Physics Unit 2,3,4 PDF

12 Unit 2 Physical Quantities In grade 8 General Science, you learned about scientific measurement. Differ- ent types of scales are used in measuremen...

12 Unit 2 Physical Quantities In grade 8 General Science, you learned about scientific measurement. Differ- ent types of scales are used in measurement. Activity 2.1 Discuss different 2.1 Scales, Standards, Units (prefixes) examples of nom- inal scales in your Scales community. Ay the end of this section, you should be able to: list the four type of scales; distinguish between the four types of scales. In general there are four data measuring scales. These are nominal scales, ordinal scales, interval scales and ratio scales. Exercise 2.1 List different ex- Nominal scales: are used for labeling variables without any number value. amples of ordinal For nominal scales there is no inherent quantitative difference among the scales. categories. Examples are: gender (male, female), hair color (black, brown). Ordinal scales: are rank-order observations. For this type of scale, there is Exercise 2.2 an underlying quantitative measurement on which the observations differ. List different ex- Example: Your class rank in the previous grades. amples of interval scales. Interval scales: have a constant interval but lack a true zero point. For this type of scale, one can add and subtract values on an interval scale, but one Key Concept: cannot multiply or divide units. Temperature in Celsius or Fahrenheit scale is an example of interval scale. T In physics scale is a set of numbers, Ratio scales: have the property of equal intervals but also have a true zero amounts, etc., used point. As a result, one can multiply and divide as well as add and subtract to measure or com- using ratio scales. Units of time (second, minute, hour), length (centimeter, pare the level of meter, kilometer), weight (milligram, gram, kilogram), volume (centimeter something. cube) and temperature in Kelvin Scale are ratio scales. T Ratio scale is an advanced scale Note that even though a ratio scale has a true zero point, the nature of the in which addition, variable is such that a value of zero will never be observed. For example human subtraction, multipli- cation and division is height is measured on a ratio scale but every human has a height greater than possible. zero. 2.1 Scales, Standards, Units (prefixes) 13 Activity 2.2 1. What is your weight in kilograms? 2. Are scales involving division of two ratio scales also themselves ratio scales? Discuss in small groups. 3. In group observe measurement activities in the surrounding (home, local market and work places) for two days and prepare a report on the what, the where, and the how of the measurements observed. 4. Based on your observation discuss the traditional and commonly used scales and units of measurement for length, mass, time, volume and tem- perature. People in different community measure physical quantities such as length, time, volume, and mass using traditional measuring units. However, each unit has different values at different time, position and conditions. Figure 2.1 Traditional measuring units. 14 Unit 2 Physical Quantities Standards Brainstorming Ay the end of this section, you should be able to: Questions appreciate the measures used in their local environment and comment What is a standard on the practice; in measurement? In list standard units of measures and their relationship with units in their your local area peo- surroundings. ple measure volume, mass and area using different measuring In the previous section you have learned different types of scales. However, in devices. Do these physics we focus more on ratio scales with defined standard units. The laws of measurements have physics are expressed in terms of basic quantities that require a clear definition. In standards? Discuss physics, the seven basic quantities are length (l), mass (m), time (t), temperature in groups. (T), current (I), amount of substance (n), and luminous intensity (I V ). All other quantities in physics can be derived from these seven basic or fundamental physical quantities. Table 2.1 Measurement of mass at different places. No. Name of student Place Measured value 1 Student A Location A 1.6 unit 2 Student B Location B 2.1 unit 3 Student C Location C 2.5 unit 4 Student D Location D 3.0 unit 5 Student E Location E 1.1 unit 6 Student F Location F 3.5 unit Activity 2.3 If your teacher orders you to report the results of a measurement to someone who T Six grade 9 stu- wishes to reproduce this measurement, a standard must be defined. Whatever is dents in different chosen as a standard: parts of Ethiopia are given the same it must be readily accessible and possesses some property that can be object and mea- measured reliably. sured its mass in the same unit as measurements taken by different people in different places must yield the shown in Table 2.1. same result. Discuss whether the measurement has a Lack of standard in measurement has many negative consequences. In Ethiopia, standard or not re- for instance, people use their palm to measure things like cotton and footsteps to gardless of personal measure the length of a plot of land. The one with a bigger palm collects much errors. cotton than the one with a smaller palm. Thus, using a palm or footsteps as a 2.1 Scales, Standards, Units (prefixes) 15 measuring device has no standard. It creates inaccuracy on measured value and bias among people. In 2019, an International Committee revised a set of standards for length, mass, Exercise 2.3 time and other basic quantities. The system established is an adaptation of the T What are the metric system and is called the SI system of units (see Figure 2.2 or CLICK HERE SI units of length, mass, and time? for further reading ). Length: Meter is the standard or international system (SI) unit for length. There are also other none SI units of length. These are centimeter (cm), millimeter (mm), and kilometer (km). Today, the meter (m) is defined as a distance traveled 1 by light in vacuum during a time of 299792458 s. Time: It is defined as the interval between two events. It is a fundamental quantity. The unit of time in SI system is second (s). The none SI units of time are minute (min), hour (hr), day, month and year. The second (s) is defined as 9 192 631 770 times the period of vibration of radiation from the cesium-133 atom. Mass: The kilogram (kg) is the standard or international system (SI) unit of mass. Figure 2.2 The SI system after the 2019 redefinition The none SI units of of mass are gram (g), milligram (mg), and tonne. The kilogram (kg) is defined by taking the fixed numerical value of the Plank constant h = m2 6.62607015 × 10−34 when expressed in the units of J s (which is equal to kg s ), where the meter and second are defined in terms of the speed of light in vacuum h∆ f (c) and the frequency of the Caesium 133 atom (∆ f ). [1kg = 1.4755214 × 1040 c2 ] Activity 2.4 T Discuss the need for standards of measurement. T Identify problems of non-standard measurement practices in your lo- cality and the country at large. Key Concept: T Standard units are conventional units which are used to measure phys- ical quantity scientifically. 1 T Meter: a distance travelled by light in vacuum during a time of 299792458 s. h∆ f T Kilogram: 1 kilogram (1kg) is 1.4755214 × 1040 c2. T Second: 9 192 631 770 times the period of vibration of radiation from the cesium-133 atom. 16 Unit 2 Physical Quantities Scientific Notation Scientific notation is a way of writing numbers that are too large or too small to be conveniently written as a decimal. This can be written more easily in scientific notation, in the general form: d × 10n Exercise 2.4 where d is a decimal number between 0 and 10 that is rounded off to a few T Write decimal places; n is known as the exponent and is an integer. If n > 0 it represents 0.000001256 in how many times the decimal place in d should be moved to the right. If n < 0, scientific notation then it represents how many times the decimal place in d should be moved to the to 3 decimal places. left. For example, 3.24 × 103 represents 3240 (the decimal moved three places to T How many signif- the right) and 3.24 × 10−3 presents 0.00324 (the decimal moved three places to icant figures are in the left). 