📚 Unit 1 Physics Homework: Measurements, Vectors and Motion (pp. 001–023) | 第一单元物理作业：测量、矢量与运动（第001–023页）
This guide covers the core ideas in Unit 1 pages 001–023, with a special focus on the 9C homework set. You will learn how to describe physical quantities, distinguish scalar and vector quantities, interpret motion graphs, and apply the SUVAT equations to solve kinematics problems. The worked methods below are designed to help you complete homework accurately and revise for A-Level Physics assessments.
本指南涵盖第一单元第001–023页的核心内容，并重点讲解9C作业。你将学习如何描述物理量、区分标量和矢量、解读运动图像，以及运用SUVAT方程解决运动学问题。以下的方法与例题旨在帮助你准确完成作业，并为A-Level物理考试做好复习。
1. SI Units and Prefixes | 国际单位制与单位前缀
Every physical quantity is expressed using the SI system. The base units include the kilogram (kg) for mass, metre (m) for length, second (s) for time, ampere (A) for electric current, kelvin (K) for temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity. Derived units such as newton (N) and joule (J) are combinations of these base units.
每个物理量都使用国际单位制表示。基本单位包括质量的千克（kg）、长度的米（m）、时间的秒（s）、电流的安培（A）、温度的开尔文（K）、物质的量的摩尔（mol）以及光强的坎德拉（cd）。像牛顿（N）和焦耳（J）这样的导出单位由这些基本单位组合而成。
When converting prefixes, you must be confident with powers of ten. Common examples include kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), and nano (10⁻⁹). In motion problems, convert all speeds to m s⁻¹ before using SUVAT equations.
在进行单位换算时，你必须熟练掌握10的幂次。常见的例子包括千（10³）、厘（10⁻²）、毫（10⁻³）、微（10⁻⁶）和纳（10⁻⁹）。在运动问题中，使用SUVAT方程前应先将所有速度换算为m s⁻¹。
| Prefix | Symbol | Power of 10 |
|---|---|---|
| kilo | k | 10³ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | μ | 10⁻⁶ |
2. Scalars and Vectors | 标量与矢量
A scalar quantity has magnitude only, while a vector quantity has both magnitude and direction. This distinction is essential because vectors cannot be added in the same simple way as scalars. For example, two forces of 3 N and 4 N acting at right angles produce a resultant of 5 N, not 7 N.
标量只有大小，而矢量既有大小又有方向。这一区别至关重要，因为矢量不能像标量那样简单相加。例如，两个成直角的力3 N和4 N产生的合力为5 N，而不是7 N。
Typical scalar quantities include distance, speed, mass, time, energy, and temperature. Typical vector quantities include displacement, velocity, acceleration, force, and momentum. Always check whether a question asks for speed or velocity, since velocity must include a direction.
常见的标量包括路程、速率、质量、时间、能量和温度。常见的矢量包括位移、速度、加速度、力和动量。作答时一定要看清题目问的是速率还是速度，因为速度必须包含方向。
| Scalar | Vector |
|---|---|
| distance | displacement |
| speed | velocity |
| mass | weight |
| energy | force |
3. Distance, Displacement, Speed and Velocity | 路程、位移、速率与速度
Distance is the total length of a path travelled by an object, and it is a scalar. Displacement is the straight-line change in position from the starting point to the final point, and it is a vector. If a runner completes one full lap of a 400 m track, the distance is 400 m but the displacement is 0 m.
路程是物体运动轨迹的总长度，是一个标量。位移是从起点到终点的直线位置变化，是一个矢量。如果一名跑步者绕400 m跑道跑完一整圈，路程为400 m，但位移为0 m。
Speed is the rate at which distance is covered, while velocity is the rate at which displacement changes. Average speed is calculated using total distance over total time. Average velocity uses net displacement over total time, so its direction matters.
速率是路程随时间变化的快慢，而速度是位移随时间变化的快慢。平均速率用总路程除以总时间计算。平均速度用净位移除以总时间计算，因此其方向很重要。
v = Δs / Δt
In this equation, v is average velocity, Δs is the change in displacement, and Δt is the time interval. The SI unit of velocity is m s⁻¹.
在这个方程中，v表示平均速度，Δs表示位移变化量，Δt表示时间间隔。速度的国际单位是m s⁻¹。
4. Acceleration | 加速度
Acceleration is the rate of change of velocity, so it is a vector quantity. A negative acceleration can mean the object is slowing down, but it can also mean the object is moving in the opposite direction depending on the chosen sign convention.
加速度是速度的变化率，因此它是一个矢量。负加速度可能表示物体在减速，但根据所选取的正方向，它也可能表示物体朝相反方向运动。
a = Δv / Δt = (v − u) / t
Here a is acceleration, u is initial velocity, v is final velocity, and t is the time taken. The SI unit of acceleration is m s⁻².
这里a表示加速度，u表示初速度，v表示末速度，t表示所用时间。加速度的国际单位是m s⁻²。
5. Motion Graphs: Displacement–Time Graphs | 位移–时间图像
A displacement–time graph shows how displacement changes with time. The gradient of the graph at any point gives the velocity. A straight line means constant velocity, while a curve means the velocity is changing.
位移–时间图像显示位移随时间的变化。图像上任意一点的斜率表示速度。直线表示速度恒定，而曲线表示速度正在变化。
If the graph is horizontal, the gradient is zero, so the object is stationary. A steepening curve indicates increasing velocity, and a flattening curve indicates decreasing velocity. The sign of the gradient shows the direction of motion.
