IGCSE CIE Physics: Kinematics Key Points | IGCSE CIE 物理：运动学考点精讲

📚 IGCSE CIE Physics: Kinematics Key Points | IGCSE CIE 物理：运动学考点精讲

Kinematics describes the motion of objects without considering the forces that cause this motion. For IGCSE CIE Physics, a solid grasp of scalars and vectors, displacement-time and velocity-time graphs, and uniform acceleration equations is essential. This revision guide walks you through every critical concept with clear explanations and common pitfalls, helping you tackle kinematics questions confidently.

运动学研究物体的运动规律，而不涉及引起运动的力。在 IGCSE CIE 物理中，牢固掌握标量与矢量、位移-时间图和速度-时间图、以及匀加速运动方程至关重要。这篇复习指南将带你梳理每个重要概念，提供清晰解释并指出常见错误，帮助你自信应对运动学题目。

1. Scalars and Vectors | 标量与矢量

A scalar quantity has magnitude only. Examples include distance, speed, mass, time, and energy. Scalar addition uses ordinary arithmetic.

标量只有大小。例如路程、速率、质量、时间和能量。标量相加使用普通算术。

A vector quantity has both magnitude and direction. Displacement, velocity, acceleration, force, and momentum are vectors. When adding vectors, you must account for direction, often by head-to-tail addition or resolving into components.

矢量既有大小又有方向。位移、速度、加速度、力和动量都是矢量。矢量相加时必须考虑方向，通常采用首尾相接法或分解为分量。

On a straight line, you can treat one direction as positive and the opposite as negative. This simplification is used often in IGCSE problems involving motion along one axis.

在直线上，你可以将一个方向规定为正，相反方向为负。IGCSE 题目中常采用这种简化方法来处理一维运动。

2. Distance and Displacement | 路程与位移

Distance is the total length of the path travelled by an object. It is a scalar and never decreases. Displacement is the shortest straight-line distance from the initial position to the final position, together with the direction.

路程是物体运动轨迹的总长度，是一个标量，且不会减少。位移是从初始位置到最终位置的最短直线距离，并带有方向。

For example, if a car travels 3 km north and then 4 km south, the total distance travelled is 7 km, but the displacement is 1 km south.

例如，一辆汽车向北行驶 3 公里，再向南行驶 4 公里，总路程为 7 公里，但位移是向南 1 公里。

3. Speed and Velocity | 速率与速度

Speed is the rate of change of distance. It is a scalar. Average speed = total distance / total time. Velocity is the rate of change of displacement. It is a vector. Average velocity = total displacement / total time.

速率是路程的变化率，是一个标量。平均速率 = 总路程 / 总时间。速度是位移的变化率，是一个矢量。平均速度 = 总位移 / 总时间。

Uniform velocity means the object moves with constant speed in a constant direction. If either speed or direction changes, the velocity changes.

匀速意味着物体以恒定的速率沿直线运动。如果速率或方向改变，速度就发生变化。

4. Acceleration | 加速度

Acceleration is the rate of change of velocity. It is a vector. a = (v – u) / t, where u is initial velocity, v is final velocity, and t is the time taken. Deceleration is simply negative acceleration (a negative value in the chosen direction).

加速度是速度的变化率，是一个矢量。a = (v – u) / t，其中 u 是初速度，v 是末速度，t 是所用时间。减速就是在所选方向上加速度为负值。

Uniform acceleration means the velocity changes by equal amounts in equal time intervals. In many IGCSE problems, acceleration is constant, such as near the Earth’s surface (g ≈ 9.8 m/s²).

匀加速度意味着在相等的时间间隔内速度的变化量相等。许多 IGCSE 题目中加速度是恒定的，比如地表附近（g ≈ 9.8 m/s²）。

5. Equations of Uniformly Accelerated Motion | 匀加速运动方程

For motion in a straight line with constant acceleration, the four key equations are:

对于匀加速度直线运动，四个关键方程如下：

1. v = u + at

2. s = (u + v) / 2 × t

3. s = ut + ½at²

4. v² = u² + 2as

Here, s is displacement, u is initial velocity, v is final velocity, a is constant acceleration, and t is time. These equations are valid only when acceleration is constant.

其中，s 是位移，u 是初速度，v 是末速度，a 是恒定加速度，t 是时间。这些方程仅在加速度恒定时有效。

In problem solving, list the known quantities and the unknown, then choose the equation that connects them without needing a variable you don’t have. Pay careful attention to signs: assign a positive direction and give all vectors appropriate + or – values.

解题时，列出已知量和未知量，然后选择包含这些量但不需要未知变量的方程。注意正负号：规定正方向，并给所有矢量赋予适当的正或负值。

6. Distance-Time Graphs | 距离-时间图

A distance-time graph plots distance (on the y-axis) against time (on the x-axis). The slope (gradient) of the graph gives the speed of the object. A straight, upward sloping line indicates constant speed; a steeper slope means a higher speed.

距离-时间图以距离（y 轴）对时间（x 轴）作图。图像的斜率（梯度）表示物体的速率。一条向上的倾斜直线表示匀速；斜率越大，速率越高。

A horizontal line means the object is stationary. A curved line indicates changing speed: if the slope increases, the object is accelerating; if it decreases, decelerating. The total distance is read directly from the y-axis; the average speed is the final distance divided by the total time.

