This is indeed a magnificent creature! I wish to buy this fine horse. Trader: Your Majesty, I have two more such horses with me in Arabia and it would be my pleasure to bring them to you. Trader: You are really kind and I am sure you will like ader merchant magnificent splendid/superb King: I am so happy to hear that. I agree to buy the other two horses as well Into Trader: l am grateful for your offer and I promise to return with the other two horses within a week's time. Scene 2 Months passed, but there was no sign of the trader. Worried and anxious, the king decided to take a stroll in the garden. There, he spotted Tenali Rama sitting under a tree and scribbling something on a piece of paper. King: What are you writing on this sheet of paper, Rama? Rama: Here is the paper. You can see for yourself. It is the list of names of people who can be called 'very foolish!. Rama showed the paper to the king. It was a list of names with the king's name at the top. King: My name is always on top of the list. I do know that you respect me. On the top of the list was writtenâ 'List of the Biggest Fools in the World! He became furious. King: How can you call your King, 'a fool?' You will have to explain it to me. Rama: lam really sorry that I had to add you as well in the list of fools. How could your Highness trust an unknown Arab horse trader, give him a huge advance, and expect him to return? ' King: What if he really comes back? Rama: If he returns with his horses after taking so much money from you, then I will put his name as the first one. So, he will be on top of the list of fools. The king realized his mistake. His anger slowly gives way to laughter. King: You are really funny, Rama. I was very unhappy, but with your witty remark, you have defused my anger and anxiety. I love your sense of humour. Rama: Dear King, you are so good to everyone! You fail to understand that you should be good to people, but should never trust strangers. The king agreed and they walked back to the palace.I'd Like to Be I'd like to be a happy clown and make everyone laugh. I'd wear big clothes, and a bright red nose, and be pleased with all I have. I'd like to be an athlete, and play basketball each day. I'd leap so high I could touch the sky, and make baskets along the way. I'd like to be a gardener and grow healthy things to eat. I'd plant my seeds, water them, and pull weeds. My garden would be hard to beat. I'd like to be a mermaid and swim in the deep blue sea. The fish and whales could tell their tales, while dolphins sang to me. I'd like to be a cowboy and ride horses every day. And then at night, I would tie them tight and feed them lots of hay. I'd like to be a dancer and twirl and jump and fly. I'd wear fluffy skirts and fancy shirts. People would clap as I danced by. I'd like to be an artist and try to paint the land. I would paint the water blue and the great skies, too. The ground would be the color of sand. I'd like to be a pirate. I would have to be brave and bold. I would sail with a crew on oceans of blue to look for treasure and gold. I'd like to be an astronaut and fly up to the moon. In outer space, I'd find a place to eat without a spoon. I'd like to be a zookeeper and care for birds and snakes. I'd give them food, and watch their moods, and on birthdays give them cakes. I'd like to be a musician and play songs every day. I would play the trumpet, or guitar and strum it, making music my own way. The moral of this lesson is to be what you can be. Dare to dream, and listen to your talents to find what you will be.Element Definition Example from Text Theme Main message or lesson Be yourself; self-acceptance Tone Authorâs attitude toward the subject Encouraging, humorous Diction Word choice Weird, perfect, brave Denotation Literal meaning of a word Weird = unusual Connotation Emotional meaning of a word Weird = negative or unique Allusion Reference to another literary or cultural work Harry Potter, The Last Battle Genre Type of writing Letter Writer Author Letter writer to her teen self Title Name of the text Just Be Yourself Dear Teen Me, Psst! Hey! You in the corner of the library with your nose stuck in a book. Yes, you. Donât recognize me without that awful perm, do you? (Remind me again why you thought that was a good idea?) Anyway, I hope you donât mind if I sit with you for a minute, but we need to talk. Donât worry about the âno talking in the libraryâ rule. Iâm sure weâll be fine. Librarians arenât as bad as they seem. Judging from the hair and braces Iâd have to guess youâre in your junior year. Yes? Thought so. Iâd forgotten how many lonely lunch hours you spent in the school library. You have some friends in the cafeteria that you could sit with, but you donât feel like you really fit in, do you? Thatâs why you joined every school club you could. I just counted and youâre in eighteen, not to mention the numerous after-school activities youâre involved in. I mean honestly, you joined the ROTC.1 You donât even like ROTC! And I wonât even bother bringing up that time you tried ballet. Iâm still having nightmares about the fifth position! Let me ask you, howâs it all working out? Not very well, am I right? By spending so much time trying to find yourself, youâre slowly losing yourself. We donât all have one single rock-star talent, and honestly, I think those of us who donât are the lucky ones. Life isnât about finding the one thing youâre good at and never doing anything else; itâs about exploring yourself and finding out who you really are on your own terms and in your own way. You donât have to exhaust yourself to do that. Oh, donât be so down in the dumps about it. Youâll eventually find something youâre good at, I promise. Itâs a long, winding road to get there, but youâll find it. Being able to spend all day doing what you love (or one of the things that you love) is the most amazing feeling in the world. And no, I wonât tell you what it is, so donât even ask me. Just remember to always be yourself, because thereâs nobody else who can do it for you. I think E. E. Cummings put it best when he said, âIt takes courage to grow up and become who you really are.