如果图像是水平的，斜率为零，表示物体静止。曲线越来越陡表示速度在增大，曲线越来越平缓表示速度在减小。斜率的正负表示运动的方向。
6. Motion Graphs: Velocity–Time Graphs | 速度–时间图像
A velocity–time graph is one of the most useful tools in kinematics. The gradient of the graph gives the acceleration, while the area between the graph and the time axis gives the displacement. You should always label regions of acceleration, constant velocity, and deceleration.
速度–时间图像是运动学中最有用的工具之一。图像的斜率表示加速度，而图像与时间轴之间的面积表示位移。你应当始终标出加速、匀速和减速的区域。
For a sloping straight line, the acceleration is constant. If the line goes below the time axis, the object is moving in the negative direction. To find total distance travelled, add the magnitudes of each area rather than simply adding signed areas.
对于倾斜的直线，加速度是恒定的。如果直线位于时间轴以下，表示物体向负方向运动。求总路程时，应将各面积的绝对值相加，而不是简单地把带符号的面积相加。
7. Equations of Motion (SUVAT) | 运动学方程（SUVAT）
The SUVAT equations describe motion with constant acceleration in a straight line. They link displacement s, initial velocity u, final velocity v, acceleration a, and time t. These equations only apply when acceleration is constant.
SUVAT方程描述匀加速直线运动。它们将位移s、初速度u、末速度v、加速度a和时间t联系起来。这些方程仅适用于加速度恒定的情况。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Before using any equation, write down the five SUVAT variables and identify which three you know and which one you need. Always use a consistent direction as positive, and convert units to SI first.
在使用任何方程之前，先写出五个SUVAT变量，确认已知哪三个量以及需要求哪个量。始终选一个一致的方向作为正方向，并先将单位换算为国际单位。
8. Free Fall and g | 自由落体与重力加速度g
Free fall is motion under gravity alone, with negligible air resistance. Near the Earth’s surface, all objects fall with the same acceleration g = 9.81 m s⁻², regardless of their mass. The direction of g is always downwards.
自由落体是仅在重力作用下的运动，空气阻力可忽略。在地球表面附近，所有物体无论质量大小，都以相同的加速度g = 9.81 m s⁻²下落。g的方向始终向下。
For an object thrown upwards, its velocity decreases by 9.81 m s⁻¹ every second until it reaches the highest point, where velocity is momentarily zero. The acceleration is still 9.81 m s⁻² downwards at this point, so acceleration is not zero.
对于向上抛出的物体，其速度每秒减小9.81 m s⁻¹，直到到达最高点，此时速度瞬间为零。这时加速度仍然是向下9.81 m s⁻²，因此加速度并不为零。
9. Resolving Vectors | 矢量分解
A vector acting at an angle can be split into perpendicular components. For a force F at angle θ to the horizontal, the horizontal component is F cos θ and the vertical component is F sin θ. This method is essential for solving problems involving tension, weight on slopes, or projectile motion.
一个与水平成角度的矢量可以分解为互相垂直的分量。对于与水平成θ角的力F，水平分量为F cos θ，竖直分量为F sin θ。这种方法对解决涉及张力、斜面上的重力或抛体运动的问题至关重要。
Fₓ = F cos θ, Fᵧ = F sin θ
After resolving, treat each direction independently using the SUVAT equations if acceleration is constant. The resultant vector can be found using Pythagoras and trigonometry when combining perpendicular components.
分解之后，如果加速度恒定，可以用SUVAT方程分别处理每个方向。合并互相垂直的分量时，可以用勾股定理和三角函数求合矢量。
10. Experimental Errors and Uncertainty | 实验误差与不确定度
In practical work from pages 001–023, measurements often include uncertainty. The absolute uncertainty is usually half the smallest division on the measuring instrument. For example, a metre ruler with millimetre divisions has an absolute uncertainty of ±0.5 mm.
在第001–023页的实验中，测量值通常包含不确定度。绝对不确定度通常是测量仪器最小刻度的一半。例如，毫米刻度的米尺绝对不确定度为±0.5 mm。
Percentage uncertainty is calculated by dividing the absolute uncertainty by the measured value and multiplying by 100%. When quantities are multiplied or divided, add percentage uncertainties. When a reading is taken repeatedly, the spread or half-range can be used as the uncertainty.
百分不确定度等于绝对不确定度除以测量值再乘以100%。当物理量相乘或相除时，应将百分不确定度相加。当重复读取数据时，可以用数据的离散范围或半范围作为不确定度。
11. Homework 9C: Strategy and Common Mistakes | 9C作业策略与常见错误
The 9C homework set usually tests motion graphs, vectors, and SUVAT applications. A reliable strategy is to read the question slowly, note the given quantities, convert units, choose the correct equation, and check whether the final answer requires a direction.
9C作业通常考查运动图像、矢量和SUVAT方程的应用。一个可靠的策略是：慢慢读题，记录已知量，换算单位，选择正确的方程，并检查最终答案是否需要方向。
- Draw a labelled diagram and choose a positive direction.
- List the SUVAT variables and mark unknown ones with a question mark.
- Check the sign of acceleration and displacement consistently.
- Convert km h⁻¹ to m s⁻¹ by dividing by 3.6.
- State final answers with units and, for vectors, a direction.
- 画出带标注的示意图并选择正方向。
- 列出SUVAT变量，用问号标出未知量。
- 始终一致地检查加速度和位移的正负号。
- 将km h⁻¹转换为m s⁻¹时除以3.6。
- 最终答案要写明单位，矢量还要写明方向。
Common mistakes include using distance when displacement is required, forgetting to square time in s = ut + ½at², and treating acceleration as zero at the peak of a projectile’s motion. Review these points before submitting your homework.
常见错误包括：应求位移时用了路程；在使用s = ut + ½at²时忘记将时间平方；在抛体运动最高点时误认为加速度为零。交作业前请复习这些要点。
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