Physics Textbook for Grade 9 PDF - Sindh Textbook Board

TE ST ED IT IO N THE TEXTBOOK OF For Grade 9 Sindh Textbook Board, Jamshoro  All rights are reserved with the SINDH T...

TE ST ED IT IO N THE TEXTBOOK OF For Grade 9 Sindh Textbook Board, Jamshoro  All rights are reserved with the SINDH TEXTBOOK, BOARD, JAMSHORO. Prepared by Association For Academic Quality (AFAQ) for Sindh Text Book Board Reviewed by Directorate of Curriculum Assessment and Research Sindh, Jamshoro Prescribed by the Board of Intermediate and Secondary Education Hyderabad, Sukkur, Larkana, Mirpurkhas and Karachi for Secondary School Examination. Approved by the Education and Literacy Department, Government of Sindh. No.SED/HCW/181/2018 Dated 22nd September, 2020 for the province of sindh Patron in Chief Ahmed Bux Narejo Chairman, Sindh Textbook Board. Managing Director Project Director Shahid Warsi Khwaja Asif Mushtaq Association for Academic Quality (AFAQ) Association for Academic Quality (AFAQ) Project Manager Cheif Supervisor Rafi Mustafa Yousuf Ahmed Shaikh Association for Academic Quality (AFAQ) Sindh Textbook Board, Jamshoro AUTHORS REVIEWERS ¶ Dr. Barkat Ali Laghari ¶ Prof. Dr. Mazhar Ali Abbasi ¶ Dr. Najam Shaikh ¶ Dr. Barkat Ali Laghari ¶ Dr. Ghulam Rasool Soomro ¶ Mr. Riaz Zafar ¶ Mr. Noor Ahmed khoso ¶ Mr. Sarwaruddin Jamali ¶ Mr. M. Kashif Mubeen ¶ Mr. Sarwar-ud-din Jamali ¶ Mr. M. Ishaq Awan ¶ Mr. M. Ishaq Awan ¶ Ms. Rozina Channar ¶ Mr. Abdul Sajid EDITORS Technical Assistance ¶ Prof. Dr. Mazhar Ali Abbasi ¶ Mr. M. Arslan Shafaat Gaddi ¶ Mr. Noor Ahmed Khoso ¶ Dr. Barkat Ali Laghari ¶ Dr. Najam Shaikh Composing Designing & Illustration Association For Academic Quality (AFAQ) Printed at:  CONTENTS UNIT NO. UNIT NAME PAGE NO. PHYSICAL QUANTITIES AND Unit 1 1 MEASUREMENT Unit 2 KINEMATICS 31 Unit 3 DYNAMICS 58 Unit 4 TURNING EFFECT OF FORCES 87 Unit 5 FORCES AND MATTER 115 Unit 6 GRAVITATION 134 Unit 7 PROPERTIES OF MATTER 157 ENERGY SOURCES AND Unit 8 176 TRANSFER OF ENERGY THERMAL PROPERTIES Unit 9 198 OF MATTER  PREFACE The century we have stepped in, is the century of Physics. The modern disciplines Physics are strongly influencing not only all the branches of science but each and every aspect human life. To keep the students. abreast with the recent knowledge, it is a must that the curricula, at all the levels, be updated regularly by introducing the rapid and multidirectional development taking place in all the branches of Physics. The recent book of Physics for class IX has been written in this preview and in accordance with the revised curriculum prepared by Ministry of Education, Govt of Pakistan, Islamabad reviewed by independent team of Bureau of Curriculum, Jamshoro sindh. Keeping in view of the importance of Physics, the topics have been revised and re- written according to the need of the time. Since long Physics was teaching only in X class, the text book was consits of 18 units which was unable to complete in working hours. It has been decided now the Physics syllabus will be divided into portions, one should teach in 9th class and other will teach 10th class. So this book is consist of 9 units which have been thoroughly revised and re- written to meet the requirement of the curriculum. Among the new editions are the introductory paragraphs, information boxes, summaries and a variety of extensive exercises which i think will not only develop the interest but also add a lot to the ut ility of the book. The Sind Textbook Board has taken great pains and incurred expenditure in publishing this book inspite to its limitations. A textbook is indeed not the last word and there is always room for improvement. While the authors have tried their level best to make the most suitable presentation, both in terms of concept and treatment, there may still have some deficiencies and omissions. Learned teachers and worthy students are, therefore, requested to be kind enough to point out the short comings of the text or diagrams and to communicate their suggestions and objections for the improvement of the next edition of this book. In the end, I am thankful to our learned authors, editors and specialist of Board for their relentless service rendered for the cause of education. Chairman Sindh Textbook Board Unit 1: Physical Quantities and Measurement Unit - 1 Unit 1: Physical Quantities and Measurement Physical Quantities And Measurement Nature is described as a pragmatic Students Learning Outcomes (SLOs) set of rules followed by all the things After learning this unit students should be able to: around us. It is something which is l Describe the crucial role of Physics in Science, much greater than the imagination Technology and Society of humans. It is observable, it is l List with brief description of various branches surprising but it is somehow of physics explainable, its architecture has been l Choose a proper instrument (meter rule, designed with very beautiful Vernier calipers, screw gauge, physical balance patterns, strict rules but with stop watch, measuring cylinder) for the simplicity. A science which explores measurement of length, diameter, mass, time the nature is Physics. and volume in daily life activities. l Interconvert the prefixes and their symbols to indicate multiple and sub-multiple for both base and derived units l Write the answer in scientific notation in measurements and calculations l Define term density with S.I unit l Determine density of solids and liquids l Describe the need of using significant figures for recording and stating results in laboratory.  Unit 1: Physical Quantities and Measurement Why do we study physics? Which device will you choose to measure the length of a small cylinder? How will you determine the thickness of a piece of wire? How will you find the volume of small stone? why ice floats while a coin sinks in the water? After Quote learning this unit you will be answer these and other similar questions. “No one undertakes research in physics with 1.1 INTRODUCTION TO PHYSICS the intention of winning One of the most basic and ancient science is the a prize. It is the joy of Physics. The word science refers to the study of a fact by discovering something collecting information through observation, presenting no one knew before.” it in a mathematical way, justifying the idea with Stephen Hawking experiment and finally making a conclusion about the fact. Thus physics can be defined as: Physics is the branch of science which observes the nature represents it mathematically and conclude with the experiment. It basically deals with the behavior and structure Do You Know! of matter and the energy that derives the matter. Physics is the branch of natural science that studies Physics Derived from matter, its motion, its behavior through space and time A n c i e n t G r e e k and the related entities of energy and force. Physics is ‘physicos’ meaning one of the most fundamental scientific disciplines, and ‘knowledge of nature’. its main goal is to understand how the universe behaves. It is a matter of fact that Physics can be considered as the mother of all sciences. The beauty of physics lies in its Laws that govern this whole universe from an atom to large scale galaxies and in its experiments from home to large scale experiment labs. Physicist are categorized into two categories: those who observe the nature solve its mysteries with available 2 Unit 1: Physical Quantities and Measurement and missing information, present their theories with mathematical approach. They are known as theoretical physicist and other are more interested