7800? Significant Figures In a number, each non-zero digit is a significant figure. Zeroes are only counted if they are between two non-zero digits or are at the end of the decimal part. For example, the number 2000 has 1 significant figure (the 2), but 2000.0 has 5 significant figures. You estimate a number like this by removing significant figures from the number (starting from the right) until you have the desired number of significant figures, rounding as you go. For example, 6.827 has 4 significant figures, but if you wish to write it to 3 significant figures it would mean removing the 7 and rounding up, so it would be 6.83. Exercise 2.5 Write the physical Prefixes quantities in Table 2.2 using appropri- In the previous section you have learned different basic units. When a numerical ate prefixes. unit is either very small or very large, the units used to define its size may be T The radius of the modified by using a prefix. A prefix is an important aspect of dealing with units. earth is 6,371,000 m Prefixes are words or letters written in front that change the meaning. Table 2.2 T The diameter lists a large set of these prefixes. The kilogram (kg) is a simple example. 1 kg is of our hair is 0.000 1000 g, or 1 × 103 g. We can replace the 103 with the prefix k (kilo). 0075 m 2.2 Measurement and Safety 17 Table 2.2 Unit Prefixes. Prefix Symbol Multiplier Exponent tera T 1 000 000 000 000 1012 giga G 1 000 000 000 109 mega M 1 000 000 106 kilo k 1 000 103 hecto h 100 102 deka da 10 101 deci d 0.1 10−1 centi c 0.01 10−2 milli m 0.001 10−3 micro µ 0.000 001 10−6 nano n 0.000 000 001 10−9 pico p 0.000 000 000 001 10−12 Key Concept: T Unit prefix is a letter or a syllable which is written directly before a unit name with no space. T Scientific notation: a system in which numbers are expressed as prod- ucts consisting of a number between 1 and 10 multiplied by an appropriate power of 10. T In a number, each non zero digit is a significant figure. 2.2 Measurement and Safety Ay the end of this section, you should be able to: Brainstorming list different instruments used to measure physical quantities such as Questions length, area, volume, mass, and time in their local area; T What is meant by measurement? list length, mass and time measuring devices; T What measuring measure length, mass and time using different units. devices are used to measure volume, mass and length in your local area? 18 Unit 2 Physical Quantities Activity 2.5 Measurement T Observe your local environment Measurement is the process of comparing an unknown quantity with another and list different quantity of its kind (called the unit of measurement). The measurement process instruments used has three key elements: to measure physical quantities. The physical quantity to be measured. T Discuss different measurement ac- The necessary measuring tools. tivities and related Units of measurements used (standard units). issues in life. Figure 2.3 Examples of measuring tools of some physical quantities. 2.2 Measurement and Safety 19 Twenty-first century civilization is unthinkable without an appropriate measure- ment tools on which everyday life depends. Modern society simply could not exist without measurement. Figure 2.3 shows some measuring devices applicable today. Measuring Length When you are measuring the length of objects, you are comparing it with the standard length. The SI unit of length is meter (m) as we discussed before. There are also non SI units of length. These are millimeter (mm), centimeter (cm) and kilometer (km). Key Concept: T Measurement of any physical quantity involves comparison with a cer- tain basic, arbitrarily chosen, internationally accepted reference standard called unit. Figure 2.4 Standard length measuring instruments. 20 Unit 2 Physical Quantities Activity 2.6 T Make groups and measure the length and width of your exercise book in meter, centimeter and millimeter. T Which measuring instrument of length can you use for measuring the diameter of a small sphere? T A farmer wants to know the length of his plots of land in meter but he has only a long rope, a 50 cm ruler and a 6 m long stick. How can he easily measure the length of his plot? Discuss in groups. Length is one of the fundamental (basic) physical quantities which describes the distance between two points. Activity 2.7 T Measure the length and width of your blackboard in meter unit. T Calculate the area of the blackboard using the above measured values in meter square unit. T Compare your results with that of your friends’. Exercise 2.6 Definition: Every physical quantity can be represented by its numerical T What mecha- nisms do people in value and unit. your locality use to measure the mass of Measurement is the comparison of an unknown quantity with the known an object? fixed unit quantity. It consists of two parts: the unit and the number indicating T Which scientific how many units are in the quantity being measured. mass measuring instrument is used For example: The length of a table is 3 meters. in your locality? In this example, 3 is the magnitude, and meter is the standard (unit) of that quantity. 2.2 Measurement and Safety 21 Key Concept: T Length is the fundamental physical quantity that describes the distance between two points. T The SI unit of length is meter (m). Activity 2.8 Measuring Mass T Visit different Measuring mass is a day to day activity in human life. People in various parts of shops in your living the world measure the mass of an object in different ways. area and observe the procedure of measuring goods Definition: Mass is a basic physical quantity. It is defined as the amount carefully. Write the of matter contained in a body. procedures and exactness of the The SI unit of mass is a kilogram (kg). There are also non SI units used measurement. to measure the mass of an object. In scientific way mass is measured by an instrument called beam balance. Activity 2.9 T Collect different simple objects such as a) a duster, b) an exercise book, c) one stick of chalk. T Measure the mass of these objects and record the measured values in a table. T Compare your recorded value with that of other groups and discuss. Key Concept: T Mass is a basic physical quantity. It is defined as the amount of matter contained in a body. TThe S.I unit of mass is the kilogram (kg). Measuring Time Figure 2.5 Different scientific mass measuring instruments. How long does it take for the sun to rise and set in your location? Do the people in your locality use the sun set and sun rise as a time measuring devise? Some 22 Unit 2 Physical Quantities people in the rural parts of Ethiopia traditionally use the position of the sun or the position of shadows of their house or trees to estimate the time. The use of sun rise and sun set as a time measuring device is called sundial. However, this way of measuring time has no standard and is not accurate. Time is the basic physical quantity. It describes the duration between the beginning and end of an event. The SI unit of time is second (s). The commonly used non SI units of time are: minute, hour, day, week, month and year. Activity 2.10 T Discuss in groups and list the names of scientific time measuring devices. T Record the activities you do from sun rise to sun set. Compare your recorded activities with that of your friend. Some of you are effectively using your time to accomplish different activities. Discuss the wise use of time in relation to its contribution for the development of our country. Key Concept: T Time is a basic physical quantity. It describes the duration between the beginning and end of an event. Figure 2.6 Different scientific time TThe S.I unit of time is second (s). measuring devices. Laboratory Safety rules A systematic and careful laboratory work is an essential part of any science program since laboratory work is the key to progress in science. The equipment and apparatus you use involve various safety hazards, just as they do for working physicists. Students should follow the general laboratory safety guidelines so that working in the physics laboratory can be a safe and enjoyable process of discovery. These safety rules are: Always wear a lab safety goggles. Avoid wearing baggy clothing, bulky jewelry, dangling bracelets, open-toed shoes or sandals. NEVER work alone in the laboratory. 