PEARSON EDEXGEL INTERNATIONAL AS / A LEVEL

PHYSICS STUDENT BOOK 1 物理学生读物 1

MILES HUDSON 迈尔斯·哈德森

PDF COMPILED BY SAAD 由 SAAD 编译的 PDF

Copyright notice 版权声明

Endorsement statement 认可声明

Acknowledgements 确认

Logos 标志

Tables 表

Text 发短信

WORKING AS A PHYSICIST 作为物理学家工作

TOPIC 1 MECHANICS 主题 1：机制

TOPIC 3
WAVES AND PARTICLE NATURE OF LIGHT
主题 3 光的波和粒子性质

3D QUANTUM PHYSICS 3D 量子物理学

4A ELECTRICAL QUANTITIES 4A 电量

ABOUT THIS BOOK 关于本书

Learning objectives 学习目标
Each chapter starts with a list of key assessment objectives.
每章都以关键评估目标列表开始。

1 A 1 VELOCITY AND ACGELERATION
1 A 1 速度和加速度

Mowemenn is fundamental to the denctioning of our univesse. Whetber you are rurring to catch a
Mowemenn 是我们大学的基础。你急于赶上
RATE OF MOVEMENT 移动速率
One of the simplest thans we can measure is how tas an abject is moving You can cakculate an arestain distance
我们可以测量的最简单的方法之一是 tas an abject 是如何移动的 You can cakculate a arestain distance

Howews the calculstion for powed will only tell you how fast an nbigect is moring Often it is also
Howews powed 的计算只会告诉你 nbigect 的 moring 有多快 通常也是

OR ${}^{v=\frac{s}{t}}\mathrm{v}=\frac{\mathrm{\Delta }s}{M}$${}^{v=\frac{s}{t}}\mathrm{v}=\frac{\mathrm{\Delta }s}{M}$quad^(v=(s)/(t))v=(Delta s)/(M)\quad{ }^{v=\frac{s}{t}} \mathrm{v}=\frac{\Delta s}{M} 或 ${}^{v=\frac{s}{t}}\mathrm{v}=\frac{\mathrm{\Delta }s}{M}$${}^{v=\frac{s}{t}}\mathrm{v}=\frac{\mathrm{\Delta }s}{M}$quad^(v=(s)/(t))v=(Delta s)/(M)\quad{ }^{v=\frac{s}{t}} \mathrm{v}=\frac{\Delta s}{M}

the messurement is reseredet to os a a colalar quasunity The
测量是 reseredet to os a a colalar quasunity
scalar. aistarce is a scalar and depplacement is a vectoc.
标量。aistarce 是标量，而 depplacement 是 vectoc。

Exam hints 考试提示

Tips on how to answer examstyle questions and guidance for exam preparation. Worked examples also show you how to work through questions and set out calculations.
有关如何回答 Examstyle 问题的提示和考试准备指南。工作示例还向您展示了如何解决问题和设置计算。

Checkpoint 检查站

• Links to other areas of Physics include previous knowledge that is built on in the topic, and future learning that you will cover later in your course.
  指向物理学其他领域的链接包括该主题所建立的先前知识，以及您将在课程后面介绍的未来学习。
• A checklist details maths knowledge required. If you need to practise these skills, you can use the Maths Skills reference at the back of the book as a starting point.
  清单详细说明了所需的数学知识。如果您需要练习这些技能，您可以使用书后面的 Maths Skills 参考资料作为起点。

TOPIC 1 MECHANICS 主题 1：机制

1A MOTION 1A 运动

MathS sKILL FOR THIS CHAPTER
MathS sKILL 本章
Unit of messuremem ieg are nemoan $n$$n$nn

