📚 Topic 516: Forces and Motion in IGCSE Edexcel Science | IGCSE Edexcel科学中的力与运动
This article provides a thorough revision of forces and motion, essential for the IGCSE Edexcel Science physics sections. Mastering scalars and vectors, analysing motion graphs, and applying Newton's laws will help you solve problems on motion, forces, and energy transfer confidently.
本文全面复习IGCSE Edexcel科学物理部分中力与运动的核心内容。掌握标量与矢量、分析运动图象并运用牛顿定律，将帮助你自信地解答有关运动、力和能量转换的问题。
1. Scalar and Vector Quantities | 标量与矢量
Scalars are physical quantities that have magnitude (size) only. Vectors have both magnitude and direction. This distinction is crucial because calculations involving vectors require direction to be taken into account. For example, when moving in a straight line, a change in direction means the vector changes even if the speed stays the same.
标量是只有大小（数量）的物理量。矢量既有大小又有方向。这一区别至关重要，因为涉及矢量的计算必须考虑方向。例如，沿直线运动时，即使速率保持不变，方向改变也意味着矢量的改变。
Common scalar quantities include speed, distance, time, mass, energy and temperature. Common vector quantities include velocity, displacement, force, acceleration, momentum and weight. A displacement of 5 m north is a vector, while a distance of 5 m is a scalar.
常见的标量有速率、路程、时间、质量、能量和温度。常见的矢量有速度、位移、力、加速度、动量和重量。向北位移5米是矢量，而路程5米是标量。
| Scalars (magnitude only) | Vectors (magnitude and direction) |
|---|---|
| Speed | Velocity |
| Distance | Displacement |
| Mass | Weight |
| Energy | Force |
Table: Comparison of scalar and vector quantities | 标量与矢量的对比
2. Speed and Velocity | 速率与速度
Speed is the rate at which distance is covered. It is a scalar and is usually measured in metres per second (m/s). The average speed can be calculated as total distance divided by total time taken.
速率是走过路程的快慢程度。它是标量，通常以米每秒（m/s）为单位。平均速率可以用总路程除以总时间来计算。
average speed = total distance ÷ total time
v = d ÷ t
Velocity is speed in a given direction, so it is a vector. If an object changes direction, its velocity changes even if its speed is constant. For uniform motion in a straight line, the magnitude of velocity equals speed.
速度是给定方向上的速率，因此是矢量。如果物体改变方向，即使速率不变，速度也会改变。对于匀速直线运动，速度的大小等于速率。
When solving problems, always check whether the question asks for speed or velocity. If a direction is required, you must give a velocity with direction, for example '25 m/s eastwards'.
解题时，始终要看清题目要求的是速率还是速度。如果需要方向，就必须给出带有方向的速度，例如“25 m/s 向东”。
3. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector quantity and is measured in metres per second squared (m/s²). An object accelerates if its speed changes, its direction changes, or both change.
加速度是速度变化的快慢。它是矢量，单位是米每二次方秒（m/s²）。如果物体的速度大小改变、方向改变或两者同时改变，物体就在加速。
acceleration = (final velocity – initial velocity) ÷ time
a = (v – u) ÷ t
Where u is the initial velocity, v is the final velocity and t is the time taken for the change. Negative acceleration (deceleration) occurs when the object slows down, meaning the final velocity is smaller than the initial velocity.
其中u为初速度，v为末速度，t为变化所用的时间。当物体减速时出现负加速度（减速度），即末速度小于初速度。
In IGCSE questions, you may need to rearrange this formula to find u, v or t. Always convert units to m/s and seconds before substituting.
在IGCSE题目中，你可能需要变换公式来求u、v或t。代入数值前一定要把单位转换成m/s和秒。
4. Distance–Time Graphs | 距离–时间图
A distance–time graph shows how an object's distance changes with time. The gradient (slope) of the line represents speed. A straight diagonal line indicates constant speed, while a horizontal line indicates the object is stationary. A curved line shows changing speed (acceleration or deceleration).
距离–时间图显示物体的距离如何随时间变化。直线的斜率表示速率。笔直的斜线表示匀速运动，水平线表示物体静止。曲线则表示速率在变化（加速或减速）。
To calculate speed from a distance– in distance ÷ change in time. For curved sections, you can draw a tangent to find the instantaneous speed at a point.
根据距离–时间图计算速率时，在直线段上选取两点，用：速率 = 距离的变化量 ÷ 时间的变化量。对于曲线段，可以画切线来求某一点的瞬时速率。
You must be able to interpret and sketch these graphs. Remember: a steeper gradient means a higher speed, and a flat section means the object has stopped.
你必须会解读并绘制这类图像。记住：斜率越陡，速率越大；水平段表示物体停止了运动。
5. Velocity–Time Graphs | 速度–时间图
Velocity–time graphs provide even more information. The gradient represents acceleration, the area under the graph represents the distance travelled, and a horizontal line shows constant velocity. A sloping line upwards shows positive acceleration, while a downward slope indicates deceleration.