2.3 Classification of Physical Quantities 23 Only books and notebooks needed for the experiment should be in the lab. Read about the experiment before entering the lab. Do not eat, drink, apply cosmetics, or chew gum in the laboratory. NEVER taste chemicals. Do not touch. Report all accidents to the teacher immediately, no matter how mi- nor. Exercise caution when working with electrical equipment. Perform only those experiments authorized by the teacher. Wash hands thoroughly after participating in any laboratory activity. 2.3 Classification of Physical Quantities At the end of this section, you should be able to: Brainstorming classify physical quantities as fundamental and derived physical quanti- Questions ties; What is the differ- ence between funda- describe derived physical quantities in terms of fundamental quantities; mental and derived differentiate between fundamental and derived units; physical quanti- ties? Some physical classify physical quantities as scalar and vector quantities. quantities have only magnitude. How- ever, other physical Physical Quantities quantities have both magnitude Definition: A physical quantity is anything that you can measure. For and direction. Can example, length, temperature, distance and time are physical quantities. you mention some examples of these Quantities that can be measured directly or indirectly are known as physical physical quantities? quantities. The measured values of physical quantities are described in terms of number and unit. Each physical quantity and its unit have a symbol. In Activity 2.7, you can observe that some physical quantities are directly mea- sured while other physical quantities are measured by combining two or more measurable quantities. For example you measured the width and length of your 24 Unit 2 Physical Quantities blackboard directly. However, the area is measured by multiplying the length and width of the blackboard - A = l × w. Physical quantities can be classified into two. Activity 2.11 Fundamental or basic physical quantities T In activity 2.7 you measured the Derived physical quantities length, width and area of the black- Fundamental or basic physical quantities: are physical quantities which can board. Discuss the be measured directly. They cannot be described in terms of other physical quan- symbols of the phys- tities. The units used to measure fundamental quantities are called fundamental ical quantities and their units. Is there units. i.e., the unit of fundamental quantity is called fundamental unit. It does any difference be- not depend on any other unit. There are seven fundamental physical quantities tween length, width as shown in Table 2.3. and area? Table 2.3 The fundamental or basic physical quantities with their units and symbol of units. Activity 2.12 Basic physical quantities Symbol Basic unit Symbol T Discuss in groups Length l meter m and classify physical Mass m kilogram kg quantities (length, Time t Second s mass, speed, vol- Temperature T Kelvin K ume, force and Current I Ampere A pressure) as funda- Amount of substance n Mole mol mental or derived. Luminous intensity Iv Candela cd Exercise 2.7 T Describe volume, density, and speed as combination of fundamental physical quantities. T Determine the units of volume, density and speed using basic units. T Discuss how to use mobile phone (Android) to measure the time, heartbeat and body temperature. Derived physical quantities: Physical quantities which depend on one or more fundamental quantities for their measurements are called derived physical quantities. The units of derived quantities which depend on fundamental units 2.3 Classification of Physical Quantities 25 for their measurement are called derived units. Area, volume, density, and speed are some examples of derived physical quantities. Table 2.4 shows some derived quantities with their units and symbol of units.. Table 2.4 Some derived physical quantities and their units. Physical quantity Symbol Formula Unit Symbol of the unit Distance meter m Speed v Time second s Mass kilogram kg Density ρ Volume meter cube m3 Velocity meter m Acceleration a Time second square s2 kg.m Force F Mass × Acceleration newton(N) s2 kgm2 Work W Force × Displacement joule (J) s2 Force kg Pressure P Area pascal (Pa) m.s2 Scalar and Vector Quantities Physical quantities can also be classified as scalar and vector quantities. Some Activity 2.13 physical quantities are described completely by a number and a unit. A number Discuss in groups with a unit is called a magnitude. However, other quantities have a direction and classify the attached to the magnitude. They cannot be described by a number and unit only. following physical Thus, physical quantities are grouped into two. These are: quantities as scalar or vector quantity: Scalar quantities mass, time, area, speed, velocity, ac- Vector quantities celeration, force, energy, work, pres- A scalar quantity is a physical quantity which has only magnitude but no sure, momentum, direction. electric current, current density, Examples are: distance, mass, time, temperature, energy etc. displacement, and temperature. A vector quantity is a physical quantity which has both magnitude and di- rection. When expressing that the car moves 50 km/h to east, this gives full information about the velocity of the car that includes magnitude and direction 26 Unit 2 Physical Quantities (50 km/h is the magnitude, and east is the direction). Because of this, velocity is a vector quantity. Examples are: displacement, acceleration, force, etc. A vector can be represented either by a single letter in bold face or by a single letter with arrow head on it. For example: displacement can be represented as ⃗ S or S. Key Concept: TPhysical quantity: anything that you can measure and describe by a number and unit.. T Fundamental physical quantities: physical quantities which can be measured directly. T Derived physical quantities: Physical quantities which depend on one or more fundamental quantities for their measurements. T Scalar quantities: Physical quantities that are described only by their magnitude. T Vector quantities: Physical quantities that are described by their mag- nitude and direction. 2.4 Unit conversion Brainstorming At the end of this section, you should be able to: Question convert units of length from one system of units to another. T How many me- convert units of mass from one system of units to another. ters, centimeters and millimeters convert units of time from one system of units to another. are there in one kilometer? In the previous section you have learned different physical quantities. These T How many grams physical quantities have SI and non SI units. It is possible to convert units from SI are there in one kilo- unit to non SI unit and vice versa. Conversion of units is the conversion between gram? How many different units of measurement for the same physical quantity, typically through seconds are there in one day? multiplicative conversion factors. The relation between meter and other non SI units is given in Table 2.5. 