â Looks like the bell is about to ring so Iâll leave you to your book. What are you reading, anyway? Oh, The Last Battle by C. S. Lewis. I should have guessed. You should give those Harry Potter books a try. I saw you roll your eyes! I know they seem like just another fad, but trust me, theyâre better than you think. Theyâve got a real future! finding out who you really are on your own terms and in your own way. You donât have to exhaust yourself to do that. Oh, donât be so down in the dumps about it. Youâll eventually find something youâre good at, I promise. Itâs a long, winding road to get there, but youâll find it. Being able to spend all day doing what you love (or one of the things that you love) is the most amazing feeling in the world. And no, I wonât tell you what it is, so donât even ask me. Just remember to always be yourself, because thereâs nobody else who can do it for you. I think E. E. Cummings put it best when he said, âIt takes courage to grow up and become who you really are.â Looks like the bell is about to ring so Iâll leave you to your book. What are you reading, anyway? Oh, The Last Battle by C. S. Lewis. I should have guessed. You should give those Harry Potter books a try. I saw you roll your eyes! I know they seem like just another fad, but trust me, theyâre better than you think. Theyâve got a real future! i need you to tell me how can i start this text and i need you to add these essential questions: What are some milestones on the path to gr owing up?, What makes an experience memorable? What makes it life changing? and then Denotation, Connotation, Allusions, Diction, Tone, Genre, Writer, Title, Theme in a table and i need u to add definitions for each one and extract examples from the textGot it â
â you want all the topics (States of Matter â Temperature â Thermal Energy â Pressure â Gas Laws, etc.) written in the same structured style (definitions, everyday examples, non-examples, short story, daily life connections, MCQs, SAQs). Hereâs a full structured lesson flow, starting with States of Matter as you requested: --- đ§ States of Matter Definition Matter exists in three main states: Solid: Definite shape & volume, particles tightly packed, vibrate in place. Liquid: Definite volume but takes the shape of its container, particles slide past one another. Gas: No definite shape or volume, particles move freely and spread out. Everyday Examples Solid: Ice cubes, table, book. Liquid: Water, milk, juice. Gas: Air in a balloon, perfume spreading, steam. Non-Examples Honey is not a solid â it flows â liquid. A rock is not a liquid â itâs rigid â solid. Water in a closed bottle is not a gas â it stays liquid. Short Story You buy a soda on a hot day: Ice cubes (solid) keep it cold. They melt into liquid water. Bubbles rise as gas carbon dioxide escapes. Everyday Life Connections Freezing water into ice. Boiling soup on the stove. Smell of perfume spreading across a room. MCQs 1. Which state has particles vibrating in place? a) Solid â
b) Liquid c) Gas d) Plasma 2. Soda fizzing when opened is: a) Liquid diffusion b) Gas release â
c) Solid melting d) Condensation SAQ (Multi-step) You leave an ice cream outside: a) What state does it start in? b) What happens as it melts? c) If left longer, what phase change might occur? d) Which type of energy increases? --- đĄ Temperature Definition Indicates average kinetic energy of particles. Measured with a thermometer. Heat flows between objects of different temperature. Everyday Examples Fever check with a thermometer. Ice cube cooling a drink. Why metal feels colder than wood at room temperature. Short Story A hot pizza slice cools when left on the table: heat flows from pizza (high T) to air (low T). MCQ Which is true about temperature? a) It measures total energy b) It measures average kinetic energy â
c) It is the same as heat d) It doesnât affect particle motion --- đĽ Thermal Energy Definition Total of all kinetic and potential energy of atoms in an object. Everyday Examples Large pot of warm soup has more thermal energy than a small hot cup. Heating water â particles move faster. Ice pack absorbs thermal energy from skin. Short Story In winter, sitting near a heater warms you up because air molecules gain kinetic energy and transfer it. MCQ At absolute zero: a) Particles vibrate slowly b) Particles move randomly c) Particles have no movement â
d) Particles expand --- ⥠Kinetic vs Potential Energy Definition Kinetic energy: energy of motion (vibrating, flowing, diffusing). Potential energy: stored in positions/forces (attractions between particles). Everyday Examples Steam in cooker: high kinetic energy. Rubber band stretched: potential energy. Short Story A bouncing ball â kinetic while moving, potential at the top of its bounce. --- đ¨ Pressure Definition Force per unit area on a surface. Everyday Examples Drinking with a straw. Bicycle tires feel hard due to air pressure. Bed of nails â force spread out, less pressure. Short Story When you open a soda bottle, pressure is released â fizzing sound and bubbles. --- đ Gas Laws (Thermal Expansion & Charlesâ Law) Definition At constant pressure, gas volume â absolute temperature. Everyday Examples Balloon expands in sunlight. Hot air balloon rises. Tires inflate slightly after driving. Short Story A sealed chips bag puffs up on an airplane as air pressure outside decreases. MCQ According to Charlesâ Law: a) Volume decreases as temperature increases b) Volume increases as temperature increases â