to test those theories with experiments are known as experimental physicists. Since from the beginning of the universe, the structure of universe is very straight forward, the Fig. 1.1Mechanics classification of physics was not that much easy but as the physicist explained the universe, they classified Physics into many branches. These branches show the spectrum and scope of Physics around us and help scientist to describe ideas in a well-organized way. The main branches of Physics are as follows. Mechanics Fig 1.2 Thermodynamics This branch of physics is mainly concerned with the laws of motion and gravitation. Thermodynamics Thermodynamics deals with heat and temperature and their relation to energy and work. Electricity Fig 1.3Electricity Electricity is the study of properties of charges in rest and motion Magnetism Magnetism is the study of magnetic properties of materials Atomic Physics Atomic physics deals with the composition structure and properties of the atom Fig 1.4 Magnetism 3  Unit 1: Physical Quantities and Measurement Hydrogen Optics Optics studies physical aspects of light and its Helium properties with the help of optical instruments. Neon Sound Sodium Sound is the study of production, properties and applications of sound waves. Mercury Nuclear physics Fig. 1.5 Atomic Physics Nuclear physics deals with the constituents, structure, behavior and interactions of atomic nuclei. Particle physics Particle Physics studies the elementary constituents of matter and radiation, and the interactions between them. Fig. 1.6 Optics Astrophysics The study of celestial objects with the help of laws of physics is known as Astrophysics. Plasma physics The study of ionized state of mater and its properties is known as Plasma Physics. Fig. 1.7 Sound Geo physics The study of internal structure of earth is known as Geo physics. Importance of Physics in Science Technology and Society Society’s reliance on technology represents the Fig. 1.8 Nuclear Physics importance of physics in daily life. Many aspects of modern society would not have been possible without 4 Unit 1: Physical Quantities and Measurement the important scientific discoveries made in the past. These discoveries became the foundation on which current technologies were developed. Discoveries such as magnetism, electricity, conductors and others made modern conveniences, such as television, computers, smart phones, medical Fig. 1.9 Particle Physics instruments, other business and home technologies possible. Moreover, modern means of transportation, such as aircraft and telecommunications, have drawn people across the world closer together all rely on concepts of physics. 1.2 MEASURING INSTRUMENTS Physics is much concerned with matter and Fig. 1.10 Astro Physics energy and the interaction between them which is explained with the help of describing the mathematical relations between various physical quantities. All physical quantities are important for describing the nature around us. A physical quantity is a physical property of a phenomenon, body, or substance that can be quantified by measurement. A physical quantity can be expressed as the combination of a magnitude expressed by a number – usually a real number – and a unit. Physical quantities Fig. 1.11 Plasma Physics are classified into two categories: u Fundamental quantities u Derived physical quantities. Physical quantities which cannot be explained by other physical quantities are called fundamental physical quantities. There are seven fundamental physical quantities and are listed in table 1.1 along with their units. Fig. 1.12 Geo Physics 5  Unit 1: Physical Quantities and Measurement Table 1.1 Fundamental quantities and their S.I units Fundamental quantities S.I Unit Symbol of Unit Length meter m Mass Kilogram kg Time second s Electric current Ampere A Temperature Kelvin K Do You Know! Amount of substance mole mol Some Physical Luminous intensity candela cd quantities are unit- Physical quantities which are explained on the less. Such as Elastic basis of fundamental physical quantities are called modulus, Plane angle derived physical quantities. and solid angle Table1.2 derived quantities and their units Derived Symbol of Quantities S.I Unit Unit Do You Know! Volume cubic meter m3 The notion of Velocity meter per second m-1s Force Newton N physical dimension Density kilogram per cubic meter kg/m3 of a physical quantity Acceleration meter per second square m/s2 was introduced by Joseph Fourier in All physical quantities are either calculated 1822 by convention, mathematically or measured through an instrument. physical quantities Scientist, Engineers, Doctors and others like are organized in a blacksmith, carpenter, and goldsmith even the workers dimensional system and ordinary human's measure those physical built upon base quantities with the help of instruments. For instance, quantities, each of your doctor uses a thermometer to tell your body which is regarded as temperature, a carpenter uses the inch tape to measure having its own the length of woods required for furniture. dimension. 6 Unit 1: Physical Quantities and Measurement A puncture mender uses air gauges to check the air pressure in the tyre. Similarly, a chemical engineer uses hydrometer for describing the density of a liquid. Measuring the physical quantity correctly with instrument is not an easy task for scientist and engineers. Scientist are seriously concerned with the accuracy of the instrument and its synchronization. Do You Know! Moreover, the instrument they design mostly for their Use of every instrument own sake of research which readably goes on to is restricted by smallest commercial market. Many of the instruments we use measurement that it today are inventions of pioneers of science. Usually, the can perform which is basic physical quantities that we use in our daily life are called least count. measured with basic and simple instruments. The Standard of Length If there is any measurement that has proven to be Do You Know! the most useful to humanity, it is length. For examples 1000m = 1km units of length include the inch, foot, yard, mile, 100cm =1m meter etc. 1cm = 10mm The length is defined as the minimum distance 1inch = 2.53cm between two points lying on same plane. 12 inch = 1 ft The meter (m) is the SI unit of length and is defined as: 1 yard = 3ft The length of the path traveled by light in vacuum during the time interval of 1/299 792 458 of a second. The basic measurement of length can be obtained with the help of a meter rod or an inch tape. Meter Rule A meter rule is a device which is used to measure length of different objects. A meter rule of length 1m is equal to 100 centimeters (cm). On meter rule each cm is divided further in to 10 divisions which Fig 1.13 Meter Rule 7  Unit 1: Physical Quantities and Measurement are called millimeters (mm). So, a meter rule can measure up to 1mm as smallest reading. It is made up of a long rigid piece of wood or steel(Fig 1.13). The zero-end of the meter rule is first aligned with one end of the object and the reading is taken where the other end of the object meets the meter rule. Vernier Caliper Fig 1.14 Vernier Calipers The Vernier Caliper is a precision instrument that can be used to measure internal and external distance extremely accurate. It has both an imperial and metric scale. A Vernier caliper has main jaws that are used for measuring external diameter, as well as smaller jaws that are used for measuring the internal diameter of objects. Some models also have a depth Fig 1.15 Digital vernier gauge. The main scale is fixed in place, while the calipers Vernier scale is the name for the sliding scale that opens and closes the jaws (Fig1.14). Reading a Vernier Caliper Step 1 Step 2 Place the object between the Note the main scale reading by jaws of the Vernier caliper counting lines before the zero line of Vernier scale Vernier Scale reading Main scale reading =2.8mm Vernier scale reading=0.6mm Main scale reading Total reading=3.4mm Step 3 Step 4 Count the next line of Vernier scale Add the two reading after zero coinciding main scale for total 8 Unit 1: Physical Quantities and Measurement CHECKING FOR ZERO OBSERVED READING CORRECTED ERROR READING 0 Main scale 1 3 Main scale 4 3.14cm (No zero error 0 Vernier scale 10 Vernier scale 0 No correction Two zero marks 10 required) coincide Reading=3.14cm No Zero error. 