Units of Acceleration | 加速度的单位

📚 Units of Acceleration | 加速度的单位

Acceleration is one of the most fundamental concepts in kinematics. It tells us how quickly an object’s velocity changes with time. In A-Level Physics, a clear understanding of what acceleration means and how its units are expressed — from the standard SI unit to various practical alternatives — is essential for solving motion problems, interpreting graphs, and setting up laboratory experiments correctly.

加速度是运动学中最基本的概念之一，它告诉我们一个物体的速度随时间变化的快慢。在 A-Level 物理中，清晰理解加速度的含义以及其单位的表达方式——从标准的 SI 单位到各种实用的替代单位——对于解决运动问题、解读图像和正确设置实验至关重要。

1. Introduction to Acceleration | 加速度简介

When we observe a car speeding up, a ball falling under gravity or a rocket launching into space, we witness acceleration. Acceleration quantifies the rate of change of velocity. If an object travels in a straight line and its speed increases by a certain amount each second, we say it undergoes uniform acceleration.

当我们观察到汽车加速、球在重力作用下下落或火箭发射升空时，我们见证的就是加速度。加速度量化了速度的变化率。如果一个物体沿直线运动，并且其速度每秒增加一定的量，我们就说它做匀加速运动。

In both everyday language and physics, acceleration means ‘getting faster’, but in physics it is defined more precisely: it includes slowing down (deceleration or negative acceleration) and changes in direction. Because velocity is a vector, acceleration is also a vector. Understanding the units used to measure it allows us to link numerical calculations with real-world observations.

在日常语言和物理学中，加速度都意味着“变快”，但在物理学中它被更精确地定义：它包括减速（负加速度）和方向的变化。由于速度是矢量，加速度也是矢量。理解用来测量加速度的单位，使我们能够将数值计算与现实世界的观察联系起来。

2. Defining Acceleration | 定义加速度

Acceleration a is defined as the rate of change of velocity with respect to time. Mathematically, average acceleration is given by:

加速度 a 定义为速度随时间的变化率。数学上，平均加速度由下式给出：

a = (v – u) / t

where v is final velocity, u is initial velocity and t is the time interval. The instantaneous acceleration is the limiting value as Δt → 0.

其中 v 是末速度，u 是初速度，t 是时间间隔。瞬时加速度是 Δt → 0 时的极限值。

Since velocity is measured in metres per second (m/s or m s⁻¹) and time in seconds (s), the unit of acceleration follows directly from this definition. This is the core idea: the unit of acceleration must represent a velocity change per unit time. In CIE A-Level Physics, you are expected to be able to derive this from first principles.

由于速度以米每秒（m/s 或 m s⁻¹）为单位，时间以秒（s）为单位，加速度的单位就直接从该定义推导出来。这就是核心思想：加速度的单位必须表示每单位时间的速度变化。在 CIE A-Level 物理中，要求你能够从基本原理推导出这一点。

3. SI Unit: Metres per Second Squared | 国际单位：米每二次方秒

The SI unit of acceleration is the metre per second squared, symbol m/s² or m s⁻². It is derived by dividing the SI unit of velocity (m/s) by the SI unit of time (s). The result is a composite unit that can be read as ‘metres per second per second’, emphasising the change of velocity per second.

加速度的国际单位制（SI）单位是米每二次方秒，符号为 m/s² 或 m s⁻²。它是将速度的 SI 单位（m/s）除以时间的 SI 单位（s）得到的。结果是一个组合单位，可以读作“米每秒每秒”，强调速度每秒的变化。

Strictly speaking, m/s² contains a negative exponent in its base form: m s⁻². When writing an answer, you can use either notation, but in equations the form m s⁻² often helps with dimensional consistency. The unit captures the idea that if an object accelerates at 1 m/s², its velocity increases by 1 m/s every second.

严格来说，m/s² 在其基本形式中包含负指数：m s⁻²。在书写答案时，你可以使用任何一种符号，但在方程式中，m s⁻² 形式通常有助于保持量纲一致性。这个单位体现了这样一种概念：如果一个物体以 1 m/s² 加速，它的速度每秒增加 1 m/s。

In CIE exam papers, both m/s² and m s⁻² are accepted. When plotting graphs, you may need to label axes with correct unit symbols, so accurate notation is important.

