Edexcel IGCSE Physics Forces and Motion: Newton’s Laws, Momentum and Graphs — 爱德思 IGCSE 物理 力与运动：牛顿定律、动量与图像

力与运动是爱德思 IGCSE 物理课程中最核心、最常考的主题之一。从描述物体如何运动的速度与加速度，到解释物体为什么运动的牛顿三大定律，再到碰撞中守恒的动量，这一单元把日常生活中无处不在的现象转化为可以计算、可以预测的物理模型。本文以爱德思 IGCSE 物理（9-1）课程大纲为基础，逐节讲解力与运动的关键概念、核心公式与典型考题思路，帮助你把零散的知识点连成完整的框架。

Forces and motion is one of the most central and frequently examined topics in the Edexcel IGCSE Physics course. From the speed and acceleration that describe how objects move, to Newton’s three laws that explain why they move, and on to the momentum conserved in collisions, this unit turns everyday phenomena into a physical model that can be calculated and predicted. Based on the Edexcel IGCSE Physics (9-1) specification, this article explains the key concepts, core equations and typical exam techniques for forces and motion, section by section, to help you connect scattered facts into a complete framework.

一、标量与矢量：物理量的两种类型 | Scalars and Vectors: The Two Kinds of Physical Quantity

在物理学中，所有的物理量都可以分为两大类：标量和矢量。标量是只有大小、没有方向的量，例如速率、距离、质量、能量、时间和温度。矢量则是既有大小又有方向的量，例如速度、位移、力、加速度和动量。理解这一区分是整个力与运动单元的基础，因为矢量之间不能像普通数字那样直接相加。

In physics, every quantity falls into one of two groups: scalars and vectors. A scalar has magnitude only and no direction, such as speed, distance, mass, energy, time and temperature. A vector has both magnitude and direction, such as velocity, displacement, force, acceleration and momentum. Understanding this distinction is the foundation of the whole forces-and-motion unit, because vectors cannot simply be added together like ordinary numbers.

矢量相加必须考虑方向。如果两个力方向相同，可以直接把大小相加；如果方向相反，则相减；如果方向成一定角度，就需要使用平行四边形法则或分解成互相垂直的分量。在 IGCSE 考试中，最常见的情况是物体只受同一直线上的力，此时规定一个正方向，把所有的力都写成带正负号的数值即可。

Adding vectors requires us to account for direction. If two forces act in the same direction, we simply add their magnitudes; if they act in opposite directions, we subtract; and if they act at an angle, we use the parallelogram rule or resolve them into perpendicular components. In the IGCSE exam, the most common situation is a body acted on by forces along a single straight line, where we choose a positive direction and write every force as a value with a sign.

下面这张表列出了本单元最常见的标量与矢量对照，建议在复习时对照记忆：

The table below lists the most common scalars and vectors in this unit, worth memorising side by side during revision:

标量 Scalar	矢量 Vector
距离 distance	位移 displacement
速率 speed	速度 velocity
质量 mass	重量 weight
能量 energy	力 force
时间 time	加速度 acceleration
温度 temperature	动量 momentum

二、速率与速度：距离与位移的区别 | Speed and Velocity: Distance vs. Displacement

速率是物体运动快慢的标量度量，定义为走过的总距离除以所用时间：速率 = 距离 ÷ 时间。速度则是一个矢量，等于位移除以时间，其中位移是物体从起点到终点的直线距离，并带有方向。例如，一名学生在 400 米跑道上跑完一圈，他走过的距离是 400 米，但位移是 0 米，因为他回到了起点。

Speed is the scalar measure of how fast an object moves, defined as total distance travelled divided by time taken: speed = distance ÷ time. Velocity is a vector equal to displacement divided by time, where displacement is the straight-line distance from start to finish with a direction. For example, a student who runs one lap of a 400 m track covers a distance of 400 m but a displacement of 0 m, because they return to the starting point.

平均速率使用总距离除以总时间计算，单位是米每秒（m/s）。在考试中，你常常需要把单位换算成标准形式，例如把 km/h 换算成 m/s：除以 3.6。还要注意平均速率的计算要使用总路程，而不是把各段速度简单平均。

Average speed is calculated as total distance divided by total time, with the unit metres per second (m/s). In the exam you will often need to convert units to standard form, for example converting km/h to m/s by dividing by 3.6. Note also that average speed uses the total journey distance, not a simple average of the individual segment speeds.

常见的陷阱是把”平均速度”当成两段速度的平均数。只有当物体在两段运动中用的时间相等时，速度的平均数才等于平均速率；否则必须用总距离除以总时间。考题经常给出前一半路程和后一半路程的不同速度，要求你求出全程的平均速率。

A common trap is to treat “average speed” as the average of two segment speeds. The average of the speeds only equals the average speed when the two parts of the journey take equal time; otherwise you must divide total distance by total time. Exam questions frequently give different speeds for the first and second halves of a journey and ask for the overall average speed.

三、加速度与速度-时间图像：从图线读懂运动 | Acceleration and Velocity-Time Graphs: Reading Motion from a Graph

加速度描述速度变化的快慢，定义为速度变化量除以所用时间：a = (v – u) ÷ t，其中 u 是初速度，v 是末速度。加速度的单位是米每二次方秒（m/s²）。加速度同样是矢量，正值表示沿正方向加速（或沿负方向减速），负值表示减速。

Acceleration describes how quickly velocity changes, defined as change in velocity divided by time taken: a = (v – u) ÷ t, where u is the initial velocity and v the final velocity. Its unit is metres per second squared (m/s²). Acceleration is also a vector: a positive value means speeding up in the positive direction (or slowing down in the negative direction), while a negative value means deceleration.

