📚 GCSE CIE Physics: Kinematics Revision Guide | GCSE CIE 物理：运动学考点精讲
Kinematics is the branch of physics that describes the motion of objects without considering the forces causing the motion. For GCSE CIE Physics, you will learn to use quantities like distance, displacement, speed, velocity and acceleration, interpret motion graphs, and apply the equations of uniformly accelerated motion. This guide breaks down every essential concept with clear explanations and worked examples to help you achieve top marks.
运动学是物理学的一个分支，描述物体的运动而不考虑引起运动的力。在 GCSE CIE 物理课程中，你将学习使用路程、位移、速率、速度和加速度等物理量，解读运动图像，并运用匀加速运动方程。本指南将每个核心概念分解为清晰的解释和范例，帮助你取得优异成绩。
1. Scalars and Vectors | 标量与矢量
In kinematics, physical quantities are classified as scalars or vectors. A scalar has magnitude (size) only, while a vector has both magnitude and direction. Understanding the difference is fundamental to describing motion correctly.
在运动学中，物理量分为标量和矢量。标量只有大小，而矢量既有大小又有方向。理解这一区别是正确描述运动的基础。
Examples of scalar quantities include distance, speed, mass and time. Distance tells you how much ground an object has covered, but not the direction. For instance, 50 metres is a scalar.
标量的例子包括路程、速率、质量和时间。路程告诉你物体移动了多长的路径，但不说明方向。例如，50 米就是一个标量。
Vectors include displacement, velocity and acceleration. Displacement is the straight-line distance in a specific direction from start to finish. If you walk 50 m east, your displacement is 50 m east, a vector quantity.
矢量包括位移、速度和加速度。位移是从起点到终点的直线距离，并指明方向。如果你向东走 50 米，位移就是向东 50 米，这是一个矢量。
When adding vectors in a straight line, positive and negative signs are used to show direction. For example, rightwards can be positive and leftwards negative. When vectors are not in a straight line, you may need to use scale diagrams or Pythagoras’ theorem for perpendicular directions.
在同一直线上相加矢量时，用正负号表示方向。例如，向右为正，向左为负。当矢量不在同一直线上时，你可能需要按比例画图或用勾股定理处理垂直方向。
2. Distance and Displacement | 路程与位移
Distance is a scalar measure of the total path length travelled by an object. It does not depend on direction, and is always positive. Displacement is a vector that measures the change in position from the starting point to the final point, together with the direction.
路程是物体运动轨迹总长度的标量量度。它与方向无关，总是正值。位移是矢量，它测量从起点到终点的位置变化，并包含方向。
Imagine a runner completing one lap on a 400 m circular track. The distance covered is 400 m, but the displacement is zero because the start and end points are the same. Displacement can be zero even when distance is large.
想象一名跑者在 400 米圆形跑道上跑了一圈。经过的路程是 400 米，但位移为零，因为起点和终点重合。即使路程很大，位移也可能为零。
In a straight-line journey, if a car travels 30 km north then 40 km south, the total distance is 70 km. The displacement, however, is 10 km south from the starting point. Always include the direction when stating displacement.
在直线运动中，如果一辆车向北行驶 30 公里，然后向南行驶 40 公里，总路程是 70 公里。然而，位移是起点以南 10 公里。陈述位移时务必包含方向。
3. Speed and Velocity | 速率与速度
Speed is the rate of change of distance and is a scalar. Average speed = total distance travelled ÷ total time taken. Velocity is the rate of change of displacement and is a vector. Average velocity = displacement ÷ time taken.
速率是路程的变化率，是标量。平均速率 = 总路程 ÷ 总时间。速度是位移的变化率，是矢量。平均速度 = 位移 ÷ 时间。
If a car travels 150 km in 3 hours, its average speed is 50 km/h. If the same car travels in a straight line east for 150 km and takes 3 hours, the average velocity is 50 km/h east. In the first example, speed is calculated from distance alone; in the second, direction matters.