在 CIE 试卷中，m/s² 和 m s⁻² 都是可接受的。绘制图像时，你可能需要用正确的单位符号标注坐标轴，因此准确的符号书写很重要。

4. Derivation of the Unit from Definition | 从定义推导单位

To understand why the unit is m s⁻², we can break it down step by step. Velocity v has dimensions of length divided by time, LT⁻¹. Its SI unit is m s⁻¹. Acceleration is change in velocity divided by time, so:

为了理解为什么单位是 m s⁻²，我们可以逐步分解。速度 v 的量纲是长度除以时间，LT⁻¹。其 SI 单位是 m s⁻¹。加速度是速度的变化除以时间，因此：

unit of a = (m s⁻¹) / s = m s⁻²

This shows that the unit of acceleration is metres per second squared. The exponent arises because seconds appear twice in the denominator: once from velocity and once from the additional time interval.

这表明加速度的单位是米每二次方秒。指数出现是因为秒在分母中出现了两次：一次来自速度，一次来自额外的时间间隔。

You can also check the unit by rearranging a kinematic equation, for example v² = u² + 2as. Rearranging for a gives a = (v² – u²)/(2s). Since v² has units m² s⁻² and s has units m, dividing gives m s⁻², which is consistent.

你也可以通过重新排列运动学方程来检查单位，例如 v² = u² + 2as。重新排列求 a 得到 a = (v² – u²)/(2s)。由于 v² 的单位是 m² s⁻²，s 的单位是 m，相除得到 m s⁻²，这是一致的。

This derivation method is a powerful check for any motion problem. If your calculated acceleration does not have units of m s⁻², you know an error has occurred.

这种推导方法是检查任何运动问题的有力工具。如果你计算出的加速度单位不是 m s⁻²，你就知道出现了错误。

5. Alternative Units in Common Use | 常用的其他单位

While m s⁻² is standard, other units appear in practical contexts. Kilometres per hour per second (km/h/s or km h⁻¹ s⁻¹) is frequently used in transport and everyday situations. For instance, a car’s acceleration might be quoted as ‘0 to 100 km/h in 8 seconds’, giving an average acceleration in km/h/s.

虽然 m s⁻² 是标准单位，但在实际情况中会出现其他单位。千米每时每秒（km/h/s 或 km h⁻¹ s⁻¹）常用于交通和日常场景。例如，一辆汽车的加速度可能被表述为“0 到 100 km/h 用时 8 秒”，从而给出以 km/h/s 为单位的平均加速度。

Centimetres per second squared (cm/s² or cm s⁻²) is used in the CGS (centimetre-gram-second) system, which is still found in some older textbooks and in certain fields like geophysics. Additionally, in some engineering contexts, acceleration may be expressed in terms of g, the standard acceleration due to gravity (9.81 m s⁻²). We will explore this later.

厘米每二次方秒（cm/s² 或 cm s⁻²）在 CGS（厘米-克-秒）单位制中使用，该单位制至今仍出现在一些旧教材和地球物理等特定领域中。此外，在某些工程情景下，加速度可能用 g（标准重力加速度，9.81 m s⁻²）的倍数来表示。我们稍后会探讨这一点。

At A-Level, you are expected to convert confidently between these different units. Always check which unit a problem provides and what the final answer requires.

在 A-Level 阶段，要求你能够自信地在这些不同单位之间进行转换。始终要检查题目给出了什么单位，以及最终答案要求使用什么单位。

6. Converting Between Units of Acceleration | 加速度单位之间的转换

Conversion between km/h/s and m/s² is a common examination task. Since 1 km = 1000 m and 1 h = 3600 s, we have:

在 km/h/s 和 m/s² 之间转换是常见的考试任务。由于 1 km = 1000 m，1 h = 3600 s，我们有：

1 km/h/s = (1000 m) / (3600 s) / s = (1000/3600) m s⁻² = 5/18 m s⁻² ≈ 0.2778 m s⁻²

Thus, to convert km/h/s to m/s², multiply by 5/18. To convert m/s² to km/h/s, multiply by 18/5 (3.6).