c) Volume is independent of temperature d) Volume and temperature are unrelated --- â
This flow covers all your slides in the same Prezi-style (definitions, examples, non-examples, story, life connections, questions). Do you want me to now add full sets of practice (10 True/False, 10 Matching, 10 Write the Term, etc.) for each section, so youâll have a complete question bank along with the lesson flow?The lucky accident Probably every Zumba fan knows this story: Alberto âBetoâ PĂŠrez invented Zumba by accident. He was an aerobics instructor in his home town of Cali, Colombia. One day he forgot the music for his class. He had some cassettes of Latin dance music in his bag. He played them and improvised the exercises: a mix of dance steps and aerobic movements. His class loved it. The music was different, the moves looked attractive and the workout was fun. Thatâs how this ultra-energetic new fitness programme was born. Before, things were not easy for Beto. As a child, he loved dancing: he watched and imitated John Travolta, but his mother had no money for dance lessons. At the age of fourteen Beto already worked to help support his family. Still, he danced when he could. In the late 1980s, a dance called the lambada became very popular. Beto won a national lambada competition when he was nineteen. After that, a dance academy in Cali contacted him with an offer: he could study dance and teach aerobics. It was then, as an aerobics instructor, that he created Zumba. He decided to take his idea to the USA. He went to Miami, Florida with little money and almost no English. Fitness centre managers were not interested in his videos at first. Then one day a gym owner said, âOK, teach me.â It was early afternoon, the gym was empty. But soon people started coming in. When they saw Beto dancing, they immediately wanted to join this new class. And so he got his first job in America. Breaking the world record for the largest Zumba class (Mandaluyong City, The Philippines). In Miami, he met Alberto Perlman and Alberto Aghion, who became his business partners. Together, the âthree Albertosâ built up Zumba to the global business it is today. The company trains thousands of certified instructors, runs classes for all age groups, sells music, training videos and clothes. According to the official website, fifteen million people around the world take part in Zumba classes to keep fit and have fun. And it all started by accident!Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: ⢠Free-falling objects do not encounter air resistance. ⢠All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs ⢠Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 ⢠a ⢠d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 ⢠(-8.00 m/s2) ⢠d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) ⢠d (16.0 m/s2) ⢠d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi ⢠t + ½ ⢠a ⢠t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) ⢠(4.1 s) + ½ ⢠(6.00 m/s2) ⢠(4.10 s)2 d = (0 m) + ½ ⢠(6.00 m/s2) ⢠(16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: ⢠An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. ⢠If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. ⢠If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. ⢠If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi ⢠t + ½ ⢠a ⢠t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) ⢠(t) + ½ ⢠(-9.8 m/s2) ⢠(t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) ⢠(t)2 -8.52 m = (-4.9 m/s2) ⢠(t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 ⢠a ⢠d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 â˘(-9.8m/s2) â˘d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) â˘d (-19.6 m/s2) ⢠d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) ⢠d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.Lesson 4 Is this an MVP?Professional Standards: Being on time is important because it shows you can follow rules like in a job. It helps you learn good habits for your future career. Shape Enhancing Learning Experience: When you arrive on time, you don't miss the start of the lesson. This helps you understand what is being taught and keeps the class running smoothly. Reducing Disruptions: If you are late, it can interrupt the lesson and make it harder for everyone to learn. Being on time helps everyone focus better . Showing Responsibility and Self-Discipline: Being on time shows you can manage your time well. This is a good skill for school and life . Supporting Academic Success: Coming to class on time helps you do better in college. You can join in discussions and finish your work on time . Building a Positive Learning Environment: When everyone is on time, the class is more positive and respectful. This makes learning more enjoyable for everyone. Identifying and Addressing Barriers: Regular attendance helps tutors notice if you have any problems that make you late. They can then help you solve these problems . Promoting Equity and Inclusivity: Being on time ensures everyone has the same chance to learn and succeed. It makes the classroom fair for all students . Conclusion: Being on time is important for learning well and developing good habits. It helps you and your classmates have a better learning experience and prepares you for the future.