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Intervals 1
QuizĀ by Jo Routh
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*Intervals 1 & 2 - Notes/FingeringsTime - 1 minutes intervalsNY-3.MD.1: Tell and write time to the nearest minute and measure time intervals in minutes1. Eat slowly, chew your food well. It takes twenty (20) minutes before your stomach sends a clear message to your brain that you're full. Take your time and savor the flavor of your meal. 2. Eat well When your body doesn't receive the required nutrients, your metabolism slows down. Metabolism is the rate at which you burn calories while resting. So, if you don't eat enough, fewer calories will be burnt and there will be less fat loss. You should eat small meals at regular intervals to keep your energy levels high. 3. Eat less red meat Red meats are high in saturated fat and should be avoided by people with high cholesterol. Chicken and fish are the best meats to consume. These meats can be baked, grilled or roasted. 4. Eat more fiber foods Add fiber to your diet, this adds bulk to your food and prevents constipation. Whole grain foods like oatmeal, bran, wheat germ and brown rice, fruits, especially with skins, prunes, etc, are all Seven (7) healthy eating habits for your guidelines: How you eat your food is as important as what you eat. So, the next time you sit down to eat, enjoy your meal by keeping these pointers in mind. Home Economics and Livelihood Education 7 Seibo College 157 good sources of fiber. Fiber helps in binding cholesterol, which results to less production of bad cholesterol. 5. Have calcium-rich foods Aside fro milk other sources of calcium and protein are red kidney beans, mustard greens, etc. Proteins can be found in meats, sprouts, soya, etc. 6. Eat foods that contain iron These include liver, fruits like watermelon, vegetables like spinach, beans, beets and broccoli, whole grains, dried fruits, especially prunes, sunflower seeds, etc. 7. Relish the flavors You may have heard some of these before. But the best good food habit, which we all seem to overlook, is to actually taste and enjoy the flavor of the food with your emotions instead of just your tongue. How can we prevent malnutrition? Following are the checklists of steps to prevent malnutrition. ļ¼ Nutrition campaign on the importance of food nutrients. ļ¼ Proper selection, preparation and serving of well-balanced meals. ļ¼ Vegetable gardening in schools and at home. ļ¼ Intensive program from the government especially for the less privileged members of the community.Make me a quiz to test basic level of 1st species counterpoint and consonant intervalsHEALTH EDUCATION 3. SPECIFIC OBJECTIVES: Students should able to know about_______ 1. definition of health education 2. aims of health education 3. objectives of health education 4. principles of health education 5. scope of health education 6. planning of health education 7. steps in planning health education 8. levels of health education 9. doctors s responsibility 4. INTRODUCTION: Health education is a term frequently used by health care professional. its aims at individual and community health. Health education is the translation of what is known about health into desirable individual and community behaviour pattern by means of an education process. Definition: āA process aimed at encouraging people to want to be healthy , to know how to stay healthy, to do what they can individually and collectively to maintain health And seek help when neededā. OBJECTIVES - To inform people or disseminate scientific knowledge about prevention of disease and promotion of health - To motivate people to change their habits and lifestyle that are harmful to their health also motivate people to adopt habits and ways of living conducive to healthy living. - To guide the people who need help to adapt and maintain healthy practices and lifestyle by showing proper community resources. --- PRINCIPLES OF HEALTH EDUCATION - Credibility Of Message: It is the degree to which the message to be communicated is perceived as trustworthy by the receiver. - Creating interest among participants: It is a psychological principle that people are unlikely to listen to things that are not of their interest. If a health programme is based on the felt needs, people will participate in the programme willingly. - Motivating the participants: Motivation is like a petrol engine that drives the mental engine. It is the fundamental desire in every person to learn. Motivation is contagious; one motivated person may spread motivation throughout the group. 13. - Enhance comprehension of content: It means health education should be based on the level of understanding, education and literacy of people at whom the teaching is directed. Teaching should be within the mental capacity of the audience. - Ensure reinforcement: Repetition at intervals is necessary to promote learning. Without reinforcement and feedback, students can go back to the pre-awareness stage. - Encourage active participation: Health education should aim at encouraging people to work actively with health workers and others in identifying their own health problems and also in developing solutions. 14. - Learning by doing: Teaching is effective when individuals actively participate in health education. Learning becomes active and quicker if the individuals are made active physically as well as psychologically. - Known to unknown: The people in a community know something and the health educator enlarges this knowledge. If the health educator links new knowledge with the old knowledge, it can enhance learning. - Maintaining good human relations: Sharing of information, ideas and feelings happens most easily between people who have a good relationship. 15. - Setting an example: The health educators should set a good example in the topic they are dealing with as it fosters better understanding. - Regular feedback: Feedback is one of the key concepts of the system approach. The health educator can modify the elements of the system in light of the feedback from his audience. For effective communication, feedback is of paramount importance - Efficient leadership: Leaders are agents of change and they can be made use of in health education work. Psychologists have shown and established that we learn best from people we respect and regard. 