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PHYSICS 2 FIRST SUMMATIVE TEST
Quiz by ROMMEL MAGCALAS
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GENERAL PHYSICS 2 (First Summative Test)WHAT IS SCIENCE? - is a way in which answers related to NATURAL events are proposed. - a way in which people can learn and UNDERSTAND events in the NATURAL WORLD - based on OBSERVABLE EVENTS - a study of the NATURAL WORLD - a method of DISCOVERY and UNDERSTANDING by using a PROBLEM-SOLVING process called the?? - A systematic body of knowledge based on observation and experimentation. FOUR COMMON CHARACTERISTICS OF SCIENCE: 1. It focuses on the NATURAL WORLD. 2. Goes through experiment. 3. Relies on evidence. 4. Passes through the scientific community. WHAT IS TECHNOLOGY? Brian Arthur (2009) defined technology as: 1. a means to fulfill a human purpose 2. assemblage of practices and components 3. a collection of devices and engineering practices available to a culture. SOCIETY ST (Science Technology) would not exist without society. WHAT IS STS? Science and Technology and Society (STS) is the study of how society, politics and culture affect scientific research and technological innovation and how these, in turn affects society, politics and culture. EVENTS IN THE HISTORY OF SCIENCE AND TECHNOLOGY THAT TRANSFORMED THE SOCIETY (IN THE WORLD) ANCIENT PERIOD 3500 BC. - 500 AD EUROPE - use of fire by Homo Erectus CA 750,000 - Stone Headed Spears CA 45,000 - Wooden bow and arrow CA 20,000 - The Minoans build palaces in Crete CA 2,000 THE AMERICAS - The Folsom people living on eastern side of the Rocky Mountain developed sophisticated tools CA 8,000. - Pottery is made in South America CA 6,000 - Olmec sculpture carves figurines and giant human heads. CA 1200 ASIA AND OCEANA - Earliest known clay pots are made in Japan CA 11,000. - Bronze is first made in Thailand CA 4000 - A lunar calendar is developed in China CA 2950 - Chinese doctors begin using acupuncture CA 2500 - The Hindu calendar of 360 days was introduced in India CA 1000 AFRICA AND MIDDLE EAST - Homo erectus uses stone tools CA 1000000 - CA 15000 in Africa, bone harpoons are used for fishing. - Clay tokens are used for record keeping in Mesopotamia CA 7500 - Mesopotamian mathematicians discover the Pythagorean Theorem MEDIEVAL PERIOD CA 500 -1500 - Dark ages because few written records and evidences remained - Scholastic tradition was established by Charlemagne - Vertical windmills, spectacles, mechanical clock, water mills, gothic style were invented - Johannes Gutenberg invented the printing press RENAISSANCE PERIOD 14TH – 17TH CENTURY - Rebirth of revival - Printing with movable type allowed Bible, secular books made in large amount - Nicolas Copernicus presented a heliocentric theory - Galileo Galilei invented telescope INDUSTRIAL REVOLUTION 18TH CENTURY - Skilled workers were set aside because of the machines - Iron production, steam engine and textile flourished - Scottish James Watt improved steam engine Robert Fulton (steam boat) - The following were invented: Light bulb, telephone, first steam powered locomotive 19TH CENTURY - Age of machine and tools - Herman Helmholtz (law of conservation of energy) - James Clark Maxwell (light as electro-magnetic wave) - Henry Becquerel (radioactivity) - Marie and Pierre Curie (radium) - Hans Christian Oersted (electric current near the magnet) - Michael Faraday (magnet produces electricity) - Atomic Theory proposed by John Dalton - Electron discovered by JJ. Thomson - Telegraph developed by Samuel Morse 20TH CENTURY - Communication, transportation, military research were developed - Personal computer was created - Intel developed microprocessor - Apple was introduced by Steve Jobs and Steve Wozniak - Internet was created (ARPANET) - Henry Ford's mass production of cars - Artificial Intelligence was invented SCIENCE, TECHNOLOGY AND SOCIETY (PHILIPPINE HISTORY) Stone Age - Archeological findings show that modern man from Asian mainland first came over land on across narrow channels to live in Batangas and Palawan about 48,000 B.C. - Subsequently they formed settlement in Sulu, Davao, Zamboanga, Samar, Negros, Batangas, Laguna, Rizal, Bulacan and Cagayan. Inventions - They made simple tools and weapons of stone flakes and later developed method of sawing and polishing stones around 40,000 B.C. - By around 3,000 B.C. they were producing adzes ornaments