如果一辆汽车行驶 150 公里用时 3 小时，其平均速率是 50 公里/小时。如果同一辆车向东沿直线行驶 150 公里，用时 3 小时，平均速度就是 50 公里/小时向东。在第一个例子中，速率仅由路程计算；在第二个例子中，方向很重要。
Instantaneous speed is the speed at a particular instant. On a distance-time graph, it is given by the gradient of the tangent at that point. For objects moving with constant speed, average speed equals instantaneous speed.
瞬时速率是某个特定瞬间的速率。在路程-时间图上，它由该点切线的斜率给出。对于匀速运动的物体，平均速率等于瞬时速率。
In the CIE exam, always check whether a question asks for speed or velocity. If direction is required, you must state it, otherwise your answer is incomplete.
在 CIE 考试中，始终要看清题目问的是速率还是速度。如果需要方向，你必须说明，否则答案不完整。
4. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector quantity measured in metres per second squared (m/s²). An object accelerates if its speed changes, its direction changes, or both.
加速度是速度的变化率。它是一个矢量，单位是米每二次方秒 (m/s²)。如果物体的速率改变、方向改变或两者都改变，物体就在做加速运动。
Average acceleration = (change in velocity) ÷ (time taken). In symbols: a = (v − u) / t, where u is initial velocity, v is final velocity, and t is time. A negative acceleration is often called deceleration or retardation.
平均加速度 = (速度变化量) ÷ (时间)。用符号表示：a = (v − u) / t，其中 u 是初速度，v 是末速度，t 是时间。负加速度通常称为减速度或负加速度。
a = (v − u) / t
If a car speeds up from 10 m/s to 30 m/s in 5 seconds, acceleration a = (30 − 10) / 5 = 4 m/s². If it slows down from 20 m/s to rest in 4 s, a = (0 − 20) / 4 = −5 m/s², meaning deceleration of 5 m/s².
如果汽车在 5 秒内从 10 m/s 加速到 30 m/s，加速度 a = (30 − 10) / 5 = 4 m/s²。如果它在 4 秒内从 20 m/s 减速到静止，a = (0 − 20) / 4 = −5 m/s²，表示减速度为 5 m/s²。
Remember that an object moving in a circle at constant speed still has an acceleration because its direction is continually changing. This acceleration is towards the centre of the circle.
记住，一个物体以恒定速率做圆周运动时，仍然有加速度，因为它的方向在持续变化。这个加速度指向圆心。
5. Distance-Time Graphs | 路程-时间图
A distance-time graph plots distance on the vertical axis and time on the horizontal axis. The gradient of the graph represents speed. A steeper line means higher speed; a horizontal line means the object is stationary.
路程-时间图以纵轴表示路程，横轴表示时间。图的斜率代表速率。线越陡表明速率越大；水平线表示物体静止。
For constant speed, the graph is a straight line with constant gradient. If the object accelerates, the graph curves upwards, becoming steeper with time. If it decelerates, the graph curves and becomes less steep.
对于匀速运动，图像是一条斜率不变的直线。如果物体加速，图像向上弯曲，随时间变陡。如果减速，图像弯曲且越来越平缓。
To find the instantaneous speed at a point on a curved graph, draw a tangent to the curve at that point and calculate its gradient. CIE often asks you to use this method.
要在弯曲图像上某点求瞬时速率，可在该点作曲线的切线，并计算其斜率。CIE 经常要求你使用这种方法。
The total distance travelled is simply the final reading on the vertical axis if the graph is always increasing. If the graph goes back towards the time axis, it indicates returning to the start, and the total distance is the sum of all movements.
如果图像始终上升，所经过的总路程就是纵轴上的最终读数。如果图像往回走向时间轴，表示返回到起点，此时总路程是所有移动路程的总和。
6. Speed-Time and Velocity-Time Graphs | 速率-时间图与速度-时间图
A speed-time graph (or velocity-time graph) has speed or velocity on the vertical axis and time on the horizontal axis. The gradient gives acceleration. The area under the graph gives the distance (for speed-time) or displacement (for velocity-time) travelled.
