Kinematics for IGCSE Physics | IGCSE 物理：运动学考点精讲

📚 Kinematics for IGCSE Physics | IGCSE 物理：运动学考点精讲

Kinematics is the branch of physics that describes motion without considering its causes. For IGCSE Physics, you will learn how to define key quantities like speed, velocity, and acceleration, and use graphs and equations to analyse motion. This article covers the essential points you need to master for your exam.

运动学是物理学中描述运动而不考虑其原因的分支。在 IGCSE 物理中，你将学习如何定义速率、速度、加速度等关键量，并使用图像和方程分析运动。本文涵盖你需要掌握的考试要点。

1. Scalars and Vectors | 标量与矢量

A scalar quantity has magnitude only, e.g., distance, speed, mass. A vector quantity has both magnitude and direction, e.g., displacement, velocity, acceleration. Understanding the difference is crucial for describing motion correctly.

标量只具有大小，例如路程、速率、质量。矢量既有大小又有方向，例如位移、速度、加速度。理解两者的区别对于正确描述运动至关重要。

When adding vectors, direction matters. For motion along a straight line, you can use positive and negative signs to represent opposite directions. This simplifies calculations involving displacement and velocity.

进行矢量相加时，方向很重要。对于直线运动，可以用正负号表示相反的方向。这可以简化涉及位移和速度的计算。

In IGCSE problems, you will often be asked to distinguish between distance (scalar) and displacement (vector). Remember: displacement is the shortest straight-line distance from start to finish, with a stated direction.

在 IGCSE 题目中，经常要求区分路程（标量）和位移（矢量）。请记住：位移是从起点到终点的最短直线距离，并需注明方向。

2. Distance and Displacement | 路程与位移

Distance is the total length of the path travelled by an object. It is always positive and does not depend on direction. Displacement is the change in position of an object; it is the straight-line distance in a specific direction.

路程是物体运动轨迹的总长度。它始终为正，且与方向无关。位移是物体位置的变化量，是特定方向上的直线距离。

If a runner completes a full lap of a 400 m track, the distance travelled is 400 m, but the displacement is 0 m because the start and end points coincide. This example highlights the key difference.

如果跑者绕 400 米跑道跑完一整圈，路程是 400 米，但位移是 0 米，因为起点和终点重合。这个例子突出了关键区别。

Always include a direction when stating a displacement, e.g., ’50 m east’. For distance, no direction is needed.

陈述位移时一定要包含方向，例如“向东 50 米”。对于路程，不需要方向。

3. Speed and Velocity | 速率与速度

Speed is a scalar quantity defined as the distance travelled per unit time: speed = distance ÷ time. Velocity is a vector quantity defined as the displacement per unit time: velocity = displacement ÷ time.

速率是标量，定义为单位时间内通过的路程：速率 = 路程 ÷ 时间。速度是矢量，定义为单位时间内的位移：速度 = 位移 ÷ 时间。

Average speed is calculated using total distance divided by total time taken. Average velocity uses net displacement divided by total time. Instantaneous speed or velocity is the value at a particular moment.

平均速率用总路程除以总时间来计算。平均速度用净位移除以总时间。瞬时速率或速度是某一特定时刻的数值。

In everyday language we often use ‘speed’ and ‘velocity’ interchangeably, but in physics you must be precise: a car travelling at a constant speed but changing direction has a changing velocity because velocity depends on direction.

在日常生活中我们常混用“速率”和“速度”，但在物理学中必须精确：一辆以恒定速率行驶但改变方向的汽车，其速度是变化的，因为速度取决于方向。

4. Acceleration | 加速度

Acceleration is the rate of change of velocity. It is a vector quantity. Acceleration = change in velocity ÷ time taken: a = (v – u) / t, where u is initial velocity, v is final velocity, and t is time.

加速度是速度的变化率。它是矢量。加速度 = 速度变化量 ÷ 所用时间：a = (v – u) / t，其中 u 是初速度，v 是末速度，t 是时间。

If an object is slowing down, the acceleration is opposite in direction to its velocity. This is often called deceleration or retardation, but in physics we still refer to it as negative acceleration.

如果物体在减速，加速度方向与速度方向相反。这常被称为减速，但在物理学中我们仍称之为负加速度。

Constant acceleration means the velocity changes by the same amount each second. When acceleration is zero, the object moves with constant velocity (uniform motion).