of seashells and pottery. Pottery flourished for the next 2,000 years until they imported Chinese porcelain. Soon they learned to produce copper, bronze, iron, and gold metal tools and ornaments. Iron Age - The Iron Age lasted from the third century B.C. to 11th century A.D. During this period Filipinos were engaged in extraction smelting and refining of iron from ores, until the importation of cast iron from Sarawak and later from China. INVENTIONS AND DISCOVERIES - They learn to weave cotton, make glass ornaments, and cultivate lowland rice and dike fields of terraced fields utilizing spring water in mountain regions. - They also learned to build boats for trading purposes. - Spanish chronicles noted refined plank built warships called caracoa suited for interisland trade raids 10TH CENTURY A.D. - Filipinos from the Butuan were trading with Champa (Vietnam) and those from Ma-I (Mindoro) with China as noted in Chinese records containing several references to the Philippines. These archaeological findings indicated that regular trade relations between the Philippines, China and Vietnam had been well established from the 10th century to the 15th century A.D. TRADING - The People of Ma-I and San-Hsu (Palawan) traded bee wax, cotton, pearls, coconut heart mats, tortoise shell and medicinal betel nuts, panie cloth for porcelain, leads fishnets sinker, colored glass beads, iron pots, iron needles and tin. SOME PRESPANISH FILIPINO SCIENCE AND TECHNOLOGY - Curative values of plants extract use as medicine - Alphabet (Alibata) - Counting Methods - Weights - Measuring system (isang gatang) - Calendar based on the periods of moon - Banaue Rice Terraces SPANISH REGIME  Religion the Catholic Church - The latter part of the 16th Century Development of schools: - Colegio de San Ildefonso-Cebu-1595 - Colegio de San Ignacio-Manila-1595 - Colegio De Nuestra Senora del Rosario-Manila 1597 - Colegio De San Jose-Manila-1601  Colegio De San Ildefonso De Cebu - In 1863 the colonial authorities issued a royal degree to reform the existing educational system. In 1871 the school of medicine and pharmacy were opened to UST, after 15 years it had granted the degree Of Licenciado En Medicina to 62 graduates.  Medicine - Development of hospitals San Juan Lazaro hospital the oldest in the far east was founded in 1578.  Roads and Bridges Among other Spanish contributions: - Arithmetic - Algebra - Geometry - Trigonometry - Physics - Hydrography - Meteorology - Navigation - Pilotage American Period and Post Commonwealth Era - BUREAU OF GOVERNMENT LABORATORIES (1901) - BUREAU OF SCIENCE (1905) - INSTITUTE OF SCIENCE (1946) RA 2067 OTHERWISE KNOWN AS THE “SCIENCE ACT OF 1958”. - This was enacted to integrate, coordinate, and intensify scientific and technological research and development and to foster invention including allocation of funds and other purposes. NATIONAL RESEARCH COUNCIL WAS ESTABLISHED ON DECEMBER 8, 1933. - Its Mandate (Nrcp) Promotes And Supports Fundamental Or Basic Research For The Continuing Total Improvement Of The Research Capability Of Individual Scientists Or Group Of Scientists; Provides Advice On Problems And Issues Of National Interest; Promotes Scientific And Technological Culture To All Sectors Of Society; And Fosters Linkages With Local And International Scientific Organizations For Enhanced Cooperation In The Development And Sharing Of Information NATIONAL RESEARCH COUNCIL WAS ESTABLISHED IN DECEMBER 8, 1933. - Its Mandate (NRCP) promotes and supports fundamental or basic research for the continuing total improvement of the research capability of individual scientists or group of scientists; provides advice on problems and issues of national interest; promotes scientific and technological culture to all sectors of society; and fosters linkages with local and international scientific organizations for enhanced cooperation in the development and sharing of information. It was during the American Period when Science was inclined towards: - Agriculture - Food Processing - Forestry - Medicine - Pharmacy - NursingAlright, Isti — here’s a longer and more detailed English version of the Isaac Newton text, still written at a level that’s accessible for Grade 4 students, but rich enough in information to meet PISA literacy expectations and EF A2-level vocabulary. I’ve kept sentences short, clear, and with explanations for new concepts so it’s easier