2.4 Unit conversion 27 Example 2.1 The distance between two houses is 200 meter. What is the distance in: a) centime- ter b) kilometer c) millimeter Given: l = 200 m Solution: a) 1m = 100 cm 200 m = ? (200 m × 100 cm) l in cm = = 20000 cm (1 m) b) 1m = 0.001 km 200 m = ? (200 m × 0.001 km) l in km = = 0.2 km (1 m) c) 1m = 1000 mm 200 m = ? 200 m × 1000 mm l in m = 1m = 200000 mm = 2 × 105 mm Table 2.5 Conversion between units of length. 1 kilometer (km) 1000 meter (m) 1 meter (m) 100 centimeter (cm) 1 meter (m) 1000 millimeter (mm) 1 centimeter (cm) 10 millimeter (mm) 1 meter (m) 0.001 kilometer (km) 1 centimeter (cm) 0.01 meter (m) 1 millimeter (mm) 0.001 meter (m) Exercise 2.8 1. Which one of the following is a suitable unit to measure the distance between the Earth and the Moon? (A) mm (B) km (C) cm (D) m (E) all 28 Unit 2 Physical Quantities 2. Which one of the following is a suitable unit to measure the diameter of electric wire? (A) mm (B) km (C) cm (D) m (E) all 3. A hydrogen atom has a diameter of about 10 nm. (a) Express this diameter in meters. (b) Express this diameter in millimeters. (c) Express this diameter in micrometers. The relationship between the SI units and non SI units of mass are shown in Table 2.6. Table 2.6 Relationship between units of mass. 1 kilogram (kg) 1000 gram (g) 1 gram (g) 0.001 kilogram (kg) 1 milligram (mg) 0.001 gram (g) 100 kilogram (kg) 1 quintal 1000 kilogram (kg) 1 tonne Example 2.2 In one of the pans of a beam balance the masses 1.5 kg, 500 g, 250 g, 25 g and 0.8 g are placed to measure the mass of unknown object. What is the mass of an object in gram and kilogram on the other side of the pan if they are in balance? Given: m = 1.5 kg , 500 g , 250 g , 25 g , 0.8 g , Required: Total mass in g and Kg Solution: Total mass =sum of masses in the pan = 1.5 kg + 500g + 250 g + 25 g + 0.8 g 2.4 Unit conversion 29 = 1500 g + 500 g + 250 g + 25 g + 0.8 g = 2275.8 g, 1000 g = 1 kg, 2275.8 g = ? 2275.8 g × 1 kg mass in kg = = 2.2758 kg 1000 g Table 2.7 The relation between different units of time. 1 minute (min) 60 second (s) 1 hour (hr) 60 minute (min) 1 day 24 hours (hrs) 1 week 7 days 1 month 30 days 1 year 365.25 days Example 2.3 Express the following times in seconds. a) 2 hours b) 0.5 hour c) 3/5 hour Solution: a) 1hr = 3600 s , 2 hr × 3600 s 2 hr =? =⇒ t = = 7200 s 1 hr b) 1hr = 3600 s , 0.5 hr × 3600 s 0.5 hr =? =⇒ t = = 1800 s 1 hr c) 1hr = 3600 s , 3 3 5 hr × 3600 s hr =? =⇒ t = = 2160 s 5 1 hr Exercise 2.9 1. How many hours, minutes and seconds are there in a day? 2. List some traditional ways of measuring time in your community. 30 Unit 2 Physical Quantities 3. Express the following time in minutes and seconds. (a) 0.25 hr. (b) 3.2 hrs. (c) 6.7 hrs. Unit Summary Scale is a set of numbers, amounts etc., used to measure or compare the level of something. There are four types of measurement scales: nominal, ordinal, inter- val and ratio. In Physics, most of the scales are ratio scales. Measurement is the comparison of an unknown quantity with a known one (standard unit). Standard units are conventional units which are used to measure physical quantities scientifically. Traditional measuring units are not exact and have no a standard. Prefixes are used to simplify the description of physical quantities that are very big or very small. Quantities that can be measured directly or indirectly are known as physical quantities. Physical quantities are characteristics or properties of an object that can be measured or calculated from other measurements. Physical quantities are classified as fundamental /or basic physical quantities, and derived physical quantities. Length, time, mass, temperature, current, amount of substance and luminous intensity are fundamental quantities in science. All other physical quantities are derived physical quantities. Meter, second, kilogram, Kelvin, Ampere, mole and candela are fundamental (basic) units. Physical quantities can be categorized as vectors or scalars. 2.4 Unit conversion 31 Meter, kilogram and Second are the SI unit of length, mass, and time respectively. SI units can be converted to non SI units and vise versa. End of Unit Questions and Problems Part I. Multiple choice 1. Which one of the following scale allows addition, subtraction, multi- plication and division? (a) Nominal scale (b) ratio scale (c) ordinal scale (d) interval scale 2. Which one of the following is NOT a fundamental physical quantity? (a) Temperature (b) density (c) time (d) mass 3. The SI standard of time is based on: (a) The daily rotation of the Earth (b) The yearly revolution of the Earth about the sun (c) 9 192 631 770 times the period of vibration of radiation from the cesium-133 atom. (d) A precision pendulum clock 4. Which one of the following is a derived SI unit? (a) Second (b) Joule (c) kilogram (d) Kelvin 5. A nanosecond is (a) 109 s (b) 10−9 s (c) 10−6 s (d) 10−12 s 6. Which one of the following method provides a more reliable mea- surement of time in daily life activities? (a) Looking the rotation of stars in the sky (b) Using a digital watch (c) Looking the position of shadows of trees (d) Looking the position of the sun on the sky 7. Which one of the following pair of physical quantities has the same unit? 32 Unit 2 Physical Quantities (a) displacement and distance (b) mass and force (c) speed and acceleration (d) volume and area 8. How many minutes is 3 hour + 10 minute + 120 s? (a) 182 min (b) 202 min (c) 212 min (d) 192 min 9. If the masses of bodies A, B, and C are 2 ton, 100 kg and 1 kg respec- tively. Then the total mass of the bodies is (a) 221 kg (b) 2101 kg (c) 2011 kg (d) 2001 kg 10. Why are fundamental physical quantities different from derived physical quantities? (a) Fundamental physical quantities are derived from derived physical quantities. (b) Derived physical quantities are derived from fundamental physical quantities. (c) Derived and fundamental physical quantities have no relation. (d) All are answers 11. Which of the following would describe a length that is 2.0 × 10−3 of a meter? (a) 2.0 km (b) 2.0 cm (c) 2.0 mm (d) 2.0 µm 12. Which quantity is a vector? (a) Energy (b) force (c) speed (d) time 13. Which one of the following lists is a set of scalar quantities? (a) length, force, time (b) length, mass, time (c) length, force, acceleration (d) length, force, mass Part II: Write true if the statement is correct and false if the statement is wrong. 1. Second is a device used to measure time. 2. Candela is a derived physical quantity. 2.4 Unit conversion 33 3. The unit of force can be derived from the units of mass, length and time. 4. One kilometer is 100 meter. 5. For a very large or very small numbers prefixes are used with SI units. 6. Scalar quantity can be described by its magnitude and direction. Part III: Short answer questions 1. What is the difference between interval scale and ratio scale? 2. How many seconds are there in 12 hours? 3. What is measurement? 4. What is the difference between traditional measuring units and scientific measuring units? 5. Define the following terms: a) Meter b) second c) kilogram d) length e) time f) mass g) Physi- cal quantity h) derived physical quantity i) fundamental physical quantity. j) scalar physical quantity k) vector physical quantity 6. Which SI units would you use for the following measurements? (a) the length of a swimming pool (b) the mass of the water in the pool (c) the time it takes a swimmer to swim a lap 7. Which instrument is used to measure the thickness of a sheet metal? 8. Write some safety rules. 9. Give three examples of scalar and vector quantities. Part IV: Workout problems 1. In one of the pans of the beam balance the masses 3 kg, 900 g, 90 g and 5 g are placed. What amount of mass should be placed on the other side of the beam balance to make it balanced? 