速率-时间图（或速度-时间图）以纵轴表示速率或速度，横轴表示时间。斜率给出加速度。图线下的面积代表经过的路程（速率-时间图）或位移（速度-时间图）。
For a horizontal line, the speed is constant and acceleration is zero. For an upward sloping straight line, acceleration is constant and positive. A downward sloping straight line indicates constant deceleration or negative acceleration.
对于水平线，速率恒定，加速度为零。对于向上倾斜的直线，加速度恒定且为正。向下倾斜的直线表示恒定的减速度或负加速度。
The area under the graph is often a simple shape: a rectangle for constant speed, a triangle for uniformly changing speed from rest, or a trapezium for accelerating from a nonzero initial speed. You must be able to calculate these areas using formulas for rectangles, triangles and trapeziums.
图线下的面积通常是简单的形状：匀速时是矩形，从静止开始匀变速时是三角形，或从非零初速度加速时是梯形。你必须能用矩形、三角形和梯形的公式计算这些面积。
Example: a velocity-time graph shows a straight line from (0, 10) to (5, 30) in m/s. The acceleration is (30 − 10)/5 = 4 m/s². The area (displacement) = area of trapezium = ½ × (10 + 30) × 5 = 100 m.
示例：一条速度-时间图显示从点 (0, 10) 到 (5, 30)（单位 m/s）的直线。加速度为 (30 − 10)/5 = 4 m/s²。面积（位移）= 梯形面积 = ½ × (10 + 30) × 5 = 100 m。
7. Equations of Uniformly Accelerated Motion | 匀加速运动方程
For motion in a straight line with constant acceleration, there are four equations, often called the SUVAT equations. The symbols used: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time. These equations only apply when acceleration is constant.
对于匀加速直线运动，有四个方程，通常称为 SUVAT 方程。所用符号：s = 位移，u = 初速度，v = 末速度，a = 加速度，t = 时间。这些方程仅适用于加速度恒定的情况。
The first equation links final velocity, initial velocity, acceleration and time:
第一个方程联系末速度、初速度、加速度和时间：
v = u + at
The second relates displacement to initial velocity, time and acceleration:
第二个方程联系位移与初速度、时间和加速度：
s = ut + ½at²
The third connects final velocity, initial velocity, acceleration and displacement without time:
第三个方程联系末速度、初速度、加速度和位移，不含时间：
v² = u² + 2as
The fourth uses average velocity to find displacement when time is known:
第四个方程利用平均速度，在已知时间时求位移：
s = (u + v)/2 × t
A typical CIE problem: a stone is dropped from rest, so u = 0. After 3 seconds, find its velocity and the distance fallen. Using g = 10 m/s² (or 9.8), v = 0 + 10 × 3 = 30 m/s; s = 0 × 3 + ½ × 10 × 3² = 45 m. Always list the known quantities and choose the appropriate equation.
典型的 CIE 问题：一块石头从静止释放，因此 u = 0。3 秒后，求其速度和下落距离。取 g = 10 m/s²（或 9.8），v = 0 + 10 × 3 = 30 m/s；s = 0 × 3 + ½ × 10 × 3² = 45 m。务必列出已知量，选择合适的方程。
8. Free Fall and Acceleration Due to Gravity | 自由落体与重力加速度
Free fall is the motion of an object under the influence of gravity alone, with no other forces like air resistance. Near the Earth’s surface, all objects fall with a constant acceleration called acceleration of free fall, g, approximately 9.8 m/s². In many CIE problems, you use g = 10 m/s² for simplicity unless told otherwise.
自由落体是仅受重力影响、无空气阻力等其他力作用下的运动。在地球表面附近，所有物体都以恒定的自由落体加速度（g，约 9.8 m/s²）下落。在许多 CIE 问题中，除非另有说明，为简便起见通常取 g = 10 m/s²。
When an object is thrown upwards, it decelerates at g until it reaches the highest point, where velocity is zero. Then it accelerates downwards at g. The motion is symmetrical: the time to go up equals the time to come down, and the speed at any point on the way up equals the speed on the way down at that height.