0 Main scale 1 3 Main scale 4 3.17cm- (+0.03)=3.14cm 0 Vernier scale 10 Vernier scale 0 10 (The positive zero zero mark on error is vernier scale is Reading=3.17cm subtracted from slightly to the right reading) Zero error is 0.03 0 Main scale 1 3 Main scale 4 3.11cm -(-0.07) 0 =3.18cm 10 Vernier scale Vernier scale 0 10 (Negative zero Zero mark on vernier scale is slightly to the error is added to left. zero error of -0.07 Reading=3.11cm the reading) Micrometer Screw Gauge Screw gauge in extensively used in engineering field for obtaining precision measurements. Micrometer screw gauge is used for measuring extremely small dimensions. A screw gauge can even measure dimensions smaller than those measured by a Vernier Caliper. Micrometer Screw gauge works on the simple principle of converting small distances into larger ones by 9  Unit 1: Physical Quantities and Measurement measuring the rotation of the screw. This “screw" principle facilitates reading of smaller distances on a scale after amplifying them (Fig 1.16). Reading A Micrometer Screw Gauge Fig 1.16 Screw Gauge Step 1 Step 2 Turn the thimble Take the main scale until the anvil and reading at the edge of the spindle gently the thimble. grip the object. Then turn the ratchet until it starts to click. Sleeve Thimble Anvil Spindle Ratchet Frame Sleeve treading= 4.5mm Thimble reads twelve division=0.12mm Total reading=4.62mm Step 3 Step 4 Take the thimble scale Now add main reading opposite the scale reading to datum line of the thimble reading. main scale. Multiply This will be the this reading with least diameter of the count i.e., 0.01mm object. 10 Unit 1: Physical Quantities and Measurement Checking For Zero Error Observed reading Corrected Reading Do You Know! 10 5 35 The kilogram, 0 2.0 30 0 0.00 originally defined as: 45 25 0.25 40 20 The mass of one cubic 15 2.25mm Zero mark on thimble scale decimeter of water at coincides with the datum line No zero error on the main scale and reading Reading = 2.0+0.25 No Correction the temperature of on the main scale is zero. = 2.25mm is required maximum density.It No zero error was replaced after the 15 40 International Metric 0 2.0 10 0.07 35 Convention in 1875 by 5 0.25 0 30 the International 25 2.32 - (+0.07) Prototype Kilogram. Zero on datum line can be =2.25mm seen. Positive Zero Error Reading=2.0+0.32 Reading =+0.07 mm =2.32mm (Count from Zero.) 5 0 2.0 30 0 0.02 25 45 0.23 20 40 2.23 - (-0.02) 15 =2.25mm Zero mark on datum line cannot be seen Reading=2.0+0.23 negative zero error =2.23mm Reading= -0.02mm (count down from 0) The Standard Of Mass The kilogram is the SI unit of mass and is equal to the mass of the international prototype of the kilogram, a platinum-iridium standard that is kept at the International Bureau of Weights and Measures Fig 1.17 Kilo gram (Fig1.17). 11  Unit 1: Physical Quantities and Measurement Do You Know! The kilogram is a cylinder of special metal about 39 millimeters wide by 39 millimeters tall that serves as 1000g = 1kg the world's mass standard. 1g = 1000mg Each country that subscribed to the 1g= 1000000mg International Metric Convention was assigned one or 1g=1000000000ng more copies of the international standards; these are 1g=0.002lb known as National Prototype Meter and Kilogram. The Physical Balance The Physical balance is an instrument used for measurement of mass. It is mostly used in laboratory. It works on the principle of moments. It consists of a light and rigid beam of brass, a metallic pillar, a wooden base, two pans, a metallic pointer and an ivory scale (Fig 1.18). The plumb line indicates whether the balance is horizontal. In ideal condition the plumb line is Fig 1.18 Physical Balance aligned with the end of the knob fixed with the pillar. When the beam is horizontal the pointer remains on zero mark on the ivory scale. The whole box has leveling screws at the bottom to set it to horizontal. The device is enclosed in a glass box to avoid wind effects. Agate knife Beam and agate plate Balancing screw Pillar Pointer Plumb Scale Pan 100 ml O In 20 C Weights Leveling Arrestment knob screw 12 Unit 1: Physical Quantities and Measurement The Electronic Balance The digital mass meter is an electronic instrument configured with integrated circuits and it works on the principal of balancing the forces. The device is turned on and set to zero then object is placed on the plate. The reading on the screen gives the mass of object. The electronic balance (Fig 1.19) is Fig 1.19 Electronic Balance available in different ranges of measurement such as Fig 1.19 Electronic Balance micro gram, milligram and kilogram etc. The Standard of Time Before 1960, the standard of time was defined in terms of the mean solar day for the year 1900. The rotation of the Earth is now known to vary slightly with time, this motion is not a good one to use for defining a time standard. Fig 1.20 Atomic Clock In 1967, the second was redefined to take advantage of the high precision attainable in a device known as an atomic clock(Fig 1.20), which uses the characteristic frequency of the cesium-133 atom as the “reference clock”. The second is now defined as 9 192 631 770 times the period of vibration of radiation from the cesium atom. Stop Watch A stopwatch is used to measure the time interval between two events. There are two types of stopwatch : Mechanical stopwatch and Digital stopwatch. Mechanical / Analogue Stopwatch A mechanical stop watch can measure a time interval up to 0.1 second (Fig1.21). It has a knob that is Fig. 1.21 Stop Watch 13  Unit 1: Physical Quantities and Measurement used to wind the spring that powers the watch. It can also be used as a start stop and reset button. The watch starts when the knob is pressed once. When pressed second time, the watch stops While the third press brings the needle back to zero. Digital Stopwatch A digital stop watch can measure a time interval up to 0.01 second (fig 1.22). It starts to indicate the time lapsed as the start/stop button is pressed. As soon as start/stop button is pressed again, it stops and indicates the time interval recorded by it between start and stop of an event. A reset button restores its initial zero Fig. 1.22 Digital stop watch setting. Now a days almost the mobile phones have a stopwatch function. Human Reaction Time As analogue or digital or watch is operated by human manually i.e., they have to be started or stopped by hand. This causes a random error in measurement of time i.e called human reaction time. For most people human reaction time is about 0.3- 0.5 s. Therefore for more accurate measurement of time intervals light gates (Fig1.23) can be used. Light gates 0.00 s 0.00 s Timer 2 Timer 1 Fig 1.23 Light gates 14 Unit 1: Physical Quantities and Measurement SELF ASSESSMENT QUESTIONS: Do You Know! Q1: What instrument will you choose to measure height of your friend? 