16. The essential attributes of a leader are as follows - Understands the needs of the community. - Provides proper guidance. - Takes initiative. - Is receptive to the views and suggestions of people. - Identifies himself with the community. Is selfless, honest, impartial, considerate and sincere. - Is easily accessible to people. 17. SCOPE OF HEALTH EDUCATION 1. Nutrition 2. Hygiene 3. Family health 4. Disease prevention and cantrol 5. Psychological health 6. Prevention of accident 7. Use of health services 8. Human biology 19. - Nutrition: The aim of nutrition education is to guide people to choose optimum and balanced diets, remove prejudices and promote good dietary habits. nutrition education is a major intervention for the prevention of malnutrition, promotion of health and improving the quality of life. 20. - Hygiene: This has two aspects: personal and environmental. Personal: The aim of personal hygiene is to promote standards of personal cleanliness . Environmental: Has two aspects: Domestic and community. All environmental sanitation programmes should include health education 21. - Family health: The family is the first defence as well as the chief reliance for the well-being of its members. One of the main tasks of health education is to promote family self-reliance, especially regarding the family's responsibilities in child bearing, child rearing, self-care and in influencing their children to adopt a healthy lifestyle. 22. - Disease prevention and control: Drugs alone will not solve health problems. Without health education, a person may fall sick again and again from the same disease. Educating the people about the prevention and control of locally endemic diseases is the first of the eight essential activities in primary health care. 23. - Psychological health: Psychological health problem can occur everywhere. There is a tendency to an increase in the prevalence of psychological diseases when there is a change in society from agriculture to an industrial economy and when people move from the warm intimacy of a village. 24. - Prevention of accidents: Accidents are a feature of the complexity of modern life. Accidents can occur in home, road and place of work. The predominant factor in accidents is carelessness that can be tackled by health education. 25. - Use of health services: Many people, particularly in rural areas, do not know what health services are available and many more do not know. There is a communication gap between the public and state health administration in the form of feedback for further improvement of health services. One of the declared aims of health education is to inform people about the health services available in their community. 26. PLANNING FOR HEALTH EDUCATION planning: is the process of making thoughtful and systemic decision about what needs to be done , how it has to be done, by whom And with what sources. 27. Principles of planning health education 1) Focus on actual current needs and context of community: It is important that plans are made with the needs and context of the community in mind. Health education should try to understand what is currently happening in the community one works in. 2) Plan for basic needs and interest of the community: Consider the basic needs and interests of the community. If the local needs and interests are not kept under consideration, the plans may not be effective. 28. 3) Planning with actual beneficiaries of health education: Plan with the people involved in the implementation of an activity. If people are included in planning, they will be more likely to participate and the plan will be more likely to succeed. 4) Identify and use all relevant community resources: It is essential that the health educator identify all the relevant resources that are locally available which could be used for benefit of people receiving the health education. 29. 5) Follow principle of flexibility: Planning should be flexible, not rigid. One should be able to modify the plans when necessary. For example, you would have to change your priorities if a new problem needing an urgent response arose. 6) A realistic plan not hypothetical: The planned activity should be achievable and take into consideration the financial, personal resources available and time constraints. Planning must be realistic; do not plan unachievable activities. 30. Steps in planning health education Planning is a continuous process. It does not just happen at the start of project . Health education must be well planned to actually improve and promote individual, family and community health 31. - Needs assessment: Conducting needs assessment is the first and probably the most important step in any successful planning process. assessment is the process of identifying and understanding the health problems of the community and their possible causes. - Identify priorities: After identifying the needs and resources of the community, the next is to identify their priorities because each community may have several problems but the urgent have to be given top priority in health education. For example: goitre 32. - Set the goals and objectives: In planning the process of health education, setting goals and objectives is the third and most essential step because these goals and objectives serve as consciously thought baseline parameters to be achieved during health education. - Develop strategies: Prior to the implementation of the health education intervention one must plan, develop and evaluate the several alternative strategies to achieve the set goals and objectives of health education because each problem and target community is quite unique. 33. - Implementation: This is the core phase of the health education process which includes carrying out the planned strategies so that the set goals and objectives of health education may be achieved. - Monitor and evaluation: This is the final step of the planning process of health education where continuous monitoring as well as end evaluation is carried out to ensure the degree to which stated goals and objectives have been achieved. 34. LEVELS/APPROACH OF HEALTH EDUCATION 35. INDIVIDUAL LEVEL - Individual Approach: The health education must first create an atmosphere of friendship and allow the individual to talk as much as possible. In this individual teaching we can discuss, argue and persuade the individual to change his behaviour. But by this we can reach to a small population and who come in contact with us. Methods of individual health education 1) Home visit 2) Personal contact/ counselling 3) Personnel letters 36. 