当物体向上抛出时，它做减速度为 g 的运动，直到最高点速度为零。然后以加速度 g 向下加速。运动是对称的：上升时间等于下降时间，且在上升路径中任一点的速度大小等于下降路径中同高度处的速度大小。
Use the SUVAT equations with a = g for vertical motion. Set the direction. Often, upward is taken as positive; then a = −g. For objects dropped from rest, u = 0, a = +g if downwards is positive.
对竖直运动使用 SUVAT 方程，并取 a = g。设定方向。通常取向上为正，则 a = −g。对于从静止下落的物体，若规定向下为正，则 u = 0，a = +g。
Example: a ball is thrown vertically upward at 20 m/s. How high does it go? Using v² = u² + 2as, with v = 0, u = 20, a = −10 (if upwards positive): 0 = 20² + 2(−10)s → s = 400 / 20 = 20 m. This is the maximum height.
示例：一球以 20 m/s 竖直上抛。它能升到多高？利用 v² = u² + 2as，v = 0，u = 20，a = −10（设向上为正）：0 = 20² + 2(−10)s → s = 400 / 20 = 20 m。这就是最大高度。
9. Interpreting Graphs in Exam Questions | 考试中图像的解读
CIE frequently tests graph interpretation skills. You may be asked to describe the motion represented by a velocity-time graph or to sketch a graph given a description of motion. Be prepared to calculate gradient and area, and to describe changes in words using phrases like ‘constant speed’, ‘accelerating uniformly’, ‘decelerating’ and ‘stationary’.
CIE 经常考查图像解读能力。你可能需要描述速度-时间图所表示的运动，或根据运动描述画出草图。准备好计算斜率和面积，并用“匀速”、“匀加速”、“减速”和“静止”等短语描述变化。
When sketching a velocity-time graph from a scenario, identify the key stages: e.g., car accelerates from rest to a steady speed, then travels at constant velocity, then decelerates to a stop. The graph will be a sloping line up, a horizontal line, then a sloping line down. The area under the graph never represents acceleration; it always represents distance or displacement.
根据情景画速度-时间草图时，要识别关键阶段：例如，汽车从静止加速到稳定速度，然后匀速行驶，然后减速停车。图像将是向上倾斜直线、水平线，然后是向下倾斜直线。图线下的面积绝不代表加速度，它始终代表路程或位移。
Common pitfall: confusing the slope of a distance-time graph (speed) with the slope of a velocity-time graph (acceleration). Make sure you read the axis labels carefully.
常见误区：混淆路程-时间图的斜率（速率）与速度-时间图的斜率（加速度）。务必仔细阅读坐标轴标签。
10. Practical Skills and Experimental Analysis | 实验技能与分析
CIE includes practical questions on motion. You need to know how to measure speed and acceleration using simple apparatus like rulers, stopwatches, light gates, and ticker timers. For example, to find the acceleration of a trolley, you can record the time taken to pass through two light gates and measure the distance between them.
CIE 包含关于运动的实验题。你需要知道如何使用尺子、秒表、光电门和打点计时器等简单仪器测量速率和加速度。例如，要测量小车的加速度，你可以记录它通过两个光电门的时间，并测量两者间的距离。
A ticker tape timer produces dots at a known frequency, say 50 Hz, so the time between dots is 0.02 s. By cutting the tape and measuring the spacing, you can calculate speed and acceleration. Equal spacing means constant speed; increasing spacing means acceleration. You can plot a velocity-time graph from the data to find acceleration as the gradient.
打点计时器以已知频率打点，例如 50 Hz，因此点之间的时间间隔为 0.02 s。通过剪断纸带并测量间距，你可以计算速率和加速度。点距相等意味着匀速；点距增大意味着加速。你可以用这些数据画出速度-时间图，以斜率求加速度。
When describing experiments, always mention how you control variables, take repeats, and reduce parallax error. Use everyday language but be precise about the physics.
在描述实验时，务必提及如何控制变量、进行重复实验和减小视差。使用通俗语言，但物理表述要准确。
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