因此，要将 km/h/s 转换为 m/s²，乘以 5/18。要将 m/s² 转换为 km/h/s，乘以 18/5（3.6）。

Example: A car accelerates at 3 m/s². In km/h/s, this is 3 × 3.6 = 10.8 km/h/s. This means its speed increases by 10.8 km/h every second. This conversion clarifies why a car that feels brisk might have a numerical acceleration in km/h/s that seems large.

例子：一辆汽车以 3 m/s² 加速。以 km/h/s 表示，就是 3 × 3.6 = 10.8 km/h/s。这意味着它的速度每秒增加 10.8 km/h。这种转换揭示了为什么一辆感觉加速轻快的汽车，其以 km/h/s 为单位的数值会显得很大。

Another useful conversion: 1 cm/s² = 0.01 m/s², so to go from cm/s² to m/s², divide by 100. Always show your working clearly in exams to avoid factor-of-ten errors.

另一个有用的转换：1 cm/s² = 0.01 m/s²，因此从 cm/s² 转换为 m/s² 要除以 100。在考试中始终要清晰地展示计算过程，以避免十倍数量级的错误。

7. Acceleration Due to Gravity (g) and Its Units | 重力加速度(g)及其单位

Near the Earth’s surface, all objects in free fall experience a downward acceleration of approximately 9.81 m s⁻², denoted by the symbol g. This is a fundamental constant in physics and has units identical to acceleration. It is often used as a benchmark to compare other accelerations.

在地球表面附近，所有自由下落的物体都经历大约 9.81 m s⁻² 的向下加速度，用符号 g 表示。这是物理学中的一个基本常数，其单位与加速度相同。它经常被用作比较其他加速度的基准。

Sometimes g is expressed in units of N/kg, because gravitational field strength (force per unit mass) has this unit. Since 1 N = 1 kg m s⁻², dividing by kg gives m s⁻². Thus 9.81 N/kg is equivalent to 9.81 m s⁻². In A-Level Physics, you must recognise the equivalence of these two units.

有时 g 用 N/kg 为单位表示，因为重力场强度（每单位质量的力）具有这个单位。由于 1 N = 1 kg m s⁻²，除以 kg 得到 m s⁻²。因此 9.81 N/kg 等同于 9.81 m s⁻²。在 A-Level 物理中，你必须认识到这两个单位的等价性。

When working with projectile motion or inclined planes, g is always taken as positive downwards. Its value may be approximated as 10 m s⁻² in some CIE problems for simplicity, unless instructed otherwise.

在处理抛体运动或斜面问题时，g 总是被视为向下为正。在一些 CIE 问题中，为了方便可能会近似取 10 m s⁻²，除非另有说明。

8. The Gal and Other CGS Units | 伽(Gal)及其他厘米-克-秒单位

In the centimetre-gram-second (CGS) system, the unit of acceleration is the gal, named after Galileo. 1 Gal = 1 cm/s². This unit is used in gravimetry and seismology. A more common subunit is the milligal (mGal), equal to 10⁻³ cm/s² or 10⁻⁵ m/s².

在厘米-克-秒（CGS）单位制中，加速度的单位是伽（Gal），以伽利略命名。1 伽 = 1 cm/s²。该单位用于重力测量和地震学。更常用的子单位是毫伽（mGal），等于 10⁻³ cm/s² 或 10⁻⁵ m/s²。

Although not required in detail for CIE A-Level Physics, knowing about the gal helps you understand that different disciplines may adopt non-SI units for historical or practical reasons. If a question mentions these units, straightforward conversion using standard prefixes is expected.

虽然 CIE A-Level 物理不要求详细了解伽，但了解它可以帮助你理解不同学科可能出于历史或实际原因采用非 SI 单位。如果考题提到这些单位，只需使用标准前缀进行简单转换即可。

For reference: 1 m/s² = 100 Gal. The Earth’s gravity is about 981 Gal. Understanding these relationships reinforces your ability to handle prefix conversions.