1) Home visit: A home visit is one of the best approaches for individual health education because it can become one of the best opportunities for health education with individuals and their families. Home visits are important to understand the real background of families, their living conditions and the environment in which they live. 37. 2) Personal contact/counseling : Personal contacts or counselling (one-to-one communication) is a helping process where one person explicitly and purposefully gives his or her time to assist people explore their situations and act on a solution. After this the counsellor needs to work together with the person to find solutions that are appropriate to their situation. 38. 3) personal letters: Personal letters may also be used for individual health education, where health educators may get an opportunity to dispatch letters or printed education material to the people in a target community. 39. GROUP LEVEL Group health education may be useful way to deliver health education massages in efficient manner. A well organized group permits sharing of experiences and skills so that people are able to learn from each other. 40. Methods of group discussion 1)Lecture method: (Chalk & Talk ) A lecture may be defined as carefully prepared oral presentation of facts organized thoughts and ideas by a qualified person. The group should not be more than 30 and talk should not exceed 15-20 minutes. By using suitable audiovisual aids. 2) Group discussion: A group is an aggregation of people interacting in a face to face situation. It is a very effective method of health communication. 41. 3) Demonstration: A demonstration is a carefully prepared presentation to show how to perform a skill. This procedure is carried out step by step before an audience. 4) Panel discussion: In a panel discussion 4-8 qualified persons talk about the topic. Sit and discuss a given topic in front of a large group/audience. The chairman opens the meeting. Panel comprises of a chair person and 4-8 speakers. After the main aspect of the subject are explored, the audience is invited to take part. 42. 5) Symposium: It is a series of speeches on a selected subject. Each expert person present it briefly and at the end of session the chair person make a comprehensive summary. Audience are allowed to raise question. 6) Workshops : It consists of series of meetings usually 4 or more with emphasis on an individual work, within the group and with the help of consultants and response personnel. 7) Role play: This is a brief acting out of an actual situation for the benefit of the audience for better understanding. 43. 8) Conference and seminars: This programmes are usually held on a regional, state/national level. Where several experts from different disciplines meet to deliberate on a particular theme, to appraise others of latest knowledge and research in a particular field. 9) Open forum: It refers to the public meeting which are held for various purposes in the community, for example: gram sabha 44. COMMUNITY LEVEL It is meant for a defined community and is not only to create awareness but also to help people understand their health problems and needs, find alternatives solutions to their problems and needs , implement them, evaluate and get feedback and accordingly do the needful. For health education at the community level, it is better to approach local leaders who are influential and who have the peopleās confidence. These may include local officers such as gramsevak, panchayat sarpanch ,police officer or block development officer etc . 45. HOSPITAL LEVEL 1) Health Education in OPD/Outdoor: The patient and his attendants have to spend a lot of time in the outpatient department for health check-up, treatment, registration, diagnosis, admission procedure etc. This period can be utilised for health education. For this, the following means/devices can be used: - Exhibiting pictures, posters, charts, bulletin board and models in the waiting hall. - Arranging group discussion, slide show, or documentary film in a proper place and on a proper topic. - Giving health education on a personal level in the consulting room. This mainly includes nutrition clinic, family planning clinic, psychiatric clinic etc. 46. - Distributing pamphlets. - Arranging street plays or nukkad naatak in the outpatient department or its neighbourhood. 47. 2) Health Education in wards/ IPD: While taking care of the patients the indoor patients, doctors s have the opportunities to educate them. This period can be fully utilised to give health education to the patients. For this the following methods can be effective: - Conversation with the patient and motivating him for change in his behaviour. - Imparting health education by arranging live demonstration for nutrition, treatment, diagnosis etc. - Providing clinical or bedside teaching. - Providing incidental teaching to patient and his attendants. 48. - Presenting examples. To describe the gains of health education in an individual suffering from the same health education in an individual suffering from the same disease and arranging a meeting between the patient and the cured old patients.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: ā¢ Free-falling objects do not encounter air resistance. ā¢ 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 ā¢ 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 ā¢ a ā¢ 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 ā¢ (-8.00 m/s2) ā¢ d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) ā¢ d (16.0 m/s2) ā¢ 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 ā¢ t + Ā½ ā¢ a ā¢ 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) ā¢ (4.1 s) + Ā½ ā¢ (6.00 m/s2) ā¢ (4.10 s)2 d = (0 m) + Ā½ ā¢ (6.00 m/s2) ā¢ (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: ā¢ 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. ā¢ 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. ā¢ 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. ā¢ 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 ā¢ t + Ā½ ā¢ a ā¢ 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) ā¢ (t) + Ā½ ā¢ (-9.8 m/s2) ā¢ (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) ā¢ (t)2 -8.52 m = (-4.9 m/s2) ā¢ (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 ā¢ a ā¢ 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 ā¢(-9.8m/s2) ā¢d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) ā¢d (-19.6 m/s2) ā¢ d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) ā¢ 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.Intervalos 1