1A THINKING BIGGER 1A 思考更大
THE BATTLE OF AGRA 阿格拉战役

Thinking Bigger 放眼大处

Skills 技能

Exam Practice 考试练习

1A EXAM PRACTICE 1A 考试练习

PRACTICAL SKILLS 实践技能

• Papers 1 and 2 will include questions based on practical activities, including novel scenarios.
  试卷 1 和 2 将包括基于实践活动的问题，包括新场景。
• Paper 3 will test your ability to plan practical work, including risk management and selection of apparatus.
  试卷 3 将测试您规划实际工作的能力，包括风险管理和设备选择。

UNIT 1 (TOPICS 1 AND 2) MECHANICS AND MATERIALS
第 1 单元（主题 1 和 2）力学和材料

• Strobe photography or the use of a video camera to analyse projectile motion
  频闪摄影或使用摄像机分析弹丸运动
• Determine the centre of gravity of an irregular rod
  确定不规则杆的重心
• Investigate the conservation of momentum using light gates and air track
  使用光门和空气轨迹研究动量守恒
• Hooke’s law and the Young modulus experiments for a variety of materials
  各种材料的胡克定律和杨氏模量实验

UNIT 2 (TOPICS 3 AND 4)
第 2 单元（主题 3 和 4）

• Estimating power output of an electric motor
  估算电动机的功率输出
• Using a digital voltmeter to investigate the output of a potential divider and investigating current/ voltage graphs for a filament bulb, thermistor and diode
  使用数字电压表研究分压器的输出，并研究白炽灯泡、热敏电阻和二极管的电流/电压图
• Determining the refractive index of solids and liquids, demonstrating progressive and stationary waves on a slinky
  测定固体和液体的折射率，在 slinky 上展示行波和驻波
  

  

Practical Skills 实践技能

ASSESSMENT OVERVIEW 评估概述

ASSESSMENT OBJECTIVES AND WEIGHTINGS
评估目标和权重

RELATIONSHIP OF ASSESSMENT OBJECTIVES TO UNITS
评估目标与单位的关系

WORKING AS A PHYSICIST 作为物理学家工作

• read real-life scientific writing in a variety of contexts and aimed at different audiences
  在各种环境中阅读针对不同受众的真实科学著作
• develop an understanding of how the professional scientific community functions
  了解专业科学界的运作方式
• learn to think critically about the nature of what you have read
  学会批判性地思考你所读内容的本质
• understand the issues, problems and challenges that may be raised
  了解可能提出的问题、问题和挑战
• gain practice in communicating information and ideas in an appropriate scientific way
  获得以适当的科学方式传达信息和想法的练习
• apply your knowledge and understanding to unfamiliar contexts.
  将您的知识和理解应用于不熟悉的环境。

MATHS SKILLS FOR PHYSICISTS
物理学家的数学技能

• Recognise and make use of appropriate units in calculations (e.g. knowing the difference between base and derived units)
  在计算中识别并使用适当的单位（例如，了解基本单位和派生单位之间的区别）
• Estimate results (e.g. estimating the speed of waves on the sea)
  估计结果（例如，估计海浪的速度）
• Make order of magnitude calculations (e.g. estimating approximately what an answer should be before you start calculating, including using standard form)
  进行数量级计算（例如，在开始计算之前估计大致应该是什么答案，包括使用标准格式）
• Use algebra to rearrange and solve equations (e.g. finding the landing point of a projectile)
  使用代数重新排列和求解方程（例如，找到弹丸的着陆点）
• Recognise the importance of the straight line graph as an analysis tool for the verification and development of physical laws by experimentation (e.g. choosing appropriate variables to plot to generate a straight line graph with experimental data)
  认识到直线图作为分析工具的重要性，通过实验验证和发展物理定律（例如，选择合适的变量进行绘制，以生成包含实验数据的直线图）
• Determine the slope and intercept of a linear graph (e.g. finding acceleration from a velocity-time graph)
  确定线性图的斜率和截距（例如，从速度-时间图中求加速度）
• Calculate the area under the line on a graph (e.g. finding the energy stored in a stretched wire)
  计算图表上线下的面积（例如，找到存储在拉伸导线中的能量）
• Use geometry and trigonometry (e.g. finding components of vectors)
  使用几何和三角函数（例如，查找向量的分量）