匀加速度意味着速度每秒变化相同的量。当加速度为零时，物体做匀速运动（恒定速度）。

5. Equations of Uniformly Accelerated Motion (SUVAT) | 匀加速直线运动方程

When acceleration is constant, we can use the SUVAT equations to relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). These are essential for solving kinematics problems.

当加速度恒定时，我们可以用 SUVAT 方程将位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）联系起来。这些方程对于解运动学问题至关重要。

v = u + a t

s = ½ (u + v) t

s = u t + ½ a t²

v² = u² + 2 a s

The variables and their meanings are summarised in the table below. You must be able to select the correct equation depending on which quantities are given and which one you need to find.

下表中总结了各变量及其含义。你必须能够根据已知量和待求量选择合适的方程。

Symbol	Quantity	SI unit
s	displacement	metre (m)
u	initial velocity	m/s
v	final velocity	m/s
a	acceleration	m/s²
t	time	second (s)

Always check that all quantities are in consistent SI units before substituting into the equations. Convert km/h to m/s by dividing by 3.6.

代入方程前，务必检查所有量都已化为一致的 SI 单位。将 km/h 换算为 m/s 需要除以 3.6。

6. Free Fall and Acceleration due to Gravity | 自由落体与重力加速度

Near the Earth’s surface, all objects fall with the same acceleration due to gravity, g, provided air resistance is negligible. The standard value of g is approximately 9.8 m/s², but for IGCSE you might be told to use 10 m/s².

在地球表面附近，只要空气阻力可忽略，所有物体都以相同的重力加速度 g 下落。g 的标准值约为 9.8 m/s²，但在 IGCSE 中你可能被要求使用 10 m/s²。

An object dropped from rest (u = 0) will have its velocity increase by g each second downwards. The equations of uniformly accelerated motion apply directly, with a = g and displacement measured vertically.

从静止（u = 0）下落的物体，其向下的速度每秒增加 g。匀加速运动方程可直接使用，其中 a = g，位移沿竖直方向测量。

If an object is thrown upwards, the acceleration is still g downwards. At the highest point, the velocity is zero momentarily, but the acceleration is still g. This is a common source of confusion.

如果物体向上抛出，加速度仍然是向下的 g。在最高点，速度瞬间为零，但加速度仍为 g。这是一个常见的混淆点。

7. Distance-Time Graphs | 距离-时间图

A distance-time graph plots distance travelled on the vertical axis and time on the horizontal axis. The gradient (slope) of the graph represents speed.

距离-时间图将所走路程标在纵轴上，时间标在横轴上。图的梯度（斜率）表示速率。

A straight, sloping line indicates constant speed. A horizontal line (zero gradient) means the object is stationary. A steeper line means a higher speed. Curved lines indicate changing speed (acceleration or deceleration).

一条倾斜的直线表示匀速。水平线（梯度为零）意味着物体静止。线条越陡表示速率越大。曲线表示变速（加速或减速）。

To find the speed at an instant, draw a tangent to the curve and calculate its gradient. The total distance travelled can be read directly from the vertical axis at any time.

要找出瞬时速率，可画出曲线的切线并计算其梯度。任何时刻的总路程可以直接从纵轴上读出。

8. Speed-Time (Velocity-Time) Graphs | 速度-时间图

A speed-time graph is one of the most powerful tools in kinematics. It plots speed (or velocity) on the vertical axis against time on the horizontal axis. The gradient of a speed-time graph gives acceleration.

速度-时间图是运动学中最强大的工具之一。它将速率（或速度）标在纵轴上，时间标在横轴上。速度-时间图的梯度表示加速度。

A horizontal line indicates zero acceleration (constant speed). A sloping straight line shows constant acceleration. A curve means the acceleration is changing.

水平线表示加速度为零（匀速）。倾斜直线表示匀加速。曲线意味着加速度在变化。

If the graph falls below the time axis, the velocity is negative, indicating motion in the opposite direction. This is important when interpreting full velocity-time graphs.

如果图线降至时间轴以下，速度为负，表示运动方向相反。在解读完整的速度-时间图时，这一点很重要。

9. Area under Speed-Time Graph | 速度-时间图下面积

The area enclosed between the speed-time graph and the time axis represents the distance travelled. For a velocity-time graph with direction, the area represents displacement (area above axis is positive displacement, below is negative).