速度–时间图提供的信息更丰富。斜率表示加速度，图线下的面积表示走过的距离，水平线表示匀速运动。向上的斜线表示正加速度，向下的斜线表示减速度。
acceleration = gradient of velocity–time graph
acceleration = (change in velocity) ÷ time
To find the distance travelled from a velocity–time graph, calculate the area between the line and the time axis. For simple shapes like rectangles and triangles, use basic area formulas. If a graph consists of several sections, add the individual areas together.
用速度–时间图求走过的距离，需要计算图线与时间轴之间的面积。对于矩形和三角形这类简单图形，使用基本面积公式即可。如果图像由多段构成，则将各段面积相加。
Typical IGCSE exam questions will ask you to sketch or analyse these graphs, so practise dividing the region into rectangles, triangles and trapeziums where necessary.
典型的IGCSE考题会要求你描绘或分析这类图像，所以要多练习在需要时将区域划分成长方形、三角形和梯形。
6. Newton's First Law of Motion | 牛顿第一运动定律
Newton's first law states that an object will remain at rest or move with constant velocity unless acted on by a resultant (net) force. This property of an object is called inertia, which depends on its mass – the greater the mass, the greater the inertia.
牛顿第一定律指出，除非受到合力（净力）的作用，否则物体将保持静止或匀速直线运动状态。物体的这一属性称为惯性，惯性取决于质量——质量越大，惯性越大。
t maintains its state of motion. When the resultant force is not zero, the object accelerates, decelerates or changes direction.
如果作用在物体上的力相互平衡（合力为零），物体就保持原来的运动状态。当合力不为零时，物体加速、减速或改变方向。
This law explains why passengers lurch forward when a car brakes suddenly – their bodies tend to continue moving forward due to inertia. Seat belts provide the unbalanced force needed to stop the passenger.
这个定律解释了为什么汽车急刹车时乘客会前倾——他们的身体由于惯性会继续向前运动。安全带提供了使乘客停下来的不平衡力。
7. Newton's Second Law of Motion | 牛顿第二运动定律
Newton's second law links resultant force, mass and acceleration. It is often expressed as:
牛顿第二定律将合力、质量和加速度联系起来。通常表示为：
resultant force = mass × acceleration
F = m × a
Where F is the resultant force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in m/s². The acceleration is always in the same direction as the resultant force.
其中F是以牛顿（N）为单位的合力，m是以千克（kg）为单位的质量，a是以m/s²为单位的加速度。加速度的方向始终与合力的方向相同。
For a given mass, a larger resultant force produces a larger acceleration. For the same force, a larger mass results in a smaller acceleration. You are often asked to calculate one variable given the other two. Remember to convert masses to kg if given in grams.
对于给定的质量，合力越大，产生的加速度越大。力相同的情况下，质量越大，加速度越小。考题中常让你由其中两个量求第三个量。如果质量以克给出，记得换算成千克。
to the concept of free fall, where the only force is gravity and the acceleration due to gravity (g) is approximately 9.8 m/s² on Earth.
该公式可变形为 a = F ÷ m 或 m = F ÷ a。它与自由落体概念密切相关，自由落体时唯一的作用力是重力，地球表面的重力加速度g约为9.8 m/s²。
8. Newton's Third Law of Motion | 牛顿第三运动定律
Newton's third law states that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These forces are often called action–reaction pairs. They act on different objects and therefore do not cancel each other out.
牛顿第三定律指出，如果物体A对物体B施加一个力，那么物体B同时对物体A施加一个大小相等、方向相反的力。这两个力常被称为作用力与反作用力对。它们作用在不同的物体上，因此不会相互抵消。
Examples include: a rocket pushing exhaust gases downwards, and the gases pushing the rocket upwards; a swimmer pushing water backwards, and the water pushing the swimmer forwards. In each case, the pair of forces are of the same type, equal in magnitude and opposite in direction.
例子包括：火箭向下喷出燃气，燃气向上推动火箭；游泳者向后推水，水向前推游泳者。在每种情况下，这对力属于同种类型，大小相等、方向相反。
To correctly identify action–reaction pairs in an exam, check that the two forces are acting on two different bodies. This is a common mistake.
要在考试中正确识别作用力与反作用力对，请检查这两个力是否作用在两个不同的物体上。这是一个常见的错误点。
9. Resultant Forces and Free-Body Diagrams | 合力与受力分析图
A resultant force is the single force that has the same effect as all the forces acting on an object combined. When forces act along the same line, the resultant can be found by simple addition or subtraction. When forces act at an angle, vector diagrams are used, but at IGCSE level you mainly deal with forces along a straight line or at right angles.