What prior knowledge do I need?
我需要什么先验知识？

• Understanding and knowledge of physical facts, terminology, concepts, principles and practical techniques
  理解和了解物理事实、术语、概念、原理和实用技术
• Applying the concepts and principles of physics, including the applications of physics, to different contexts
  将物理学的概念和原理（包括物理学的应用）应用于不同的环境
• Appreciating the practical nature of physics and developing experimental and investigative skills based on the use of correct and safe laboratory techniques
  欣赏物理学的实用性，并在使用正确和安全的实验室技术的基础上发展实验和调查技能
• Communicating scientific methods, conclusions and arguments using technical and mathematical language
  使用技术和数学语言交流科学方法、结论和论点
• Consideration of the implications, including benefits and risks, of scientific and technological developments
  考虑科学和技术发展的影响，包括利益和风险
• Understanding how society uses scientific knowledge to make decisions about the implementation of technological developments
  了解社会如何利用科学知识来做出有关技术发展实施的决策
  Understanding of how scientific ideas change over time, and the systems in place to validate these changes
  了解科学思想如何随时间变化，以及验证这些变化的系统
  

  

What will I study later?
我以后会学习什么？

• Knowledge and understanding of further physical facts and terminology, deeper concepts, principles and more complex practical techniques
  了解和理解进一步的物理事实和术语、更深的概念、原理和更复杂的实践技术
• Practical skills and techniques for some key physics experiments
  一些关键物理实验的实用技能和技巧
• How to communicate information and ideas in appropriate ways using appropriate terminology
  如何使用适当的术语以适当的方式传达信息和想法
• The implications of science and their associated benefits and risks
  科学的影响及其相关的益处和风险
• The role of the scientific community in validating new knowledge and ensuring integrity
  科学界在验证新知识和确保完整性方面的作用
• The ways in which society uses science to inform decision making
  社会利用科学为决策提供信息的方式
  

  

1 STANDARD UNITS IN PHYSICS
1 物理学标准单位

LEARNING OBJECTIVES 学习目标

• Understand the distinction between base and derived quantities.
  了解基数和派生量之间的区别。
  ■ Understand the idea of a fixed system of units, and explain the SI system.
  ■ 理解固定单位制的概念，并解释 SI 制。

BASE AND DERIVED QUANTITIES
基础数量和派生数量

SI UNITS 国际单位制

For each of the base units, a meeting is held every four or six years of the General Conference on Weights and Measures, under the authority of the Bureau International des Poids et Mesures in Paris. At this meeting, they either alter the definition, or agree to continue with the current definition. As we learn more and more about the universe, these definitions are gradually moving towards the fundamental constants of nature.
对于每个基本单位，在巴黎国际计量局的授权下，每四年或六年召开一次度量衡大会会议。在这次会议上，他们要么改变定义，要么同意继续当前的定义。随着我们对宇宙的了解越来越多，这些定义正逐渐朝着自然界的基本常数发展。