供参考：1 m/s² = 100 伽。地球重力大约为 981 伽。理解这些关系可以加强你处理前缀换算的能力。

9. Dimensional Analysis of Acceleration | 加速度的量纲分析

Dimensional analysis uses the base dimensions of mass (M), length (L) and time (T) to check the consistency of equations. For acceleration, the dimension is length divided by time squared:

量纲分析利用质量（M）、长度（L）和时间（T）的基本量纲来检验方程的一致性。对于加速度，量纲是长度除以时间的平方：

[a] = LT⁻²

This means any formula purporting to give an acceleration must yield dimensions LT⁻². For example, in F = ma, force has dimensions MLT⁻²; dividing by mass M gives LT⁻², confirming the equation is homogeneous.

这意味着任何声称给出加速度的公式必须得出 LT⁻² 的量纲。例如，在 F = ma 中，力的量纲是 MLT⁻²；除以质量 M 得到 LT⁻²，确认该方程是齐次的。

If you derive an expression for acceleration and find dimensions like L²T⁻¹, you know it is incorrect. This is a key skill: always verify the units of your answer. In practical exam questions, you may be asked to determine the base units of a constant given an equation involving acceleration.

如果你推导出一个加速度表达式并发现其量纲如 L²T⁻¹，你就知道它是错误的。这是一项关键技能：始终要验证答案的单位。在实际考试题目中，你可能会被要求根据包含加速度的方程确定常数的基本单位。

Using dimensional analysis can also help you recall that the unit m s⁻² is equivalent to m⋅s⁻², and there is no kilogram involved unless the equation includes mass. This clarity reduces confusion between acceleration and force.

使用量纲分析还可以帮助你记住，单位 m s⁻² 等同于 m⋅s⁻²，除非方程中包含质量，否则不会涉及千克。这种清晰度可以减少加速度和力之间的混淆。

10. Acceleration as a Vector: Sign and Direction | 加速度作为矢量：符号和方向

Although the unit of acceleration (m/s²) is scalar in magnitude form, acceleration itself is a vector. When we describe the magnitude of an acceleration, we give a positive number with its unit, say 5 m/s². But to fully specify the acceleration, we must include direction, for example ‘5 m/s² due east’ or ‘−5 m/s² along a chosen axis’.

虽然加速度的单位（m/s²）在大小形式上是标量，但加速度本身是矢量。当我们描述加速度的大小时，会给出一个带有单位的正数，例如 5 m/s²。但要完整描述加速度，必须包含方向，例如“向东 5 m/s²”或“沿选定轴的 −5 m/s²”。

The sign in front of the unit indicates direction relative to a defined positive direction. In one-dimensional motion, negative acceleration can mean deceleration or acceleration in the negative direction. It is the combination of the sign of velocity and the sign of acceleration that determines whether the object speeds up or slows down. This level of care with signs is crucial when writing answers in CIE structured questions.

单位前的符号表示相对于定义的正方向的方向。在一维运动中，负加速度可以表示减速或沿负方向的加速。正是速度符号和加速度符号的组合决定了物体是加速还是减速。在 CIE 结构化问题中写答案时，这种对符号的谨慎处理至关重要。

Always keep the unit symbol m s⁻² as a magnitude identifier; add the vector direction in words or using unit vectors i, j in two-dimensional problems.

始终将单位符号 m s⁻² 视为大小的标识；在二维问题中用文字或单位矢量 i、j 添加矢量方向。

11. Typical Values and Orders of Magnitude | 典型值和数量级

Knowing typical accelerations in m/s² helps you judge whether your calculated answer is sensible. A family car might accelerate at about 2–3 m/s², while a high-performance car can reach 10 m/s². A sprinter leaves the blocks at around 3–5 m/s². An elevator typically accelerates upward at 1–1.5 m/s².