1 hour = 60 min Q2: Can you describe how many seconds are there in a 1 hour = 3600 sec year? 1min=60sec Q3: Which instrument will you choose to measure your 1sec=1000ms mass? 1sec=1000000ms 1.3 PREFIXES The Physical quantities are described by the scientist in terms of magnitudes and units. Units play a vital role in expressing a quantity either base or derived. Prefixes are useful for expressing units of physical quantities that are either very big or very small. A unit prefix is a specifier. It indicates multiples or fractions of the units. Units of various sizes are commonly formed by the use of such prefixes. The prefixes of the metric system, such as kilo and milli , represent multiplication by powers of ten. Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognized by standards organizations. Human Pyramid Mosquito 100 Mountain Hair 10,000 Moon 1,000,000 100,000,000 Cells er Sm Moon 10,000,000,000 DNA gg Distance all 1,000,000,000,000 Bi Solar Atoms System 100,000,000,000,000 re Nearest 10,000,000,000,000,000 Nucleus 1,000,000,000,000,000,000 Star Electron ? 100,000,000,000,000,000,000 Galaxy 10,000,000,000,000,000,000,000 ? Nearest 1,000,000,000,000,000,000,000,000 Galaxy Neutrino ? 100,000,000,000,000,000,000,000,000 ? Visible Universe 1,000,000,000,000,000,000,000,000,000 1,000,000,000,000,000,000,000,000,000,000 ? Edge of 100,000,000,000,000,000,000,000,000,000,000 the known 10,000,000,000,000,000,000,000,000,000,000,000 Planck ? Scale by 100’S Table 1.3 SI pre fixes 15  Unit 1: Physical Quantities and Measurement SI Prefixes Prefix Symbol Meaning Multiplier Multiplier (Numerical) (Exponential) Greater than 1 tera T trillion 1 000 000 000 000 1012 giga G billion 1 000 000 000 109 mega M million 1 000 000 106 kilo k thousand 1 000 103 hecto h hundred 100 102 deka da ten 10 101 Less than 1 Unit 1 *deci d tenth 0.1 10-1 *centi c hundredth 0.01 10-2 *milli m thousandth 0.001 10-3 *micro m millionth 0.000 001 10-6 *nano n billionth 0.000 000 001 10-9 pico p trillionth 0.000 000 000 001 10-12 femto f quadrillionth 0.000 000 000 000 001 10-15 atto a quintillionth 0.000 000 000 000 000 001 10-18 SELF ASSESSMENT QUESTION: Q4: Can you tell if the size of a nucleus is up to 10-15m. What prefix shall we use to describe its size? 1.4 SCIENTIFIC NOTATION Scientific notation or the standard form is a simple method of writing very large numbers or very Scientific Notation small numbers. In this method numbers are written as Exponent powers of ten. Thus calculation of very large or very small numbers becomes easy. m x 10 n Numbers in Scientific Notation are made up of three parts: The coefficient, the base and the exponent. coefficient base u The coefficient must be equal to or (Not zero) greater than one u The base must be 10 u The exponent can be negative or positive. 16 Unit 1: Physical Quantities and Measurement Worked Example 1 Convert mass of Sun 2 000 000 000 000 000 000 000 000 000 000 kg. into Scientific Notation. Solution Step 1: Since, MSun = 2 000 000 000 000 000 000 000 000 000 000 kg It's obvious that in this value decimal lies at the end. Step 2: Converting into scientific notation Move the decimal to left writing in terms of base of ten 30 Msun = 2.00 ´ 10 kg. Quick Lab Note: power of exponent is taken as positive not to be Fill a tub with water to certain confused as we have displaced decimals but not level and mark. numbers. Put some ice in it and observe Worked Example 2 the water level carefully as well as floating or sinking. Convert mass of an electron 9.11 x 10-31 kg into standard form. Remove the ice from the tub without being melt and put a Solution balloon in it and then observe. Step 1: The decimal lies in the middle of the value. -31 Likewise, put a spoon in that Since, melectron = 9.11 ´ 10 kg tub and observe. Step 2: Move the decimal 31 steps towards left Again put an empty can of melectron = 0.000 000 000 000 000 000 000 000 000 000 coke and observe. 911 kg Can you tell which of all four 1.5 DENSITY AND VOLUME has more density? And which has more volume? The three common phases or states of matter are solid, liquid and gas. A solid maintains a fixed shape and a fixed size, even if same force is applied it not readily change its volume. A liquid does not maintain a Do You Know! fixed shape it takes on the shape of its container. But, 1 liter = 1000cm 3 like a solid it is not readily compressible, and its volume 1m3 = 1000 litr can be changed significantly only by a large force. 17  Unit 1: Physical Quantities and Measurement However, a gas has neither a fixed shape nor a fixed volume- it will expand to fill its container. Often we find the large weight woods floating on the surface of water. However, an iron needle sinks into the water. We say iron is “heavier” than wood. This cannot really be true rather we should say like iron is “denser” than wood. Physicist are concerned with a physical quantity, a property of matter which may help to define the nature of matter in terms of its mass and space. Measuring the Volume For density to be measured or calculated we first need to find the volume of substances. Most of solid geometrical shapes have formulae for their volume which is obtained through different parameters such as radius, height, depth, width, base and length, but for irregular objects, liquids and gases this approach is unusual. The volume of liquids can be measured with the help of Cylinders, and Beakers. Measuring Cylinder Measuring cylinder is a glass or plastic cylinder with a scale-graduated in cubic centimeters or milliliters (ml)(fig1.24). It is used to find the volume of liquids. When a liquid is poured, it rises to a certain height in the cylinder. The level of liquid in the cylinder is noted and volume of the liquid is obtained. In order to read the volume correctly we should keep Eye level Meniscus the eye in level with the bottom of the meniscus of the liquid surface as you learned in previous grade. Fig. 1.24 Measuring Cylinder 18 Unit 1: Physical Quantities and Measurement 1. Volume of Liquid Quick Lab A volume of about a liter or so can be measured Take a measuring cylinder of 1 liter capacity at full place it using a measuring cylinder. When the liquid is poured in a beaker. into the cylinder the level on scale gives the volume. Fill cylinder full with water. Most measuring cylinders have scales marked in milliliters (ml) or cubic centimeters (cm3). It should be Pour a stone of irregular shape in it gradually. noted that while recording the value from cylinder the eyes should maintain the level with the value. Angular As you pour the stone in the observation may result a false reading of the volume. cylinder, the water from cylinder drops into the beaker. 