• The kilogram is the unit of mass; it is equal to the mass of the International Prototype Kilogram, as in fig $\mathbf{A}$$\mathbf{A}$A\mathbf{A}.
  千克是质量单位;它等于国际原型千克的质量，如图 $\mathbf{A}$$\mathbf{A}$A\mathbf{A} 所示。
• The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
  第二个是辐射的9192631770持续时间，对应于铯 133 原子基态的两个超精细能级之间的跃迁。
• The metre is the length of the path travelled by light in vacuum
  米是光在真空中行进的路径长度
• during a time interval of $\frac{1}{299792458}$$\frac{1}{299792458}$(1)/(299792458)\frac{1}{299792458} of a second (see fig B).
  在一秒的 $\frac{1}{299792458}$$\frac{1}{299792458}$(1)/(299792458)\frac{1}{299792458} 时间间隔内（见图 B）。
• The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to $2\times {10}^{-7}$$2\times {10}^{-7}$2xx10^(-7)2 \times 10^{-7} newton per metre of length.
  安培是恒定电流，如果保持在两个无限长、圆形横截面可以忽略不计的平行直导体中，并在真空中相距 1 m，则在这些导体之间产生的力等于每米长度的 $2\times {10}^{-7}$$2\times {10}^{-7}$2xx10^(-7)2 \times 10^{-7} 牛顿。
• The kelvin, unit of thermodynamic temperature, is the fraction $\frac{1}{273.16}$$\frac{1}{273.16}$(1)/(273.16)\frac{1}{273.16} of the thermodynamic temperature of the triple point of water.
  开尔文是热力学温度的单位，是水的三相点的热力学温度的分数 $\frac{1}{273.16}$$\frac{1}{273.16}$(1)/(273.16)\frac{1}{273.16} 。
• The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of carbon-12. (When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles or specified groups of such particles.)
  摩尔是一个系统的物质量，它包含的基本实体与 0.012 公斤碳 12 中的原子一样多。（使用摩尔时，必须指定基本实体，可以是原子、分子、离子、电子、其他粒子或此类粒子的指定组。

EXAM HINT 考试提示

LEARNING TIP 学习小贴士

DERIVED UNITS 派生单位

POWER PREFIXES 电源前缀

SKILLS PROBLEM SOLVING 技能 解决问题

1. Refer to table B and answer the following questions:
   请参阅表 B 并回答以下问题：
   (a) Pick any quantity that you have studied before and explain how its base unit equivalent is shown.
   （a） 选择您之前研究过的任何数量，并解释其基本单位当量是如何显示的。
   (b) All of the derived quantity units are named after scientists. Compare their names and abbreviations. What do you notice?
   （b） 所有派生的量单位都以科学家的名字命名。比较它们的名称和缩写。您注意到了什么？
2. Write the following in standard form:
   以标准格式编写以下内容：
   (a) 9.2 GW （a） 9.2 吉瓦
   © 6400 km © 6400 公里
   (b) 43 mm （b） 43 毫米
   (d) 44 ns. （d） 44 纳秒。
3. Write the following using an appropriate prefix and unit symbol:
   使用适当的前缀和单位符号编写以下内容：
   (a) 3600000 joules （a） 3600000 焦耳
   © 10 millionths of an ampere
   © 10 万分之一安培
   (b) 31536000 seconds （b） 31536000 秒
   (d) 105000 hertz. （d） 105000 赫兹。

2 ESTIMATION 2 估计

LEARNING OBJECTIVES 学习目标

Estimate values for physical quantities. Use your estimates to solve problems.
估计物理量的值。使用您的估计值来解决问题。