34 Unit 2 Physical Quantities 2. For each of the following symbols, write out the unit in full and write what power of 10 it represents: (a) micro g (b) mg 3. The doctor wants to know the age of his patient and asks him how 1 old he is. The patient replies that he is 25 2 years old. What is the age of the patient in month? 4. The student wants to measure the length of the classroom using a tape meter. The tape meter reads 8m and 40 cm. What is the length of the classroom in cm? 5. How many minutes are there in 3 days? 6. If the area of a single ceramic is 0.25 m 2 , how many ceramics are used to cover a floor of a classroom whose area is 40m 2 ? 7. The distance between Sun and the Earth is about 1.5 × 1011 m. Ex- press this distance using prefix. 8. The volume of the Earth is on the order of 1021 m 3. (a) What is this in cubic kilometers (km 3 )? (c) What is it in cubic centimeters (cm 3 )? 9. For each of the following, write the measurement using the correct symbol for the prefix and the base unit: (a) 101 nanoseconds (b) 10 milligrams (c) 72 gigameters. Unit 3 Motion in a Straight Line Introduction In this unit, you will be introduced to the basic concepts of motion. We encounter Brainstorming Question motion in our day-to-day activities and have enough experience about it. You might have learnt in lower grades that everything in the universe moves. It is T What do you because of this that motion is one of the key topics in physics. We use the basic think is motion? Give some examples concepts of distance, displacement, speed, velocity and acceleration to express of motion that you motion. There are different types of motions. Motion in a straight line is one of encounter in your the simplest forms of motion in a specific direction. The motions of a car on a daily life. road, the motion of a train along a straight railway track or an object falling freely are examples of one-dimensional motion. At the end of this unit, you should be able to: describe motion in terms of frame of reference, displacement, speed, ve- locity, and acceleration; draw diagrams to locate objects with respect to a reference; solve problems involving distance, displacement, speed, velocity and acceleration; make practical measurements of distance, displacement, average speed, average velocity and acceleration. 35 36 Unit 3 Motion in a Straight Line 3.1 Position, Distance and Displacement At the end of this section, you should be able to: define motion, position, and displacement; describe motion in terms of frame of reference; differentiate between position, distance and displacement; draw diagrams to locate objects with respect to a reference frame. The most convenient example to explain about position, distance and dis- placement is your daily travel from your home to your school. When you go to school, your journey begins from your home. Your home is your original position. After some time, you will reach your school. Your school is your final position. In this process, you are continuously changing your position. While traveling from home to school, you are increasing the gap between your present position and your home. This continuous change of position is known as motion. Note that your change of position is observed by considering the distance from your school to home. Your home is taken as a reference frame. Motion is a continuous change in position of an object relative to the position of a fixed object called reference frame. Key Concept: T A frame of reference is a set of coordinates that can be used to deter- mine positions of objects. T Motion is the change in the position of the object with respect to a fixed point as the time passes. A body is said to be at rest in a frame of reference when its position in that reference frame does not change with time. If the position of a body changes with time in a frame of reference, the body is said to be in motion in that frame of reference. The concepts of rest and motion are completely relative; a body at rest in one reference frame may be in motion with respect to another reference frame. For example, if you are 2 m from the doorway inside your classroom, then your reference point is the doorway. Your classroom can be used as a reference frame. In the classroom, the walls are not moving, and can be used as a fixed frame of reference. We commonly use the origin as a fixed reference point to describe motion along a straight line. 3.1 Position, Distance and Displacement 37 Exercise 3.1 T Assume you are sitting on a horse and the horse is moving at a certain speed. Are you at rest or in motion? Discuss it by taking two frames of reference: the horse itself and some fixed point on the ground. Key Concept: Position T Position is a To describe the motion of a particle, we need to be able to describe the position measurement of a location, with of the particle and how that position changes as the particle moves. Motion is respect to some the change in the position of the object with respect to a fixed point as the time reference point passes. For one-dimensional motion, we often choose the x axis as the line along (usually an origin). which the motion takes place. Positions can therefore be negative or positive with respect to the origin of the x-axis. Figure 3.1 shows the motion of a rider in a straight line. Its position changes as it moves. Have you ever used Google Maps to locate your geographical position while you are moving from some place to another? Google Maps is a Web-based service that provides detailed information about geographical regions and sites around the world. In addition to conventional road maps, Google Maps offers aerial and satellite views of many places. Google Maps provides you with the longitude (east-west position) and latitude (north-south position) coordinates of a location or position of a place. Figure 3.1 A rider in motion changes its position as it moves. 38 Unit 3 Motion in a Straight Line You can see how far you have travelled and how you travelled from place to place, such as walking, biking, driving or on public transport. The following steps guide you to get started using Google Maps: Step 1: At first you need to open the Google Maps software application on your Android phone, tablet or computer. For more information, click here to see Google Maps https://www.google.com/maps/ Step 2: Search for a place or tap it on the map. Step 3: In the bottom right, tap directions. Step 4: To add destination you have to go to the top right and tap more and then add a stop. Exercise 3.2 T What is the dis- Distance (S) tance around a standard football Distance travelled is a measure of the actual distance covered during the motion of field? a body. In other words, distance is the total path length traveled by the body. The T Is distance a pos- distance travelled does not distinguish between motion in a positive or negative itive or negative direction. This means that it is a scalar physical quantity. The SI unit of distance is quantity? meter (m), though it can also be measured in other non-SI units such as kilometer (km), miles (mi), centimeter (cm), etc. The symbol for distance is S. Pictorial representation of the distance covered by a runner is shown in Figure 3.2. Figure 3.2 The distance covered by a runner. 