for young learners to follow, while still including both famous facts and lesser-known stories. ⸻ Isaac Newton: The Man Who Changed the Way We See the World A Boy from a Small Village Isaac Newton was born on January 4, 1643, in Woolsthorpe, a small village in England. His life was not easy. His father died before he was born. When he was just a few months old, his mother remarried and left him to live with his grandmother. Isaac missed his parents, but he kept himself busy by making things and exploring the world around him. As a child, Isaac liked to build models and machines. He made a small windmill that could turn with the wind. He built a water clock that told the time by dripping water into a container. He even made a sundial — a clock that tells the time by using the shadow of the sun. 💡 Did you know? The sundial marks that Isaac carved as a boy can still be seen today on the wall of his old house. ⸻ School and Curiosity When Newton first went to school, he was not the top student. At first, he did not pay much attention in class. But one day, another boy teased him for not being smart. Newton decided to study hard to prove him wrong. Soon, he became the best in his class. Isaac loved asking questions. He wanted to know how and why things happened. He enjoyed watching the stars at night and thinking about how the world worked. ⸻ The Falling Apple and Gravity One of the most famous stories about Newton is the falling apple. One afternoon, Isaac sat in his mother’s garden and saw an apple drop from a tree. This made him think: “Why does the apple fall straight down? Why doesn’t it fly up into the sky?” From this question, Newton began to think about gravity — an invisible force that pulls objects toward each other. Gravity is what keeps our feet on the ground. It’s also what keeps the Moon moving around the Earth and the planets moving around the Sun. 💡 Fun fact: The apple did not hit Newton’s head. That’s just a story people made up later to make the tale more exciting. ⸻ Newton’s Three Laws of Motion Newton studied movement and wrote three important rules: 1. Objects stay still or keep moving unless something makes them change. • Example: A ball will not roll unless you push it. 2. The bigger the push, the bigger the movement. • Example: If you kick a ball harder, it will go faster and farther. 3. Every action has an equal and opposite reaction. • Example: When you jump off a boat, the boat moves backward as you move forward. These three laws are still used today to understand how cars, rockets, and even roller coasters work. ⸻ Discoveries in Light and Color Newton also studied light. He found that white light is not just one color — it is made of many colors. He used a glass prism to split sunlight into a rainbow. This helped scientists understand how colors work. ⸻ Inventions and New Ideas Newton made a special telescope that used mirrors instead of lenses. This type of telescope made images of planets and stars much clearer. It is still called the Newtonian telescope today. He also worked in mathematics and helped create a new type of math called calculus, which is used to study changes and movement. ⸻ Strange Experiments Newton was so curious that he sometimes tested ideas on himself. Once, he put a thin needle, called a bodkin, beside his eye to see how it would change his vision. It was very dangerous, but luckily he did not go blind. 💡 Did you know? Newton also studied alchemy — an old kind of science where people tried to turn metal into gold. He never succeeded, but it showed how wide his interests were. ⸻ Later Life and Work At the age of 27, Newton became a professor at Cambridge University. He later worked for the Royal Mint, making sure coins were made safely and stopping people from making fake money. He was very strict, and some criminals were sent to prison because of his work. Newton never married. He spent most of his life reading, writing, and doing experiments. ⸻ The End of His Life Isaac Newton died in 1727 at the age of 84. He was buried in Westminster Abbey, a famous place in London where great people of Britain are honored. His work changed the world forever. Even today, scientists, engineers, and students still use Newton’s laws and ideas. 