ORDER OF MAGNITUDE 数量级

In physics, it can be very helpful to be able to make approximate estimates of values to within an order of magnitude. This means that the power of ten of your estimate is the same as the true value. For example, you are the same height as the ceiling in your classroom, if we consider the order of magnitude. The ceiling may be twice your height, but it would need to be ten times bigger to reach the next order of magnitude.
在物理学中，能够将值近似估计到一个数量级以内可能非常有帮助。这意味着您估计值的 10 的幂与真实值相同。例如，如果我们考虑数量级，您与教室中的天花板高度相同。天花板可能是你高度的两倍，但它需要大十倍才能达到下一个数量级。
This is made clearer if we express all values in standard form and then compare the power of ten. You are likely to be a thousand times taller than an ant, so we would say you are three orders of magnitude larger.
如果我们以标准形式表示所有值，然后比较 10 的幂，这会更清楚。你可能比蚂蚁高一千倍，所以我们会说你大三个数量级。
typical ant height: $1.7\mathrm{mm}=1.7\times {10}^{-3}\mathrm{m}$$1.7\mathrm{mm}=1.7\times {10}^{-3}\mathrm{m}$1.7mm=1.7 xx10^(-3)m1.7 \mathrm{~mm}=1.7 \times 10^{-3} \mathrm{~m}
典型的蚂蚁高度： $1.7\mathrm{mm}=1.7\times {10}^{-3}\mathrm{m}$$1.7\mathrm{mm}=1.7\times {10}^{-3}\mathrm{m}$1.7mm=1.7 xx10^(-3)m1.7 \mathrm{~mm}=1.7 \times 10^{-3} \mathrm{~m}
typical human height: $1.7\mathrm{m}=1.7\times {10}^{\circ }\mathrm{m}$$1.7\mathrm{m}=1.7\times {10}^{\circ }\mathrm{m}$1.7m=1.7 xx10^(@)m1.7 \mathrm{~m}=1.7 \times 10^{\circ} \mathrm{m}
典型人体身高： $1.7\mathrm{m}=1.7\times {10}^{\circ }\mathrm{m}$$1.7\mathrm{m}=1.7\times {10}^{\circ }\mathrm{m}$1.7m=1.7 xx10^(@)m1.7 \mathrm{~m}=1.7 \times 10^{\circ} \mathrm{m}

fig A We are three orders of magnitude taller than an ant.
图 A 我们比蚂蚁高三个数量级。
In many situations, physicists are not interested in specific answers, as circumstances can vary slightly and then the specific answer is incorrect. An order of magnitude answer will always be correct, unless you change the initial conditions by more than an order of magnitude. So a physicist could easily answer the question ‘What is the fastest speed of a car?’ because we don’t really want to know the exact true value. To give an exact answer would depend on knowing the model of car, and the weather and road conditions, and this answer would only be correct for that car on that day. By estimating important quantities, like a typical mass for cars, we can get an approximate - order of magnitude - answer. The reason for doing so would be that it allows us to develop ideas as possible or impossible. Also it helps us focus on developing the ideas along lines that will eventually be feasible when we get to developing a specific solution. This reduces time and money wasted by following ideas that are impossible. It also
在许多情况下，物理学家对具体的答案不感兴趣，因为情况可能会略有不同，然后具体的答案是不正确的。数量级的答案始终是正确的，除非您将初始条件更改了一个数量级以上。因此，物理学家可以很容易地回答“汽车的最快速度是多少”这个问题，因为我们真的不想知道确切的真实值。给出确切的答案将取决于了解汽车的型号、天气和路况，而这个答案仅适用于当天的那辆车。通过估计重要的量，例如汽车的典型质量，我们可以得到一个近似的 - 数量级 - 答案。这样做的原因是它允许我们尽可能或不可能地发展想法。此外，它还有助于我们专注于沿着最终在我们开发特定解决方案时可行的思路发展想法。这减少了因遵循不可能的想法而浪费的时间和金钱。它还
helps us quickly notice any miscalculations in an answer to a question. If we used an equation to calculate the answer to the fastest speed of a particular car in particular conditions, and the answer came out as 300000000 metres per second (the speed of light), we would immediately know that the answer is wrong, and re-check the calculation.
帮助我们快速注意到问题答案中的任何计算错误。如果我们用一个方程来计算特定汽车在特定条件下的最快速度的答案，答案是每秒 300000000 米（光速），我们会立即知道答案是错误的，并重新检查计算。

table A Examples of object scales changing with powers of ten.
表 A 对象比例随 10 的幂而变化的示例。
FERMI QUESTIONS FERMI 问题