2. Regular solid Drop the stone in cylinder completely If an object has a regular shape its volume can be calculated Calculate the volume of water ejected out of cylinder. For instance: Volume of a rectangular block = length x width x height Volume of water ejected is the volume of the stone. Volume of a cylinder = p ´ radius2 ´ height 3. Irregular solid Rock For an irregular solid its volume is calculated by lowering the object in a partially filled measuring cylinder (fig 1.25). The rise in the level on the volume scale gives the volume of that object. Thus the volume of irregular solid is calculated by subtracting the original volume of liquid from the raised volume of liquid. The total volume is found. The volume of the solid is measured in a separate experiment and then Rock subtracted from the total volume. Fig 1.25. Volume Irregular shaped Solid 19  Unit 1: Physical Quantities and Measurement Density The term density of a substance is defined as Do You Know! mass of substance (m) per unit volume (V). It is denoted During the Cold War between by Greek letter ρ (rho). m ρ= Russia and America. There was V a race of Astrophysics. America Density is characteristic property of any pure was facing the period of racism. A Black lady mathematician substance. Objects made of a particular pure substance named Katherine solved the such as pure Gold can have any size or mass but its problem of putting the first density will be same for each. orbital satellite. Recommended! In accordance with the above equation mass of a Watch movie “Hidden Figures” substance can be expressed as Observe the importance of Reliable Numbers. m = ρV 3 -3 The S.I unit for density is kg/m kgm. Sometimes dens of substances is given in gm/ cm3. The 3 density of Aluminum is 2.70 gm/cm which is equal to 2700 Kg/m3. Do You Know! Measuring the Density In Jordan there is sea known as 'Dead Sea' It is to be noted that there are two ways of The humans in that sea while finding the density of a substance either swimming does not sink! This is because the water of mathematically or experimentally by taking density sea is much more salty than of water at 4oC as a reference which is sometimes normal, which raises the known as relative density or 'Specific gravity'. It has density of water. no unit, it is a number whose value is the same as that of the density in g/cm3. density of substance relative density = density of water 20 Unit 1: Physical Quantities and Measurement Worked Example 4 What is the mass a solid iron wrecking ball of radius 18cm. if the density of iron is 7.8 gm/cm3? Solution: Step 1: write known physical quantities with units and point out the quantity to be found. Density of iron ball ρ = 7.8 gm/cm3 = 7.8 ´ 1000 kg/ m3 Radius of iron ball is r = 18cm = 18 ´ 10-2 m = 0.18m Volume of the iron ball is V = (4/3) ´ π ´ r3 = (1.33) ´ 3.14 3 ´ (0.18m)3 V = 0.024m Step 2: write down the formula and rearrange if necessary m=ρ´V Step 3: put the values in formula and calculate Since mass of iron ball is m = ρ ´ V = (7.8 x 103) ´ (0.024) m = 187.2 kg SELF ASSESSMENT QUESTIONS: Q5: How can you identify which gas is denser among the gases? Q6: Can you tell how hot air balloon works? 1.6 SIGNIFICANT FIGURES Engineers and scientist around the world work with numbers either representing a large or small magnitude of a physical quantity. The engineers are however interested in the accuracy of a value as they mostly work on estimation but scientist especially physicist are more concerned in the accuracy of these numbers. For instance, an engineer records the speed of wind and explains it on an average. On the other hand, for the physicist, the speed of earth on its course, the 21  Unit 1: Physical Quantities and Measurement speed of light in vacuum the mass or charge on an electron is just not a matter of numbers but accurate numbers. The numbers of reliably known digits in a value are known as significant figures. Table 1.4 Rules for determining significant figures Rule Example 1. All non-zeroes are 2.25 (3 significant figures) significant 2. Leading zeroes are 0.00000034 (2 significant NOT significant figures) 3. Trailing zeroes are 200 (1 significant figure) significant ONLY if 200. (3 significant figures) an explicit decimal 2.00 (3 significant figures) point is present 4. Trapped zeroes are 0.00509 (3 significant figures) significant 2045 (4 significant figures) Worked example 5 How many significant figures are there in the area of a cylinder whose diameter is 5 cm Solution: Step 1: write known physical quantities and point out the unknown quantity Diameter of the cylinder is d = 5cm = 5 ´ 10-2 m = 0.05m Radius of cylinder is r = d/2 = 2.5 ´ 10-2 m = 0.025m Step 2: write down formula and rearrange if necessary The area of the cylinder is A = p ´ r2 = 3.14 ´ (0.025m)2 = 2 0.0019m Step 3: put value in formula and calculate 2 Thus area of cylinder can be written as A = 1.9 mm Thus, there are two significant numbers in the value 1 and 9. 22 Unit 1: Physical Quantities and Measurement SELF ASSESSMENT QUESTIONS: Q7: Determine the number of significant figures in 00.6022009 SUMMARY u Physics is the branch of science which deals with studies of matter its composition, properties, and interaction with energy. u The branches of Physics are classified on the basis of different areas of study with different approaches. u There are two types of physicist, theoretical and experimental physicist. u Physics define mathematical relation between physical quantities. A physical quantity has magnitude and unit. u Physical quantity are mainly classified into two categorize (i) Base or fundamental quantities (ii) Derived physical quantities. u Base quantities are length, mass, time, temperature, current, luminous intensity, and amount of substance. u The standard of length is meter can be measured by measuring tape , or meter rule. u The standard of mass is kilogram can be measured by physical balance. u The standard of time is second can be measured by stop watch. u The measured or calculated values either macroscopic or microscopic can be expressed in Scientific Notations. u The volume of liquid is calculated or measured with help of measuring cylinder 23  Unit 1: Physical Quantities and Measurement u The volume of irregular objects can be calculated through measuring cylinder with displacement of water. u The density of a pure substance is its characteristic property it is the ratio of mass per unit volume. u The density of objects can be calculated with the help of water as a reference known as specific gravity also known as relative density. u Prefixes can be used to represent large or smaller values of a physical quantity. u The most accurate or reliable numbers of a value are known as significant figures. 24 Unit 1: Physical Quantities and Measurement ACTIVITIES CONCEPT MAP Physics Quantities Based on its types, Based on existing or has is divided into not direction, divided into Base Quantities Derived Quantities Scalar Quantity Vector Quantity There are For examples For examples 1. Length · Area · Distance Displacement 2. Mass Volume · Speed Velocity 3. Time Force · Energy Work 4. Temperature · Energy · Volume, Force 5. Electric current · Density etc. 6. Luminous intensity 7. Amount of substance Physics Quantities Length Mass Time Volume Meter Kilogram Seconds Liter Ruler/ Spring Balance/ Measuring cylinder/ Measuring Stopwatch/clock Electronic balance/ flask/ beaker/pipette Tape Beam balance Multiple Basic Sub multiple Multiple Basic Sub multiple km m mm Min, hour Second (s) ms Multiple Basic Sub multiple Liter Milliliter Metric kg mg l ml Tone (t) 25  Unit 1: Physical Quantities and Measurement End of Unit Questions Section (A) Multiple Choice Questions (MCQs) 6 7 cm 1. The Figure 1.26 shows part of a Vernier scale, what is 0 the reading on the Vernier scale Fig 1.26 a) 6.50 cm b) 6.55 cm c) 7.00 cm d) 7.45 cm 2. Ten identical steel balls each of mass 27g, are 3 immersed in a measuring cylinder having 20cm of 3 water. The reading of water level rises to 50cm. What is the density of the steel? a) 0.90 gm/cm3 b) 8.1 gm/cm3 c) 9.0 gm/cm3 d) 13.5gm/cm3 3. An object of mass 100g is immersed in water as shown in the figure 1.27, what is the density of the material from which object is made? Fig 1.27 a) 0.4gcm3 b) 0.9gcm3 c) 1.1 gcm3 d) 2.5gcm3 4. What is