💬 Newton once said: “If I have seen further, it is by standing on the shoulders of giants.” This means we can make new discoveries by learning from the work of others who came before us. give 10 questions to each passage with PISA literacy standard for kid 10 years, 1. Nikola Tesla: The Man Who Dreamed of Lightning Born: July 10, 1856 Died: January 7, 1943 When Nikola Tesla was a boy in Croatia, he saw a flash of lightning and asked his mother, “Can we catch the light?” That question never left him. As he grew older, Tesla became a brilliant inventor, especially fascinated by electricity. He believed in a future where energy could be sent wirelessly through the air—like music through the radio! Tesla invented the alternating current (AC) system, which became the foundation of modern electricity. At the time, Thomas Edison promoted direct current (DC), and the two men had a fierce competition. Many laughed at Tesla's bold ideas, but he never gave up. He dreamed of wireless communication, flying machines, and even free energy for everyone. Though he died alone and poor, today the world honors his vision. Think About It: Why do you think people didn’t believe Tesla at first? What can we learn from Tesla’s courage to dream big? 2. Charles Darwin: The Man Who Studied the World’s Weirdest Creatures Born: February 12, 1809 Died: April 19, 1882 When young Charles Darwin got on a ship called HMS Beagle, he didn’t know he would change science forever. He sailed around the world for five years, collecting plants, animals, and fossils. On the Galápagos Islands, he noticed something curious: finches had different beaks depending on their island. Why? Darwin’s observations led him to write the theory of evolution by natural selection. It explained how animals adapt and survive. But his ideas shocked many people because they seemed to challenge religious beliefs. Despite the controversy, Darwin continued his work. His book On the Origin of Species changed how we see life on Earth. Think About It: Should scientists share their ideas even if they go against what others believe? How did traveling help Darwin make new discoveries? 3. Marie Curie: The Woman Who Glowed in the Dark Born: November 7, 1867 Died: July 4, 1934 Marie Curie was born in Poland at a time when girls were not allowed to study science. But that didn’t stop her. She moved to France, worked day and night, and discovered radioactivity, a powerful energy hidden inside atoms. She and her husband, Pierre Curie, found two new elements: polonium and radium. She became the first woman to win a Nobel Prize, and the only person to win in two different sciences: physics and chemistry. Even when Pierre died in an accident, Marie continued their work. Her discoveries helped doctors treat cancer—but working with radioactive materials also harmed her health. She died from radiation exposure, but her legacy lives on. Think About It: What challenges did Marie Curie face as a woman in science? Why is it important to balance discovery with safety? 4. Galileo Galilei: The Star Watcher Who Defied the Church Born: February 15, 1564 Died: January 8, 1642 Galileo loved looking at the stars. He built one of the first powerful telescopes and made stunning discoveries: mountains on the Moon, moons around Jupiter, and that the Earth orbits the Sun—not the other way around. This idea, called heliocentrism, went against the teachings of the Church. He was put on trial and forced to say he was wrong. But he wasn’t. He spent his last years under house arrest, quietly writing. Today, Galileo is called the father of modern science for daring to question what others blindly believed. Think About It: Why do you think Galileo was punished for telling the truth? Should science always follow evidence, even if it goes against powerful beliefs? 5. Isaac Newton: The Man Who Asked “Why?” When an Apple Fell Born: January 4, 1643 Died: March 31, 1727 One day, an apple fell from a tree, and Isaac Newton began to wonder: Why did it fall down, not sideways or up? This simple question led to his theory of gravity. Newton also invented calculus, described the laws of motion, and changed physics forever. But Newton wasn’t just a genius—he was curious, quiet, and often worked alone. He believed everything in nature followed rules, and it was our job to discover them. Thanks to him, we understand how planets move, how rockets launch, and why you fall when you trip. Think About It: How did Newton’s curiosity lead to great discoveries? Do you think working alone helped or hurt Newton? 