速度-时间图与时间轴所围成的面积代表所走路程。对于带方向的速度-时间图，面积代表位移（时间轴上方面积为正位移，下方面积为负位移）。

You can calculate areas using simple geometric shapes: rectangles, triangles, and trapeziums. For non-linear graphs, you may be asked to estimate the area by counting squares or approximate with shapes.

你可以用简单的几何形状计算面积：矩形、三角形和梯形。对于非线性图像，可能要求通过数格子或用形状近似来估算面积。

This principle is vital for solving problems where the acceleration is not constant, because the SUVAT equations cannot be applied directly.

这一原理对于解决非匀加速问题至关重要，因为此时不能直接使用 SUVAT 方程。

10. Motion under Gravity and Vertical Projection | 竖直方向抛体运动

When an object is projected vertically upwards, it decelerates at g until it stops momentarily, then accelerates downwards at g. Taking ‘up’ as positive, acceleration a = -g during the whole flight.

当物体竖直向上抛出时，它以加速度 g 减速直至瞬间停止，然后以 g 向下加速。若取“向上”为正方向，则整个飞行中加速度 a = -g。

The time to reach maximum height equals the time to fall back to the starting point if air resistance is negligible. The launch speed equals the landing speed (but opposite in direction).

如果空气阻力可忽略，物体上升至最大高度所用的时间等于落回出发点所用的时间。发射速率等于落地速率（方向相反）。

You can use the SUVAT equations with a = -9.8 m/s². At the maximum height, v = 0. Common IGCSE questions ask for maximum height or total time of flight.

你可以使用 SUVAT 方程，取 a = -9.8 m/s²。在最大高度处，v = 0。常见的 IGCSE 题目会要求计算最大高度或总飞行时间。

11. Experiments: Measuring Speed and Acceleration | 实验：测量速率和加速度

In the laboratory, average speed can be measured by timing how long an object takes to travel a known distance, using a ruler and stopwatch. For more accuracy, light gates connected to a timer are used.

在实验室中，可以用尺子和秒表测量物体通过已知距离所用的时间，从而计算出平均速率。为了更准确，可使用连接计时器的光电门。

To measure acceleration, you can use a trolley on a sloping track, ticker tape and a ticker timer. The dots on the tape show the motion: increasing gaps mean acceleration.

要测量加速度，可以使用倾斜轨道上的小车、纸带和打点计时器。纸带上的点显示运动情况：点间距增大表示加速度。

One classic experiment determines g by free fall. A ball bearing is dropped from rest past two light gates a known distance apart; the time between them gives the acceleration using s = ut + ½at², with u=0.

经典的测量 g 的实验是自由落体法。让钢球从静止下落，通过两个相距已知距离的光电门；根据时间使用 s = ut + ½at²（u=0）即可求出加速度。

Always repeat measurements, calculate averages, and plot graphs where possible to reduce random errors.

始终重复测量，计算平均值，并尽可能画出图表以减少随机误差。

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

Confusing distance with displacement is a top mistake. Always check whether a question asks for a scalar or vector quantity. Include direction for vectors.

混淆路程和位移是最常见的错误。始终检查题目要求的是标量还是矢量。对于矢量要写出方向。

Using inconsistent units leads to wrong answers. Convert all speeds to m/s, distances to m, and times to s before using formulas unless the question specifies otherwise.

单位不一致会导致错误答案。在使用公式前，除非题目另有说明，否则将所有速率换算为 m/s、距离换算为 m、时间换算为 s。

Misinterpreting graphs: the gradient of a distance-time graph is speed, the gradient of a speed-time graph is acceleration, and the area under a speed-time graph is distance. Do not mix these up.

误读图像：距离-时间图的梯度是速率，速度-时间图的梯度是加速度，速度-时间图下的面积是路程。不要混淆这些概念。

When an object is thrown upwards, many students forget that acceleration is still g downwards at the highest point. The velocity is zero, not the acceleration.

当物体向上抛出时，许多学生忘记在最高点加速度仍然是向下的 g。速度为零，加速度不为零。

Practise drawing tangent lines on curved graphs to find instantaneous speed or acceleration. Show your working clearly and always write the formula before substituting numbers.

练习在曲线图上画切线以求瞬时速率或加速度。清晰展示解题步骤，并在代入数值前先写出公式。

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Kinematics for IGCSE Physics | IGCSE 物理：运动学 考点精讲