the reading of this micrometer in figure 1.28 20 0 5 15 a) 5.43mm b) 6.63mm 10 c) 7.30mm d) 8.13mm 5 5. A chips wrapper is 4.5 cm long and 5.9 cm wide. Its Fig 1.28 area upto significant figures will be a) 30 cm² b) 28 cm² c) 26.55 cm² d) 32 cm² 26 Unit 1: Physical Quantities and Measurement 6. A worldwide system of measurements in which the units of base quantities were introduced is called a) prefixes b) international system of units c) hexadecimal system d) none of above 7. All accurately known digits and first doubtful digit in an expression are known as a) non-significant figures b) significant figures c) estimated figures d) crossed figures 8. If zero line of Vernier scale coincides with zero of main scale, then zero error is a) positive b) zero c) negative d) one 9. zero error of the instrument is a) systematic error b) human error c) random error d) classified error 10. Length, mass, electric current, time, intensity of light and amount of substance are examples of a) base quantities b) derived quantities c) prefixes d) quartile quantities 27  Unit 1: Physical Quantities and Measurement Section (B) Structured Questions 1. Column A Action Column B Branch Cooking Bar B.Q Thermodynamics Turning the Bulb on Riding a bicycle Looking for Giant Galaxies Producing a loud sound Describing an atom Obtaining energy from Earth 2. Physical Quantity S.I Unit Type Ampere m3 Sec Base Temperature Base N 3 Density Kg per m Acceleration 3. Convert the following values. a) 230 cm = ______________m b) 250 g = _____________kg c) 0.5 s = ________________ms d) 0.8 m = ____________mm e) 350ms = ________________s f) 1.2Kg = _____________g 28 Unit 1: Physical Quantities and Measurement 4. An engineer measures the width of an aluminum sheet using Vernier caliper as shown in fig 1.29 2 3 4 5 a)What is the measurement of the width of 0 5 10 aluminum sheet b)Which gives more precise measurement Vernier caliper, Screw Gauge or meter rule? Fig 1.29 5. A pendulum swings as shown if figure 1.30 from X to Y and back to X again i) What would be the most accurate way of measuring time for one oscillation? with the help of a Stop Watch. a) Record time for 10 oscillations and multiply by 10 b) Record time for 10 oscillation and divide by 10 c) Record time for one oscillation d) Record time from X to Y and double it ii) Suggest an instrument for measuring time period more accurately. X Y Prefixes Fig. 1.30 6. write the correct prefix of notion a) 75000m = 750 __________ b) 2/1000 sec = 1 __________ c) 1/1000000 g = 1 _________ d) 1000000000 m = 1_________ Scientific Notation 7. Write values in standard and scientific notation a) The radius of 1st orbit of Hydrogen atom is r = 0 0.53 A = __________ b) 1 light year is 2628000000000m = ___________ c) Vacuum pressure 2.7 x 10-4 torr = __________ 29  Unit 1: Physical Quantities and Measurement Density and Volume 8. A wooden piece is made in different shapes take length (l) = radius (r) = 2m Calculate its volume as a: cm3 cm3 a) Sphere b) Cube c) Cylinder d) Pyramid Measuring e) Cylinder cylinder Water level with solid 9. Find the density of wood as sphere and cube if the mass of wood is 1kg. Is there any change Water level without in density due to shape? solid 10. A measuring cylinder (fig 1.31) is filled with 500cc Water water. A stone of mass 20g is immersed in to the Irregular solid cylinder such that ,water level rises up to 800cc. Which statement is correct? a) The difference between the readings gives the density of stone. Fig 1.31 b) The difference between the readings gives volume of the stone c) The final reading gives the density of stone d) The final reading gives the volume of stone Significant Figures 11. Write significant numbers in the following values. a) 980 has ________ Significant numbers. b) 91.60 has _______ Significant numbers. c) 10010.100 has ________Significant numbers. d) 0.0086 has ______Significant numbers. 30 Unit 2: Kinematics Unit - 2 Unit 2: Kinematics KINEMATICS The word Kinematics is derived Students Learning Outcomes (SLOs) from Greek Word kinema. After learning this unit students should be able to: How an object changes its position l Describe using examples how objects can be at rest in space in a certain time interval and in motion simultaneously. without considering the causes of motion it is the study of motion of l Identify different types of motion i.e., translatory, bodies without any reference of (linear, random, and circular); rotatory and vibratory force. motions and distinguish among them. l Define with examples distance, displacement, speed, velocity and acceleration (with units) l Differentiate with examples between distance and displacement, speed and velocity. l Differentiate with examples between scalar and vector quantities. l Represent vector quantities by drawing. l Plot and interpret distance-time graph and speed- time graph l Determine and interpret the slope of distance-time and speed-time graph l Determine from the shape of the graph, the state of a body (i) at rest (ii)moving with constant speed (iii) moving with variable speed l Calculate the area under speed-time graph to determine the distance traveled by the moving body. l Solve problems related to uniformly accelerated motion using appropriate equations l To rearrange the equation according to the requirement of the problem l Solve problems related to freely falling bodies using 2 10 m/s as the acceleration due to gravity. 31  Unit 2: Kinematics When you throw a ball straight up in the air, how high does it go? When a glass slips from your hand, how much time do you have to catch it before it hits the ground? How will you describe the motion of a jet fighter being catapulted down the deck of an air craft carrier? These and some other similar questions you will learn to answer in this unit. The branch of physics which is related with the study of motion of objects is called Mechanics. It is divided in two parts (i) Kinematics (ii) Dynamics The word kinematics is derived from Greek word Fig 2.1, Car with “Kinema” which means motion. respect to tree at rest position Kinematics is the branch of Mechanics which deals with motion of objects without reference of force which causes motion. 2.1 REST AND MOTION Have a look around in your classroom, You can observe various things like, table, chairs, books etc all are in state of rest. A car is in the state of rest with respect to trees and bushes around it Fig 2.1. Thus rest can be defined as: A body is said to be in rest if it does not change its position with respect to its surroundings. A train is stationed at the platform. A person can Fig 2.2, Train at station notice that the train does not changes its position with respect to its surroundings, hence the train is in the state of rest Fig 2.2. But as soon as the train starts moving its position continuously changing with respect to its surroundings. Now we can say that the train is in motion. Thus motion can be defined as: 32 Unit 2: Kinematics A body is said to be in motion if it changes its position with respect to its surroundings. Rest and Motion are Relative State No body in the universe is in the state of absolute rest or absolute motion. If a body is at rest with respect to some reference point at the same time, it can also be in the state of motion with respect to some other reference point. For example, A Passenger sitting in a moving bus is at rest because passenger are not changing their Fig 2.3, A moving bus position with respect to other passengers or objects in the bus as shown in fig 2.3. But for another observer outside the bus noticed that the passengers and objects inside the bus are in motion as they are changing their position with respect to observer standing at the road. Similarly a passenger flying on aeroplane is in motion when observed from ground but at the same times he is at rest with reference to other passengers on board. SELF ASSESSMENT QUESTIONS: Q 1. Define Kinematics. Q 2. When is a body said to be in state of rest? Q 3. How are rest and motion related to each other? 