A fig B Enrico Fermi was one of the developers of both nuclear reactors and nuclear bombs, along with other work on particle physics, quantum physics and statistical mechanics. He was awarded the 1938 Nobel Prize for Physics for the discovery of new radioactive elements and induced radioactivity.
A 图 B 恩里科·费米 （Enrico Fermi） 是核反应堆和核弹的开发者之一，还参与了粒子物理学、量子物理学和统计力学方面的其他工作。他因发现新的放射性元素和诱导放射性而获得 1938 年诺贝尔物理学奖。
Enrico Fermi was an Italian physicist who lived from 1901 to 1954. He was a pioneer of estimation. What have become known as Fermi questions are seemingly specific questions, to which
恩里科·费米 （Enrico Fermi） 是一位意大利物理学家，生活在 1901 年至 1954 年之间。他是估算的先驱。后来被称为费米问题的东西似乎是具体的问题，其中
only an order of magnitude answer is expected. It is common for the question to appear very difficult, as we do not have enough information to work out the answer. One of Fermi’s most interesting thought experiments was a consideration of whether or not alien life exists. Over a lunch with other scientists in 1950, Fermi surprised the group by asking ‘Where is everybody?’ referring to extraterrestrials. There seems to be no evidence of the existence of alien life. That is still as true today as it was in 1950. However, when Fermi made an estimation of what would be necessary for an extraterrestrial civilisation to travel to visit us, his estimate came out at a much shorter amount of time than the age of our galaxy.
预计只有一个数量级的答案。这个问题看起来非常困难是很常见的，因为我们没有足够的信息来找出答案。费米最有趣的思想实验之一是考虑外星生命是否存在。1950 年，在与其他科学家共进午餐时，费米惊讶地问道：“大家都在哪里？似乎没有证据表明外星生命的存在。今天和 1950 年一样，这仍然适用。然而，当费米估计出外星文明访问我们所需要的条件时，他的估计结果比我们银河系的年龄要短得多。

$\mathrm{\Delta }$$\mathrm{\Delta }$Delta\Delta fig C The Fermi Paradox: even the most conservative estimates of the requirements of exploring the galaxy mean that aliens should reach Earth within ten million years of their life beginning. If they existed, they would be here.
$\mathrm{\Delta }$$\mathrm{\Delta }$Delta\Delta 图 C 费米悖论：即使是对探索银河系要求的最保守估计也意味着外星人应该在其生命开始后的一千万年内到达地球。如果他们存在，他们就会在这里。
You need to work out what steps are needed to make an estimation. First, think about what steps you would take to reach an answer, if you could have any information you wanted. Then, when the necessary data is not all available, make an estimate for the missing numbers. Making sensible assumptions is the key to solving Fermi questions.
您需要弄清楚进行估算需要哪些步骤。首先，考虑一下如果您可以获得任何您想要的信息，您将采取哪些步骤来获得答案。然后，当必要的数据并非全部可用时，对缺失的数字进行估计。做出合理的假设是解决费米问题的关键。

WORKED EXAMPLE 工作示例

CHECKPOINT 检查站

SKILLS ADAPTIVE LEARNING 技能自适应学习

1. Give an order of magnitude estimate for the following quantities:
   为以下数量给出一个数量级估计值：
   (a) the height of a giraffe
   （a） 长颈鹿的身高
   (b) the mass of an apple
   （b） 苹果的质量
   © the reaction time of a human
   © 人类的反应时间
   (d) the diameter of a planet
   （d） 行星的直径
   (e) the temperature in this room.
   （e） 这个房间的温度。
2. Answer the following Fermi questions, showing all the steps and the assumptions and estimates you make.
   回答以下 Fermi 问题，显示您所做的所有步骤以及假设和估计。
   (a) How many tennis balls would fit into a soccer stadium?
   （a） 一个足球场可以容纳多少个网球？
   (b) How many atoms are there in your body?
   （乙）你体内有多少个原子？
   © How many drops of water are there in a swimming pool?
   © 游泳池里有多少滴水？
   (d) In your lifetime, how much money will you make in total?
   （d） 在你的一生中，你总共会赚多少钱？
   (e) How many Fermi questions could Enrico Fermi have answered whilst flying from Rome to New York?
   （e） 恩里科·费米 （Enrico Fermi） 在从罗马飞往纽约的飞机上能回答多少个费米问题？