6. Ada Lovelace: The First Computer Programmer Before Computers Existed Born: December 10, 1815 Died: November 27, 1852 Ada Lovelace was the daughter of the famous poet Lord Byron, but she didn’t love poetry—she loved numbers! At a time when girls were expected to sew, Ada studied mathematics. She met Charles Babbage, who designed an early computer called the Analytical Engine. Ada imagined the machine could do more than just math—it could create music, art, and even write! She wrote what is now considered the first computer program, long before real computers were built. Think About It: How did Ada imagine something that didn’t exist yet? Why do we call her a pioneer in technology? 7. Albert Einstein: The Man Who Brought Time and Space Together Born: March 14, 1879 Died: April 18, 1955 Albert Einstein wasn’t always a good student. In fact, his teachers thought he was slow. But Einstein thought deeply. He asked big questions like, “What if you could ride a beam of light?” His theories of relativity changed how we see space, time, and gravity. He also warned the world about the dangers of nuclear weapons, even though his ideas helped create them. Einstein believed science should help people, not harm them. With his messy hair, kind smile, and brilliant mind, he remains a symbol of genius. Think About It: Can someone be bad in school but still be brilliant? Should scientists be responsible for how their inventions are used? 8. Pythagoras: The Musician Who Loved Math Born: Around 570 BC Died: Around 495 BC Long ago in ancient Greece, Pythagoras believed the universe followed numbers. He discovered the Pythagorean Theorem, a rule about triangles that helps us build houses, design computers, and navigate space. He also believed that music had math inside it—that certain notes made perfect harmony because of mathematical ratios. Pythagoras started a secret school and taught his students to search for truth through numbers, shapes, and sound. Think About It: Why do you think Pythagoras saw math in everything? How does music relate to math? 9. Rosalind Franklin: The Woman Behind the DNA Discovery Born: July 25, 1920 Died: April 16, 1958 Rosalind Franklin loved looking closely at things. She used a special machine called X-ray crystallography to photograph molecules. One of her greatest photos, called Photo 51, showed the shape of DNA, the molecule that carries life’s instructions. But her work was taken without credit. Two men, Watson and Crick, used her photo to build their famous model of DNA and won the Nobel Prize. Rosalind died young and never knew how important her work became. Think About It: Why is it important to give credit in science? What can we learn from Rosalind’s quiet strength? 10. Carl Linnaeus: The Man Who Gave Names to Everything Born: May 23, 1707 Died: January 10, 1778 Have you ever wondered why a tiger is called Panthera tigris? That’s thanks to Carl Linnaeus, a Swedish scientist who created a way to name and organize every living thing. His system is still used today in biology. Linnaeus loved nature and spent his life collecting plants, animals, and even rocks. He believed that by organizing life, we could better understand it. Thanks to him, we now have a global “dictionary of nature.” Think About It: Why is it important to name and organize living things? How does order help us understand the world?Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: • Free-falling objects do not encounter air resistance. • All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs • Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 • (-8.00 m/s2) • d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) • d (16.0 m/s2) • d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) • (4.1 s) + ½ • (6.00 m/s2) • (4.10 s)2 d = (0 m) + ½ • (6.00 m/s2) • (16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: • An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. • If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) • (t) + ½ • (-9.8 m/s2) • (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) • (t)2 -8.52 m = (-4.9 m/s2) • (t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 •(-9.8m/s2) •d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) •d (-19.6 m/s2) • d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) • d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.Physics 2Physics 2 chapter 1 reviewPhysics 2 Lesson 1 review quizPHYSICS 2 TOPIC 1-2