2.2 TYPES OF MOTION We observe around us that all objects in universe are in motion. However the nature of their motion is different, some objects move along circular path, other move in straight line while some objects move back and forth only. There are three types of motion. (i) Translatory motion (linear, circular and random) (ii) Rotatory motion (iii) Vibratory motion. 33  Unit 2: Kinematics (I) Translatory Motion Different objects are moving around in different ways. You can observe how various objects are moving? Which objects move along a circular path? Which objects move along a linear path? Fig 2.4 A train moving A train is moving along a straight track in Fig 2.4. you along a straight track can observe that every part of the train is moving along that straight path. This is called translatory motion. Translatory motion can be defined as: When all points of a moving body move uniformly along the same straight line, such motion is called translatory motion. Fig 2.5 Moving bus (a) Linear Motion: We observe many objects moving along straight line. The motion of a bus in a straight line on road is called linear motion Fig. 2.5. Thus the linear motion can be defined as: Motion of a body along a straight line is called linear motion. (b) Circular Motion: Fig 2.6 An artificial satellite An artificial satellite moving around the Earth along circular path is an example of circular motion Fig 2.6. Thus circular motion can be defined as: Motion of a body along a circular path is called circular motion. (c) Random Motion You must have observed the motion of flies, Fig 2.7 Random motion insects and birds? They suddenly change their 34 Unit 2: Kinematics direction. The path of their motion is always irregular. This type of motion is known as random motion. The random motion can be defined as : Irregular motion of an object is called random motion. The motion of butterfly, house fly, dust and smoke particles along zigzag paths are examples of Fig 2.8 (a) Spinning top random motion. The motion of the particles of a gas or a liquid known as the Brownian motion which is an example of random motion Fig2.7. (ii) Rotatory Motion Have you noticed the type of motion of fan and spinning top? Every point of the top moves in a circle around a fixed axis. Thus every particle of the top Fig 2.8 (b) A wheel possess circular motion Fig 2.8(a). But the top as whole moves around an axis which passes through top itself so the motion of top is rotatory Thus rotatory motion can be defined as: The motion of the body around a fixed axes which passes through body itself is called spin or rotatory motion. The motion of a wheel about the axle, the motion Fig 2.8 (c) Ferris wheel of a rider on the Ferris wheel are some examples of rotatory motion Fig 2.8 (a, b, c). (iii) Vibratory Motion Look at the motion of child in swing Fig 2.9(a). when swing is pulled away from its mean position and then released, the swing start moving back and forth about the mean position. This type of motion is called vibratory or oscillatory motion. Thus vibratory motion Fig 2.9 (a) Motion of child can be defined as: in swing 35  Unit 2: Kinematics Back and forth motion of a body about its mean position is called vibratory or oscillatory motion. There are many examples of vibratory or oscillatory motion in daily life. for example, motion of the clock’s pendulum Fig 2.9 (b). Distinguish between Translatory, Vibratory and Rotatory Translatory Rotatory Vibratory Motion Motion Motion A body moves The spinning of The body move along a straight a body about its back and forth line. axis. about mean Fig 2.9 (b) Clock’s pendulum position. Movement of an The motion of an The body moves object from one o b j e c t a b o u t up and down. place to another. fixed point. All particles of The motion of a An object repeat the rigid body rigid body about its motion itself. move with the a fixed axis. same velocity at Every particle of every instant of body move in a time. circular path SELF ASSESSMENT QUESTIONS: Q 4. Define Translatory Motion? Q 5. What is vibratory motion? Q 6. Differentiate between translatory motion, rotatory motion and vibratory motion. 2.3 DESCRIBING MOTION The motion of an object can be described by specifying its position, change in position. speed, velocity and acceleration. 36 Unit 2: Kinematics (i) Distance and Displacement 16km A person can use three different paths to move 6km from place A to an other place B. It can be used to illustrate meaning of distance and displacement Fig A B 2.10. 24km What if the person moves back from B to A along any of the three paths. The person covers the distance is Fig 2.10 either 16 km (purple path) or 24 km (red path). Distance and displacement While the person is back at A so, the net displacement becomes zero. Thus distance and displacement can be differentiated as follows: Distance Displacement Ø T h e t o t a l l e n g t h Ø The distance covered by moving measured in straight body without line in a particular mentioning direction line. of motion. Ø I t i s a n s c a l a r Ø It is a vector quantity. quantity. Ø The S.I unit is metre Ø The S.I unit is metre (m). (m). Ø The distance traveled Ø The displacement of by the person from A the person is 6 km to B is either 16 km from A to B due west ( purple path) or 24 of A. km (red path) 37  Unit 2: Kinematics (ii) Speed and Velocity Do You Know! The speed of an object determines how fast an Average speed of object is moving? It is rate of change of position of an different animals object. There are many ways to determine speed of an and objects : object. These methods depend on measurement of two Speed Animal /Object quantities. (kmh-1) u The distance traveled White-tailed deer 48 Ren deer 60-80 u The time taken to travel that distance cheetah 100-120 Thus the average speed of an object can be Walking man 6 calculated as: Grand prix car 360 Speed = distance traveled Passenger jet 900 Sound 1200 time taken Space shuttle 36000 S V= t The equation for average speed in symbols can be written as : S............... V= (eq 2.1) t Where, “V” is the speed of the object, “S” distance traveled by it and “t”time taken by it. Thus average speed can be defined as: Distance covered by an object in a unit time is called speed. The equation (2.1) gives only average speed of the body it can not be said that it was traveling with uniform speed or non uniform speed. For example, a racing car can be timed by using a stop watch over a Fig 2.11 fixed distance say, 500m Fig 2.11. Dividing distance by A racing car time gives the average speed, but it may speed up or slow down along the way. Speed is a scalar quantity and its S.I unit is ms-1. 