了解以 m/s² 为单位的典型加速度值，有助于你判断计算出的答案是否合理。家用汽车的加速度大约为 2–3 m/s²，而高性能汽车可达 10 m/s²。短跑运动员起跑时的加速度约为 3–5 m/s²。电梯通常以 1–1.5 m/s² 的加速度向上运动。

Free-fall acceleration on Earth is 9.81 m/s², on the Moon about 1.6 m/s². A centrifuge may produce accelerations of thousands of m/s², often expressed as multiples of g. By having a mental reference, you can spot unrealistic results, such as a cricket ball accelerating at 500 m/s² from a bowler’s hand.

地球上的自由落体加速度为 9.81 m/s²，月球上约为 1.6 m/s²。离心机可产生数千 m/s² 的加速度，通常以 g 的倍数表示。通过建立心理参考，你可以识别出不切实际的结果，例如板球从投手手中以 500 m/s² 加速。

Always convert to SI before comparing. For instance, a quoted acceleration of ’10 km/h/s’ is only about 2.78 m/s², which is quite modest.

在比较之前，一定要转换成 SI 单位。例如，一个标称“10 km/h/s”的加速度仅约为 2.78 m/s²，实际上是相当适中的。

12. Common Mistakes and Exam Tips | 常见错误与考试技巧

One frequent error is confusing velocity units with acceleration units. Students might write m/s when they mean m/s² or vice versa. Always think conceptually: acceleration is a rate of change of velocity, so an extra time division appears. Checking the unit of your final answer against the definition is a quick validation.

一个常见的错误是将速度单位与加速度单位混淆。学生可能会在本意是 m/s² 时写成 m/s，或者相反。始终要从概念上思考：加速度是速度的变化率，因此会出现额外的时间除法。根据定义检查最终答案的单位是一种快速的验证方法。

Another pitfall is incorrect conversion from km/h to m/s. Remember: 1 km/h = 1000/3600 m/s = 5/18 m/s. When converting km/h/s to m/s², you must apply this factor once to the velocity part. Similarly, failing to include the square when converting m/s² to cm/s²: 1 m/s² = 100 cm/s², not 100 cm/s²? Actually, since 1 m = 100 cm, 1 m/s² = 100 cm/s² (because time unit stays the same). But if you had cm/s² to m/s², you divide by 100. Make sure you don’t square the length conversion erroneously — it’s already linear.

另一个陷阱是从 km/h 到 m/s 的错误转换。记住：1 km/h = 1000/3600 m/s = 5/18 m/s。当将 km/h/s 转换为 m/s² 时，你只需要对速度部分应用这个因子。同样，在将 m/s² 转换为 cm/s² 时未能正确包含平方关系：1 m/s² = 100 cm/s²（因为时间单位保持不变）。但如果你从 cm/s² 转换到 m/s²，则除以 100。确保不要错误地对长度转换进行平方——它已经是线性的了。

Exam tip: When a question gives a velocity-time graph, the gradient of the line gives the acceleration. The unit of that gradient is (m/s)/s = m/s². Always label the gradient with the correct unit. If the graph uses km/h on the y-axis, convert to m/s first, or state the unit as km/h/s, but then be aware that this is not an SI unit and may require conversion if used in further calculations. Always read the question to see if a specific unit is requested.

考试技巧：当题目给出速度-时间图像时，图线的斜率代表加速度。该斜率的单位是 (m/s)/s = m/s²。始终用正确的单位标注斜率。如果图像中 y 轴使用 km/h，请先转换为 m/s，或者声明单位为 km/h/s，但要意识到这不是 SI 单位，如果用于进一步计算可能需要转换。始终仔细读题，看是否有特定的单位要求。

Finally, keep your working clear and separate numerical values from units. A structured layout, such as writing ‘a = Δv / t = (20 m/s) / (5 s) = 4 m/s²’, minimises unit errors and helps examiners award marks.

最后，保持计算过程清晰，将数值和单位分开。有条理的布局，例如写出“a = Δv / t = (20 m/s) / (5 s) = 4 m/s²”，可以最大限度减少单位错误，并帮助考官授予分数。

Published by TutorHao | Physics Revision Series | aleveler.com

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