TOPIC 1 MECHANICS 主题 1：机制

1A MOTION 1A 运动

MATHS SKILLS FOR THIS CHAPTER
本章的数学技能

• Units of measurement (e.g. the newton, $N$$N$NN )
  测量单位（例如牛顿、 $N$$N$NN ）
• Using Pythagoras’ theorem, and the angle sum of a triangle (e.g. finding a resultant vector)
  使用勾股定理和三角形的角和（例如，求结果向量）
• Using sin, cos and tan in physical problems (e.g. resolving vectors)
  在物理问题中使用 sin、cos 和 tan（例如解析向量）
• Using angles in regular 2D structures (e.g. interpreting force diagrams to solve problems)
  在常规 2D 结构中使用角度（例如，解释力图以解决问题）
• Changing the subject of an equation (e.g. re-arranging the kinematics equations)
  更改方程的主题（例如，重新排列运动学方程）
• Substituting numerical values into algebraic equations (e.g. calculating the acceleration)
  将数值代入代数方程（例如计算加速度）
• Plotting two variables from experimental or other data, understanding that $y=mx+c$$y=mx+c$y=mx+cy=m x+c represents a linear relationship and determining the slope of a linear graph (e.g. verifying Newton’s second law experimentally)
  从实验或其他数据中绘制两个变量，理解 $y=mx+c$$y=mx+c$y=mx+cy=m x+c 代表线性关系并确定线性图的斜率（例如，通过实验验证牛顿第二定律）
• Estimating, by graphical methods as appropriate, the area between a curve and the $x$$x$xx-axis and realising the physical significance of the area that has been determined (e.g. using a speed-time graph)
  通过适当的图形方法估计曲线和 $x$$x$xx 轴之间的面积，并实现已确定面积的物理意义（例如，使用速度-时间图）

1A 1 VELOCITY AND AGGELERATION
1A 1 速度和聚合

LEARNING OBJECTIVES 学习目标

• Calculate values using equations for velocity and acceleration.
  使用速度和加速度方程计算值。
  

  

  
  $\mathrm{\Delta }$$\mathrm{\Delta }$Delta\Delta fig $\mathbf{A}$$\mathbf{A}$A\mathbf{A} These runners are accelerating to a high speed.
  $\mathrm{\Delta }$$\mathrm{\Delta }$Delta\Delta 图 $\mathbf{A}$$\mathbf{A}$A\mathbf{A} 这些跑步者正在加速到高速。

LEARNING TIP 学习小贴士

DID YOU KNOW? 您是否了解？

LEARNING TIP 学习小贴士

RATE OF MOVEMENT 移动速率

AVERAGE AND INSTANTANEOUS SPEED
平均速度和瞬时速度

In most journeys, it is unlikely that speed will remain constant throughout. As part of his training programme, an athlete in fig A wants to keep a record of his speed for all races. From rest, before the starting gun starts the race, he accelerates to a top speed. However, the race timing will be made from start to finish, and so it is most useful to calculate an average speed over the whole race. Average speed is calculated by dividing the total distance for a journey by the total time for the journey. Thus it averages out the slower and faster parts of the journey, and even includes stops.
在大多数旅程中，速度不太可能在整个过程中保持不变。作为训练计划的一部分，图 A 的一名运动员希望记录他所有比赛的速度。从休息开始，在发令枪开始之前，他加速到最高速度。但是，比赛时间将从头到尾进行，因此计算整场比赛的平均速度是最有用的。平均速度的计算方法是将旅程的总距离除以旅程的总时间。因此，它平均了旅程中较慢和较快的部分，甚至包括停靠点。
Instantaneous speed can be an important quantity, and we will look at how to measure it in the next topic.
瞬时速度可能是一个重要的量，我们将在下一个主题中研究如何测量它。