38 Unit 2: Kinematics Uniform speed An object covers an equal distance in equal interval of time its speed is known as uniform speed. Velocity Velocity means speed of an object in a certain direction. Velocity is a vector quantity. thus velocity of an object can be defined as: Rate of change of displacement with respect to time is called velocity. Change in displacement Velocity = time taken Dd............... v= (2.2) t Here d is displacement of the moving object, t is time taken by object and v is velocity. SI unit of velocity -1 is ms. The velocity of an object is constant when it moves with constant speed in one direction. The velocity of object does not remain constant when it changes direction with out changing its speed, or it changes speed with no change in direction. Thus average velocity of an object is given by total displacement Velocity = total time taken Uniform velocity: A body is said to have uniform velocity if it cover equal distance in equal interval of time in a particular direction. 39  Unit 2: Kinematics Worked Example 1 A car travels 700m in 35 seconds what is the speed of car? Solution Step 1: Write the known quantities and point out quantities to be found. d=700m t=35s v=? Step 2: Write the formula and rearrange if necessary. d v= t Step 3: Put the value in formula and calculate 700 v= = 20ms - 1 35 -1 Thus the average speed of car is 20ms. Worked Example 2 -1 The speed of train is 108 kmh. How much distance will be covered in 2 hours? Solution Step 1: Write the known quantities and point out quantities to be found. 108 km 108 ´ 1000 m v= = = 30ms -1 h 3600 s t = 2h = 2 ´ 3600s = 7200s d=? Step 2: Write the formula and rearrange if necessary d v= t d = v´t Step 3: Put value in formula and calculate d = 30 ´ 7200 = 216000m Thus distance traveled by train is 216000m. 40 Unit 2: Kinematics Acceleration An object accelerates when its velocity changes. Since velocity is a vector quantity so it has both velocity magnitude and direction. Thus acceleration is produced when ever: Acceleration u Velocity of an object changes Fig 2.12 (a) Velocity of this car is u Direction of motion of the object changes, increasing u Speed and direction of motion of the object change. Thus acceleration can be defined as: Rate of change of velocity of an object with respect to time is called acceleration. change in velocity Acceleration = time taken Dv Q Dv = vf - vi a= t velocity v -v \ a = f i............... (eq 2.3) t Acceleration Acceleration is a vector quantity. Its SI unit is Fig 2.12 (b) metre per second per second (ms-2). Velocity of this car is When velocity of an object increases or decreases decreasing with passage of time, it causes acceleration. The increase in velocity gives rise to positive acceleration Fig 2.12(a). It means the acceleration is in the direction of velocity. Whereas acceleration due to decrease in velocity is negative and is called deceleration or retardation Fig 2.12(b).The direction of deceleration is opposite to that of change velocity. Uniform Acceleration A body has uniform acceleration, if the velocity of body changes by an equal amount in every equal time period. 41  Unit 2: Kinematics When the change i.e., increase or decrease in the velocity of an object is same for every second then its acceleration is uniform. when velocity of an object is increasing by 10 ms-1 every second ,the acceleration is -2. 10ms.When the velocity of the object is decreasing by 10ms every second, the deceleration is 10 ms-2. Thus, -1 uniform acceleration can be defined as: A constant rate of change of velocity is called uniform acceleration. The uniform acceleration can be calculated by using following formula : D V vf - vi a= = Dt t2 - t1 -1 Where vf= initial velocity ( in ms ); vi= final velocity ( in ms-1); t1= time at which an object is at initial velocity u (in s); t2 = time at which an object is at final velocity v ( in s); Dv= change in velocity (in ms-1) Dt= time interval between t1 and t2(in s) Worked Example 3 A bus start from rest and travels along a straight path its -1 velocity become 15ms in 5 seconds. Calculate acceleration of the bus? Solution: Step 1. Write the known quantities and point out quantities to found. vi = 0 ms-1 -1 vf = 15 ms t = 5 second a=? 42 Unit 2: Kinematics Step 2: Write the formula and rearrange if necessary v -v a= f i t Step 3: Put the value in formula and calculate. a = 15 - 0 = 15 -2 = 3ms 5 5 -2 Acceleration of bus is 3ms. Worked Example 4 N A motorcyclist moving along a straight path applies breakes to slow down from 10ms-1 to 3ms-1 in 5 seconds. Calculate its acceleration. o Solution Step 1. Write the known quantities and point out W E quantities to be found. vi = 10ms-1 vf = 3ms -1 S t = 5 second a=? Step 2. Write the formula and rearrange if necessary. v -v a= f i t Step 3: Put the value in formula and calculate. -7 = -1.4 ms-2 a = 3 - 10 = 5 5 -2 Deceleration of motorcycle is -1.4 ms. The negative sign shows the retardation in opposite direction of velocity. Self Assessment Questions: Q 7. Define Speed. Q 8. What is velocity? Q 9. Define acceleration. 43  Unit 2: Kinematics 2.4 SCALARS AND VECTORS All physical quantities are divided into two types on the bases of information required to describe them completely. u Scalars u Vectors Scalars There are certain physical quantities that can be described through their magnitude and a suitable unit. This information is enough to describe them, For example the mass of a watermelon is 3kg, where 3 is the magnitude and kg is a suitable unit such quantities are called scalar quantities. Thus we can define scalar quantities as: The physical quantities that have magnitude and a suitable unit are called scalar quantities. The other examples of scalar quantities are speed, temperature, mass, density etc. Vectors Some physical quantities need direction along with their magnitude and unit for their complete description. For example, a bus traveling with a velocity of 50ms-1 in the direction of North. The vector quantities can be defined as: The physical quantities which are completely specified by magnitude with suitable unit and particular direction are called as “Vector” quantities. Force ,acceleration , momentum, torque and magnetic field are the examples of vector quantities 44 Unit 2: Kinematics SELF ASSESSMENT QUESTIONS: Q 10. Define Vector. Q 11. Differentiate between vector and scalar quantities. Representation of vector: N -1 Vector diagram is an easy way to represent a s 50m vector quantity. The directed line segment can be used 30o to represent a vector. The length of the line segment W E gives the magnitude of the vector and arrow head gives its direction. For example, Fig 2.14 represents velocity -1 o of a car travailing at 50ms in the direction of 30 North S of East. Fig. 2.14 2.5 GRAPHICAL ANALYSIS OF MOTION 25 Graph gives the complete information about the 20 motion of the object based on the measured physical quantities such as distance, speed, time etc. distance/m 15 10 Distance - Time Graphs 5 A bus travels along a straight road from one bus 0 3 5 1 2 4 stop to another bus stop. The distance of the bus from time/s first bus stop is measured every second. The possible Fig. 2.15 (a) motion of the bus is shown by three examples. Uniform speed The vertical axis gives rise of the graph while 25 horizontal axis shows its run. The rise divided by run is 20 called gradient. distance/m 15 The gradient on the distance time graph is numerically 10 equal to the speed. When bus travels with uniform speed, the 5 distance time graph is a straight line. Fig 2.15(a) shows 0 1 2 5 3 4 graph of the motion of bus with steady speed, the line time/s rises 5 m on the distance scale for every 1 seconds on Fig.2.15 (b) the time scale. Non-uniform speed 45  Unit 2: Kinematics 25 20 Gradient= =5 20 4 distance/Km 15 Thus speed = 5 ms-1. 10 when bus travels with non-uniform speed, the 5 distance time graph is a curve. Fig 2.15(b) shows motion 0 1 2 3 4 5 of the bus, for this case the speed rises every