3.1 Position, Distance and Displacement 39 Displacement When an object moves, it changes its position. This change of position in a certain direction is known as displacement. A displacement is described by its magnitude and direction. Hence, it is a vector quantity. Displacement is independent of the path length taken. For example, you travel from your home to school. After school, you travel o your home. Therefore, the change in your position when you return back to your home is zero. In this case, we say that your displacement is zero. The SI unit of displacement is the same as the SI unit of distance that is meter (m). Figure 3.3 shows the difference between distance and displacement of the motion covered from point A to point B. Figure 3.1 shows a student on a bicycle at position S⃗i at time t i. At a later time, t f , the student is at position S⃗f. The change in the student’s position, S⃗f − S⃗i , is called a displacement. We use the Greek letter ∆ (uppercase delta) to indicate the change in a quantity; thus, the change in ⃗ S can be written as △⃗ S = S⃗f − S⃗i (3.1) Figure 3.3 Illustration of Distance and displacement. Key Concept: T Displacement is the change in an object’s position. Table 3.1 Difference between distance and displacement. Distance Displacement It is the length of path travelled It is the shortest distance between by an object in a given time. the initial and final positions. It is a scalar quantity. It is a vector quantity. It depends on the path followed It depends o the initial and final by the object. positions of the object, but not necessarily on the path followed. It can be more than or equal to Its magnitude can be less than or the magnitude of displacement. equal to the distance. 40 Unit 3 Motion in a Straight Line Activity 3.1 T Three students walked on a straight line. The first student walked 200 m to the right from a reference point A, then returned and walked 100 m to the left and then stopped. The second student walked 200 m from point A to the right, then returned and walked 300 m to the left and stopped. The third student walked 200 m to the right from point A, then returned and walked 200m to the left and stopped at point A. Discuss in groups about the total distance and displacements of the first, the second and the third student. Example 3.1 A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her displacement? (b) What distance does she ride? (c) What is the magnitude of her displacement? Solution: To solve this problem, we need to find the difference between the final position and the initial position while taking care to note the direction on the axis. a) Displacement: The rider’s displacement is △⃗ S = S⃗f − S⃗i = 1 km west. The displace- ment is negative if we choose east to be positive and west to be negative. b) Distance: The distance traveled is 3 km + 2 km = 5 km. c) The magnitude of the displacement is 1 km. Exercise 3.3 Exercise 3.4 T What is the dis- placement if the T Given the following values for the initial position S i and final position final position is the S f , check whether the value of the net displacement is positive or negative. same as the initial position? a) S f = (5, 0) and S i = (−1, 0) b) S f = (10, 0) and S i = (−15, 0) c) S f = (6, 0) and S i = (4, 0) 3.2 Average Speed and Instantaneous Speed 41 3.2 Average Speed and Instantaneous Speed At the end of this section, you should be able to: differentiate between average speed and instantaneous speed; compute the average speed of a body; moving in a straight line covering a certain distance in a given time; estimate the speed of moving bodies in your surroundings. Speed is a quantity that describes how fast a body moves. Speed is the rate at which an object changes its location. Like distance, speed is a scalar quantity because it has a magnitude but no direction. Since speed is a rate, it depends on the time interval of motion. Its symbol is v. In other words, speed is the distance covered by a moving body per unit time. The SI unit of speed is meter per second (m/s). Other units of speed include kilometer per hour (km/h) and miles per hour (mi/h). The mathematical equation used to calculate speed is Distance speed = (3.2) time s v = (3.3) t One of the most obvious features of an object in motion is how fast it is moving. Exercise 3.5 In your journey from home to school, you walk slowly for some time, and you run T In Figure ??, what another time to cover the total distance. This shows that the speed for the walk does the speedome- and the speed for the run are different. In this regard, we define average speed. ter read? Speed and average speed are not the same although they are derived from the same formula. The average speed is defined as the total distance travelled divided by the total time it takes to travel that distance: Total distance covered Average speed = (3.4) Total time taken Figure 3.4 Speedometer. (3.5) stot vav = (3.6) ttot During a typical trip to school by car, the car undergoes a series of changes in its 42 Unit 3 Motion in a Straight Line speed. If you were to look at the speedometer readings at regular intervals, you would notice that it changes. The speedometer of a car gives information about the instantaneous speed of the car. It shows the speed of the car at a particular instant in time. The speed at any specific instant is called the instantaneous speed. To calculate the instantaneous speed, we need to consider a very short time interval-one that approaches zero. For example, a school bus undergoes changes in speed. Mathematically the instantaneous speed is given ∆s vins = as ∆t → 0 (3.7) ∆t Instantaneous speed and average speed are both scalar quantities. When you solve the average of all instantaneous speeds that occurred during the whole trip, you will get the average speed. Exercise 3.6 T What are the Example 3.2 differences and similarities between A car covers a distance between two towns which are 80 km apart. If it takes the car average speed and 1hr and 30 minutes to travel between the two towns, calculate the average speed instantaneous of the car in m/s. speed? Solution: The car takes 1hr and 30 minutes to travel between the two towns. This time is the same as 1.5 hrs. Therefore, the average speed of the car is given by, s v av = t with s = 80 km and t=1.5 hrs, v av becomes, (80 km) v av = = 53.33 km/hr (1.5 hr s) However, we are required to calculate the average speed in m/s. For this purpose, we use 1 km = 1000 m and 1 hr = 3600 s. Hence, km 1000 m v av = 53.33 = 53.33 × = 14.81 m/s hr 3600 s Exercise 3.7 T If the car is trav- Example 3.3 elling at 120 km/h, How far does a student walk in 1.5 hrs if her average speed is 5 m/s?. what is the car’s speed in m/s. 3.3 Average Velocity and Instantaneous Velocity 43 Solution: To find the distance, we rewrite the equation as st v av = tt s = v av t m s = 5400 s × 5 s = 27000 m 3.3 Average Velocity and Instantaneous Velocity At the end of this section, you should be able to: differentiate between average velocity and instantaneous velocity; compute the average velocity of a body moving in straight line covering a certain displacement in a given time. Where an object started and where it stopped does not completely describe the motion of the object. Velocity is a physical quantity that describes how fast a body moves as well as the direction in which it moves. Hence, velocity is a vector quantity. Its symbol is ⃗ v (v with an arrow on the head). The SI unit of velocity is meter per second (m/s). Other units of velocity include kilometer per hour (km/h) and miles per hour (mi/h). Key Concept: T Velocity is the rate of change of displacement. Suppose that the positions of a car are S⃗i at time t i and S⃗f at time t f. If the details of the motion at each instant are not important, the rate is usually Figure 3.5 The average velocity of expressed as the average velocity. Average velocity (v⃗av ) of a body is the total the car tells how fast and in which displacement covered by that body in a specified direction divided by the total direction the car is moving. time taken to cover the displacement. Analytically it can be written as ⃗ Sf − ⃗ Si ∆⃗S v⃗av = = (3.8) tf − ti ∆t where S⃗f is the final position at final time t f and S⃗i is the initial position at time t i. Average velocity points in the same direction as the displacement. If the 44 Unit 3 Motion in a Straight Line displacement points in the positive direction, the average velocity is positive. If the displacement points in the negative direction, the average velocity is negative. Key Concept: T Average velocity is the total displacement of a body over a time interval. Exercise 3.8 To determine the velocity at some instant, such