合力是指与作用在物体上的所有力总效果相同的单一力。当力沿同一直线作用时，合力可通过简单的相加或相减求得。当力互成角度时，需使用矢量图，但在IGCSE阶段主要处理沿直线或互成直角的力。
A free-body diagram shows all the forces acting on a single object by means of arrows. The length of each arrow represents the magnitude, and the direction shows the force direction. Common forces include weight (downwards), normal reaction (upwards), thrust, friction and tension.
受力分析图用箭头表示作用在一个物体上的所有力。箭头的长度表示力的大小，方向表示力的方向。常见的力有重力（向下）、法向反作用力（向上）、推力、摩擦力和张力。
To find the resultant, add forces in the same direction and subtract those in opposite directions. For example, if an engine provides a forward force of 500 N and friction is 200 N backwards, the resultant force is 300 N forwards.
求合力时，将同向的力相加，反向的力相减。例如，如果发动机提供 500 N 向前的力，摩擦力为 200 N 向后，则合力为 300 N 向前。
10. Stopping Distance and Safety | 制动距离与安全
The stopping distance of a vehicle is the sum of the thinking distance and the braking distance. Thinking distance is how far the car travels while the driver reacts; braking distance is the distance covered after the brakes are applied until the vehicle stops.
车辆的停车距离是反应距离与制动距离之和。反应距离是司机做出反应期间汽车行驶的距离；制动距离是从踩下刹车到车辆完全停止所经过的距离。
stopping distance = thinking distance + braking distance
Factors increasing thinking distance include tiredness, alcohol, drugs and distractions. Factors increasing braking distance include wet or icy roads, worn tyres, poor brakes, and high speed. Because braking distance is proportional to the square of the speed, doubling the speed quadruples the braking distance.
增加反应距离的因素包括疲劳、酒精、药物和分心等。增加制动距离的因素包括路面湿滑或结冰、轮胎磨损、刹车不良以及高速行驶。由于制动距离与速度的平方成正比，车速加倍会使制动距离变为原来的四倍。
Understanding stopping distance is essential for road safety, and IGCSE questions often ask you to explain these factors and the effect of speed on safety.
理解停车距离对于道路安全至关重要，IGCSE题目常要求你解释这些因素以及车速对安全的影响。
11. Momentum | 动量
Momentum is a property of moving objects, defined as the product of mass and velocity. It is a vector quantity, measured in kg m/s.
动量是运动物体的一种属性，定义为质量与速度的乘积。它是矢量，单位为 kg m/s 。
momentum = mass × velocity
p = m × v
The principle of conservation of momentum states that in a closed system (with no external forces), the total momentum before an event (collision or explosion) equals the total momentum after the event. This principle allows you to calculate unknown velocities in interactions.
动量守恒定律指出，在一个封闭系统中（没有外力作用），事件（碰撞或爆炸）前的总动量等于事件后的总动量。利用该原理可以计算相互作用中的未知速度。
In a collision, momentum can be transferred; the object with larger mass tends to have a smaller change in velocity. In an explosion, stationary objects fly apart with equal and opposite total momentum, so the total momentum remains zero.
碰撞中动量会发生转移；质量较大的物体往往速度变化量较小。爆炸时，静止的物体向相反方向分开，总动量大小相等方向相反，因此总动量保持为零。
Common exam calculations involve trolley collisions, car crashes, and recoil of guns. Always determine the direction of velocity and assign positive or negative signs accordingly.
常见的考试计算涉及小车碰撞、汽车相撞以及枪支反冲。始终要确定速度方向，并相应地赋予正负号。
12. Practical Tips and Common Pitfalls | 备考技巧与常见误区
Many students lose marks by confusing speed and velocity, or by forgetting to include direction when a vector is required. Always read the question carefully: if asked for a velocity, your answer must include direction.
许多学生因混淆速率与速度，或忘记在需要矢量时给出方向而失分。务必仔细读题：如果要求速度，答案必须包含方向。
o kg. Use the formula triangles for F = m×a, p = m×v, and a = (v-u)/t to rearrange easily.
代入公式时，检查单位是否统一。将千米换算为米，小时换算为秒，克换算为千克。利用F = m×a、p = m×v和a = (v-u)/t的公式三角形，可轻松进行公式变形。
In motion graphs, be precise: label axes correctly, and show clear trends. If a graph asks for distance, remember that the area under a velocity–time graph must be calculated, not just read off.
在运动图象中，要力求精确：正确标记坐标轴，清晰显示变化趋势。如果题目要求根据速度–时间图求路程，要记住需要计算图线下的面积，而不能直接从轴读值。
Practise past paper questions that combine Newton's laws and motion graphs. This will build your confidence in selecting the right formula and interpreting physical situations.
多练习将牛顿定律与运动图象结合的历年真题。这能增强你选择正确公式和解读物理情境的信心。
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