水平线表示物体静止。曲线表示速率在变化：如果斜率增大，物体在加速；如果斜率减小，物体在减速。总路程直接从 y 轴读取；平均速率 = 总路程 / 总时间。

Note: a distance-time graph cannot show negative distance because distance is a scalar. It never goes down.

注意：距离-时间图不会出现负距离，因为路程是标量，图像永远不会下降。

7. Speed-Time and Velocity-Time Graphs | 速度-时间图

A velocity-time graph plots velocity (or speed if direction is not considered) against time. The gradient gives the acceleration: a positive gradient means acceleration in the positive direction, a negative gradient means deceleration (or acceleration in the negative direction).

速度-时间图以速度（若不考虑方向则为速率）对时间作图。斜率表示加速度：正斜率表示向正方向加速，负斜率表示减速（或向负方向加速）。

The area under a velocity-time graph represents the displacement (if velocity includes direction) or distance travelled (if speed is used). For a curve, count squares or use area formulas. A horizontal line indicates constant velocity.

速度-时间图下的面积表示位移（若速度含方向）或运动的路程（若使用速率）。对于曲线，采用数格子的方法或面积公式。水平线表示匀速运动。

Common graph shapes: a straight line through the origin in a v-t graph means uniform acceleration from rest; a straight line not through the origin means uniform acceleration with an initial velocity; a horizontal line followed by a sloping line downwards represents constant velocity then uniform deceleration to rest.

常见图像形状：速度-时间图中通过原点的直线表示从静止开始匀加速；不通过原点的直线表示有初速度的匀加速；水平线后接着向下倾斜的线表示先匀速后匀减速至静止。

8. Free Fall | 自由落体

Free fall is the motion of an object under the influence of gravity alone, with no air resistance. Near the Earth’s surface, all objects experience a constant acceleration due to gravity, g ≈ 9.8 m/s², directed downwards.

自由落体是物体仅在重力作用下、不受空气阻力影响的运动。在地表附近，所有物体都会受到恒定的重力加速度 g ≈ 9.8 m/s²，方向竖直向下。

In IGCSE problems, you often treat upward as positive, making acceleration a = -g when the object moves upward, and +g when it falls downward. The same kinematic equations apply, but you must include the correct sign for displacement, velocity, and acceleration.

在 IGCSE 题目中，常规定向上为正，因此物体向上运动时加速度 a = -g，向下运动时 a = +g。同样的运动学方程适用，但必须代入位移、速度和加速度的正确符号。

9. Determining g by Free Fall Experiment | 通过自由落体实验测定 g

A typical IGCSE experiment involves dropping a steel ball from a known height and measuring the time it takes to fall. Using a trapdoor and an electromagnet, or light gates, you record time accurately. Since u = 0, s = ½gt², so g = 2s / t².

典型的 IGCSE 实验包括让一个钢球从已知高度下落并测量下落时间。使用活板门和电磁铁，或光门，可以精确计时。因为初速度为 0，根据 s = ½gt²，可得 g = 2s / t²。

To improve accuracy, repeat for multiple heights and plot a graph of 2s against t². The gradient equals g. Sources of error include air resistance, reaction time, and the delay in the electromagnet releasing the ball.

为提高准确度，对不同高度重复实验，并绘制 2s – t² 图。斜率即为 g。误差来源包括空气阻力、反应时间和电磁铁释放钢球的延迟。

10. Motion under Gravity: Vertical Projection | 重力作用下的运动：竖直抛体

When a ball is thrown vertically upward, it decelerates at g until it momentarily stops at the highest point, then accelerates downward at g. The time to go up equals the time to come down to the same level (ignoring air resistance). The symmetry means the speed upon returning to the starting point equals the initial speed, but direction is opposite.

将一个球竖直向上抛出，球以 g 减速直到最高点瞬时静止，再以 g 向下加速。忽略空气阻力时，上升时间等于落回到同一水平面的时间。对称性意味着重返抛出点时的速率与初速率相等，但方向相反。

Use the kinematic equations with a = -g (if upward is positive). At maximum height, v = 0. Total displacement over the entire journey is zero if it returns to the start.

使用运动学方程，规定向上为正，则 a = -g。在最大高度处 v = 0。若返回出发点，全程的总位移为 0。

11. Problem Solving Strategies | 解题策略

First, sketch a diagram and define the positive direction. Write down the five quantities: s, u, v, a, t. Identify which three are known and which one you need to find. Choose the equation that links exactly these four quantities.

首先，画出简图并规定正方向。列出五个量：s、u、v、a、t。确定哪三个已知，需要求哪个。选择恰好包含这四个量的方程。

Check units: convert all quantities to SI units (m, s, m/s, m/s²). If the object falls freely, a = ±g depending on sign convention. For graph questions, carefully read axes labels and use gradient for rate and area for displacement/distance. When in doubt, recall the definitions.

检查单位：将所有量换算成国际单位（m、s、m/s、m/s²）。若物体自由下落，根据符号规定取 a = ±g。对于图像题，仔细阅读坐标轴标签，利用斜率求变化率，利用面积求位移/路程。有疑问时，回归定义。

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IGCSE CIE Physics: Kinematics Key Points | IGCSE CIE 物理：运动学 考点精讲