as t = 1.0 s, or t = 2.0 s etc., T Does the average we study a small time interval near that instant. As the time intervals becomes speed the same as smaller and smaller, the average velocity over that interval becomes instantaneous the magnitude of velocity. Instantaneous velocity of a body is its velocity at any time t. For a body the average velocity? that undergoes uniform motion, the velocity of the body is uniform and the Explain. average velocity and the instantaneous velocity are the same. Instantaneous velocity can be positive or negative. The magnitude of the instantaneous velocity is known as the instantaneous speed. Exercise 3.9 T In 2003 Tirunesh Dibaba won the world junior cross-country title by completing a 5,000-metre in 14 min 39.94 sec (junior world record) and secured the gold at the International Association of Athletics Federations (IAAF) world track and field championships, becoming the youngest-ever world champion in her sport. Calculate her average speed. Key Concept: T Instantaneous velocity is the velocity of a body at a specific instant in time. Example 3.4 A student attained a displacement of 360 m north in 180 s. What was the student’s average velocity? Solution: We know that the displacement is 360 m north and the time is 180 s. We can use the formula for average velocity to solve the problem. ∆⃗ S 360 m m ⃗ v av = = North = 2 North ∆t 180 s s 3.3 Average Velocity and Instantaneous Velocity 45 Example 3.5 A girl jogs with an average velocity of 2.4 m/s east. What is her displacement after 40 seconds? Solution: Given: ⃗ v av = 2.4m/s east, t = 40 seconds Solution: The displacement of the girl is m ∆⃗ S =⃗ v av ∆t = 2.4 (40 s)east = 96 m East s Exercise 3.10 Example 3.6 T Athlete 1 com- pletes 100m in 55 A bus moving along a straight line towards west covers the following distances in seconds and athlete the given time intervals. Calculate the average velocity of the bus for each time 2 completes the interval. same distance in 50 S in km 20 60 100 140 seconds. Compare t in hour 0 1 2 3 their average speeds. Which athlete has Solution: higher average By computing the displacement of the bus for each time interval, we can calculate speed? the average velocity of the bus as follows. Between t 0 = 0 and t 1 = 1 hr ∆S⃗1 = S⃗1 − S⃗0 = 60 km − 20 km = 40 km The average velocity during this time interval is ∆S⃗1 40 km km v⃗1 = = = 40 ∆t 1 1 hr hr Between t 1 = 1 hr and t 2 = 2 hr ∆S⃗1 = S⃗2 − S⃗1 = 100 km − 60 km = 40 km The average velocity of the bus during this time interval is ∆S⃗2 40 km km v⃗2 = = = 40 ∆t 2 1 hr hr Between t 2 = 2 hr and t 3 = 3 hr ∆S⃗1 = S⃗2 − S⃗2 = 140 km − 100 km = 40 km 46 Unit 3 Motion in a Straight Line The average velocity during this time interval is ∆S⃗3 40 km km v⃗3 = = = 40 ∆t 3 1 hr hr Therefore, for each time interval, the average velocity of the car is constant. This implies that the car is undergoing uniform motion. Note: You can convert km/hr into m/s by the relation: km 1000 m 10 m 1 = = hr 60 × 60 s 36 s 3.4 Acceleration At the end of this section, you should be able to: define acceleration; calculate the average acceleration of a body if its velocity changes from some initial value to final value in a given time. The discussion of motion with varying velocity can be dealt with by the intro- duction of the concept of acceleration. Acceleration is a vector quantity and is a measure of how much the velocity of an object changes in a unit of time (in m one second). Acceleration is denoted by ⃗ a and its SI unit is s2 , that is, meters per second squared or meters per second per second. For example, if a runner travelling at 10 km/h due east slows to a stop, reverses direction, and continues her run at 10 km/h due west, her velocity has changed as a result of the change in direction, although the magnitude of the velocity is the same in both directions. Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed) or in direction, or both as shown in Figure. 3.6. Acceleration is, therefore, a change in speed or direction, or both. Key Concept: Figure 3.6 (a) positive acceleration (car speeding up) and (b) negative T Acceleration is the rate of change of velocity. acceleration (car slowing down). If the initial velocity of a body is v i at a time t i , and the final velocity is v f at a time t f , the average acceleration is, from the definition, 3.4 Acceleration 47 ⃗ vf −⃗vi ⃗aav = (3.9) tf − ti If a body starts from rest, then the initial velocity is zero (⃗ v i = 0). If the velocity of a body decreases, then the final velocity is less than the initial velocity. Such motion is called decelerating motion. Deceleration is called a negative acceleration. If the body comes to rest, the final velocity is zero (v⃗f = 0). Exercise 3.11 T If the initial and final velocities of a car are the same, what will be its acceleration? T Is the direction of the acceleration always in the direction of the velocity? Example 3.7 A train moving in the east direction accelerates from rest to 36 km/h in 20 s. What is the average acceleration during that time interval? Given: v⃗i = 0, ⃗ v f = 36 km/h, ∆t = 20 s, Required: ⃗ a av =? Solution: km v⃗f − v⃗i 36 h −0 ⃗ a av = = ∆t 20 s m 10 s −0 m ⃗ a av = = +0.5 t o east 20 s s2 km m Note that 36 h is equivalent to 10 s. The plus sign in the answer means that acceleration is to the right. This is a reasonable conclusion because the train starts from rest and ends up with a velocity directed to the right (i.e., positive). So, acceleration is in the same direction as the change in velocity. Example 3.8 48 Unit 3 Motion in a Straight Line A car travelling at 7.0 m/s along a straight road accelerates 2.5 m/s 2 to reach a speed of 12.0 m/s. How long does it take for this acceleration to occur? Given: v i = 7.0 m/s, v f = 12.0 m/s, a av = 2.5 m/s 2 , Required: ∆t =? Solution: v f − vi 12.0 m/s − 7.0 m/s ∆t = = =2 s a av 2.5 m/s 2 3.5 Uniform Motion At the end of this section, you should be able to: define uniform motion; give examples of uniform motion. Uniform motion is the motion of an object along a straight line with a constant velocity or speed in a given direction. In a uniform motion, an object travels equal distances in fixed intervals of time. In fact, a moving body does not have a uniform speed throughout its motion. Sometimes the body speeds up or slows down, and other times it moves with a constant speed. This is why describing motion in terms of average quantities (average speed and average velocity) is highly important. Some examples of a uniform motion are a car moving on a straight road with a fixed speed (as shown in Figure 3.7) and an airplane flying with constant speed in a given direction. Figure 3.7 A car moving with a constant speed without changing the direction of mo- tion. 3.6 Graphical Representation of Motion 49 Key Concept: TMotion at a constant velocity or uniform motion means that the position of the object is changing at the same rate. The uniform rectilinear motion has the following properties: The acceleration is zero (a=0) because neither the magnitude of the velocity nor its direction changes. On the other hand, the average and instantaneous velocities have the same values at all times. Exercise 3.12 T Consider the fol- 3.6 Graphical Representation of Motion lowing S-t graph of At the end of this section, you should be able to: two cars in motion plot s-t and v-t graphs; on a straight line as shown in Figure 3.8. define the slope of a motion; Which car is moving faster and why? calculate the velocity from S-t graph and acceleration from v-t graph. The motion of an object travelling even in a straight line can be complicated. The object may travel forwards or backwards, speed up or slow down, or even stop. Where the motion remains in one dimension, the information can be presented in graphical form. The main advantage of a graph compared with a table is that it allows the scope of the motion to be seen clearly. Position-Time Graph A position-time graph indicates the position of an object at any time for motion that occurs over an extended time interval. The data from Table 3.2 can be presented by plotting the time data on a horizontal axis and the position data on a vertical axis, which is called a position-time graph. The graph of the runner’s Figure 3.8 The s-t graph for a uni- motion is shown in Figure ??. To draw this graph, first plot the runner’s recorded form motion. positions; then, draw a line that best fits the recorded points. To determine the velocity or speed of the runner, consider the meaning of the slope. Start with the mathematical definition of slope. 