ACCELERATION 加速度

EXAM HINT 考试提示

CHECKPOINT 检查站

1. The athlete in fig $\mathbf{B}$$\mathbf{B}$B\mathbf{B} has taken 36 seconds from the start to reach the 300 m mark as shown. Calculate:
   如图所示，图 $\mathbf{B}$$\mathbf{B}$B\mathbf{B} 中的运动员从开始花了 36 秒到达 300 米大关。算：
   (a) his average speed during this 36 seconds
   （a） 他在这 36 秒内的平均速度
   (b) his average velocity due north during this 36 seconds
   （b） 他在这 36 秒内正北的平均速度
   © his average velocity due east during this 36 seconds.
   © 在这 36 秒内，他的平均速度正东。
2. A driver in a car travelling at about $40.2\mathrm{km}{\mathrm{h}}^{-1}$$40.2\mathrm{km}{\mathrm{h}}^{-1}$40.2kmh^(-1)40.2 \mathrm{~km} \mathrm{~h}^{-1} sees a cat run onto the road ahead.
   一名司机开着一辆 $40.2\mathrm{km}{\mathrm{h}}^{-1}$$40.2\mathrm{km}{\mathrm{h}}^{-1}$40.2kmh^(-1)40.2 \mathrm{~km} \mathrm{~h}^{-1} 车，看到一只猫跑到前面的道路上。
   (a) Convert $40.2\mathrm{km}{\mathrm{h}}^{-1}$$40.2\mathrm{km}{\mathrm{h}}^{-1}$40.2kmh^(-1)40.2 \mathrm{~km} \mathrm{~h}^{-1} into a speed in $\mathrm{m}{\mathrm{s}}^{-1}$$\mathrm{m}{\mathrm{s}}^{-1}$ms^(-1)\mathrm{m} \mathrm{s}^{-1}.
   （a） 转换为 $40.2\mathrm{km}{\mathrm{h}}^{-1}$$40.2\mathrm{km}{\mathrm{h}}^{-1}$40.2kmh^(-1)40.2 \mathrm{~km} \mathrm{~h}^{-1} 的速度 $\mathrm{m}{\mathrm{s}}^{-1}$$\mathrm{m}{\mathrm{s}}^{-1}$ms^(-1)\mathrm{m} \mathrm{s}^{-1} 。
   (b) The car travels 16.5 m whilst the driver is reacting to the danger. What is his reaction time?
   （b） 当驾驶员对危险做出反应时，汽车行驶了 16.5 m。他的反应时间是什么时候？
   © The car comes to a stop in 2.5 s . What is its deceleration?
   © 汽车在 2.5 秒内停下。它的减速是多少？
3. An electron in an $X$$X$XX-ray machine is accelerated from rest to half the speed of light in $1.7\times {10}^{-15}\mathrm{s}$$1.7\times {10}^{-15}\mathrm{s}$1.7 xx10^(-15)s1.7 \times 10^{-15} \mathrm{~s}. Calculate:
   射线机中的电子在 $X$$X$XX 中从静止加速到光速的一半。 $1.7\times {10}^{-15}\mathrm{s}$$1.7\times {10}^{-15}\mathrm{s}$1.7 xx10^(-15)s1.7 \times 10^{-15} \mathrm{~s} 算：
   (a) the speed the electron reaches in $\mathrm{m}{\mathrm{s}}^{-1}$$\mathrm{m}{\mathrm{s}}^{-1}$ms^(-1)\mathrm{m} \mathrm{s}^{-1}
   （a） 电子达到的速度 $\mathrm{m}{\mathrm{s}}^{-1}$$\mathrm{m}{\mathrm{s}}^{-1}$ms^(-1)\mathrm{m} \mathrm{s}^{-1}
   (b) the acceleration the electron experiences.
   （b） 电子经历的加速度。