50 Unit 3 Motion in a Straight Line Table 3.2 Table 3.2: Position-time table for the runner. Position vs. time Time (s) Position (m) 0 0 1 5 2 10 3 15 4 20 5 25 6 30 Slope is the rise over the run. ⃗ rise ∆S Slope = = = v⃗av (3.10) run ∆t Therefore, if we take any two points in a straight line, the speed from the S-t graph is (5.0 − 0)m (10.0 − 5.0)m m Sl ope = = = 5.0 (1.0 − 0)s (2.0 − 1.0)s s to the positive x-direction. This shows that the displacement increased by 5.0 m in 1.0s. The S-t graph gives a constant velocity. Key Concept: T The slope of a position-time graph represents the average velocity of an object. Velocity- Time Graph A graph of velocity against time shows how the velocity of an object changes with time. Just as a displacement-time graph shows how far an object has moved, a velocity-time graph shows how its velocity changes during the motion of the object. Table 3.3 shows the data for a car that starts at rest and speeds up along a straight line of a road. The velocity-time graph obtained by plotting these data points is shown in Figure 3.9. The positive direction has been chosen to be the same as that of the motion of the car. Notice that this graph is a straight line, 3.6 Graphical Representation of Motion 51 which means that the car is speeding up at a constant rate. The rate at which the car’s velocity is changing can be found by calculating the slope of the velocity- time graph. Consider a pair of data points that are separated by 1 s, such as 4.0 s and 5.0 s. At 4.0 s, the car is moving at a velocity of 20.0 m/s. At 5.0 s, the car is travelling at 25.0 m/s. Thus, the car’s velocity increased by 5.0 m/s in 1.00 s. The rate at which an object’s velocity changes is called the acceleration of the object. When the velocity of an object changes at a constant rate, the object has a constant acceleration. Table 3.3: Velocity vs. time of a car Time (s) Velocity (m/s) 0 0 1 5 2 10 3 15 Figure 3.9 The slope of a velocity- 4 20 time graph is the acceleration of 5 25 the object. Activity 3.2 Key Concept: Plot a-t graph from TThe slope of a velocity-time graph represents the acceleration of an the above v-t data object. and discuss in groups about the In a uniform motion, the v-t graph is a horizontal line as shown in Figure 3.10 value of the acceler- indicating that the velocity is constant at any given time. The area under the v-t ation as time goes. graph in a uniform motion represents the distance covered by the object. The area of the rectangle in Figure 3.10 is given by, ar ea = b × h = v t = s, which is equal to the distance covered by the object. Activity 3.3 Discuss in groups and determine the slope of the v-t graph in a uniform motion? Speed Limit and Traffic Safety Figure 3.10 The v-t graph of a uni- form motion. Have you ever noticed a traffic sign of a speed limit shown in the Figure 3.11? What does it indicate and what is its importance? 52 Unit 3 Motion in a Straight Line The above Figure 3.11 shows that drivers are required to keep the speed of their cars at 80 km/hr or below. Drivers violating this speed limit will be charged by the traffic police as they may cause danger. Nowadays, vehicles moving with very high speed are the main causes for the death of thousands of people and several property damages as they cannot be controlled easily during accident Figure 3.12 Traffic accident. as indicated in Figure 3.12. One can easily read the speed of a car from the speedometer. Speedometer is a device used to measure the instantaneous speed of a car. It is very important to keep the speed of cars at optimum level to save lives and avoid property damages. Activity 3.4 T Discuss in groups and identify the type of vehicles causing human/ani- mal deaths and property damages in your area. Can you guess the percent- age of the accidents caused by violation of speed limits? Discuss in groups and report to you teacher. Also suggest possible solutions. Figure 3.11 Speed limit in a typical city road. 3.6 Graphical Representation of Motion 53 Virtual Laboratory Click on the following link to perform virtual laboratory on motion in straight line under the guidance of your teacher. 1. The Moving Man PhET Experiment Unit Summary In this unit, you have learnt the following main points. Motion in a straight line is one of the simplest forms of motion in a specific direction and is called rectilinear motion. An object is in motion if it changes position relative to a reference point Motion can be described by distance, speed, displacement, and velocity, where displacement and velocity also include direction. Distance is a physical quantity which describes the length between two points (places) and is the total path length travelled by a body. Distance is a scalar quantity. Displacement is the change in position of a body in a certain direc- tion. The speed of an object can be calculated by dividing the distance traveled by the time needed to travel the distance. The velocity of an object is the speed of the object with its direction of motion. Average velocity is displacement over the time period during which the displacement occurs. If the velocity is constant, then average velocity and instantaneous velocity are the same. Acceleration occurs whenever an object speeds up, slows down, or changes direction. Uniform motion is the motion of an object along a straight line with a constant velocity or speed in a given direction. 54 Unit 3 Motion in a Straight Line The slope of a position-versus-time graph at a specific time gives instantaneous velocity at that time. On a speed-time graph, a horizontal line represents zero acceleration or constant speed. End of Unit Questions and Problems Part I: Conceptual questions and workout problems 1. How are average velocity and instantaneous velocity related in a uniform motion? 2. What does the area under velocity against time graph describe in a uniform motion? 3. If the slope of the graph is zero in a distance against time graph, what can one conclude about the motion of the body? 4. When do we say that the acceleration of a body is (a) positive? (b) negative? 5. Here are three pairs of initial and final positions, respectively; along an x axis. Which pairs give a negative displacement: (a) -3 m, 5 m; (b) -3 m, -7 m; (c) 7 m, -3 m? 6. An athlete covers a 100 m distance in 55 seconds. Calculate the average speed of the athlete. 7. A car moves with a steady speed of 60 km/hr for 2 hours between two towns A and B. If the average speed of the car for the round trip is 50 km/hr, then compute the speed of the car when it moves from B to A. 8. Based on the distance against time graph of a certain car shown in the Figure below, answer the following questions. 3.6 Graphical Representation of Motion 55 (a) What is the initial position of the car? Take your reference frame at the origin. (b) How fast is the car going? 9. A man riding a horse maintained an average speed of 30km/hr to cover the distance between two villages A and B in 45 minutes. How far apart are villages A and B? 10. An airplane lands with an initial velocity of 70.0 m/s and then decel- m erates at 1.50 s2 for 40.0 s. What is its final velocity? 11. The following table describes the distance covered by a body moving along a straight