速度-时间图像是 IGCSE 考试的核心工具。图像上每一点的斜率（梯度）表示该时刻的加速度；图像与时间轴围成的面积表示物体在这段时间内走过的位移。一条水平的直线表示匀速运动；一条向右上方倾斜的直线表示匀加速运动；一条向右下方倾斜的直线表示匀减速运动。

The velocity-time graph is a core tool in the IGCSE exam. The gradient at any point on the graph gives the acceleration at that moment, and the area between the graph and the time axis gives the displacement during that interval. A horizontal straight line shows constant velocity; a line sloping upward shows uniform acceleration; a line sloping downward shows uniform deceleration.

直线运动还有三个重要的运动学方程，用于在已知部分量的情况下求未知量：v = u + at，s = ut + ½at²，以及 v² = u² + 2as。使用它们的关键是确定已知量和未知量，并统一单位（米、秒、米每秒）。

For motion along a straight line there are also three important equations of motion, used to find an unknown quantity when others are known: v = u + at, s = ut + ½at², and v² = u² + 2as. The key to using them is identifying what is known and what is unknown, and keeping units consistent (metres, seconds, metres per second).

四、牛顿第一定律：惯性与平衡力 | Newton’s First Law: Inertia and Balanced Forces

牛顿第一定律指出：物体在不受合力（或合力为零）的情况下，会保持静止或匀速直线运动状态。换句话说，物体的运动状态不会自己改变，必须有一个不为零的合力来改变它。物体保持原有运动状态的这种性质叫做惯性。

Newton’s first law states that an object remains at rest or moves with constant velocity unless acted on by a resultant (unbalanced) force. In other words, an object’s state of motion will not change by itself; a non-zero resultant force is needed to change it. This tendency of an object to keep its current state of motion is called inertia.

惯性与质量有关：质量越大的物体惯性越大，越难改变其运动状态。这也是为什么推动一辆满载的卡车比推动一辆空购物车困难得多。在太空中，没有摩擦和空气阻力，一个被推动的物体可以永远以恒定速度飞行，这正是牛顿第一定律的体现。

Inertia is related to mass: the greater the mass, the greater the inertia, and the harder it is to change the object’s motion. This is why pushing a fully loaded truck is far harder than pushing an empty shopping trolley. In space, where there is no friction or air resistance, an object once pushed can travel at constant velocity forever, which is exactly what Newton’s first law predicts.

平衡力意味着所有作用在物体上的力相互抵消，合力为零，此时物体要么静止，要么匀速直线运动。注意区分”平衡力”与牛顿第三定律中的”作用力与反作用力”：平衡力作用在同一个物体上，而作用力与反作用力作用在两个不同的物体上。

Balanced forces mean all forces acting on the body cancel out, giving zero resultant force, in which case the object is either at rest or moving with constant velocity. Be careful to distinguish “balanced forces” from the “action and reaction” pairs of Newton’s third law: balanced forces act on the same object, whereas action and reaction forces act on two different objects.

五、牛顿第二定律：F=ma 与力、质量、加速度的关系 | Newton’s Second Law: F = ma and the Link Between Force, Mass and Acceleration

牛顿第二定律把合力、质量和加速度联系起来：F = ma。合力（单位牛顿，N）等于质量（千克，kg）乘以加速度（米每二次方秒，m/s²）。这个公式告诉我们：加速度与合力成正比，与质量成反比。质量相同时，力越大加速度越大；力相同时，质量越大加速度越小。

Newton’s second law links resultant force, mass and acceleration: F = ma. The resultant force (in newtons, N) equals mass (in kilograms, kg) multiplied by acceleration (in metres per second squared, m/s²). This equation tells us that acceleration is proportional to the resultant force and inversely proportional to mass: for a given mass, a bigger force gives a bigger acceleration; for a given force, a bigger mass gives a smaller acceleration.

一个重要的特例是重量：物体因受到重力而产生的力，W = mg，其中 g 是重力场强度，在地球表面约为 9.8 N/kg（考试中常取 10 N/kg）。注意重量和质量的区别：质量是物体含有物质的多少，单位是千克，不随位置改变；重量是重力作用在物体上的力，单位是牛顿，会随行星不同而变化。

An important special case is weight: the force on an object due to gravity, W = mg, where g is the gravitational field strength, about 9.8 N/kg at the Earth’s surface (often taken as 10 N/kg in exams). Note the difference between weight and mass: mass is the amount of matter in an object, measured in kilograms and unchanged by location; weight is the force of gravity on the object, measured in newtons and different on different planets.

在考试中，F = ma 常用于两类问题：一是已知质量和加速度求合力，二是已知合力和质量求加速度。常见陷阱是忘记”合力”二字，直接把某个单独的力代入公式。解题时要先画出受力分析图，找出所有作用在物体上的力，再计算合力。

In exams, F = ma is used for two main kinds of problem: finding the resultant force from known mass and acceleration, or finding acceleration from known resultant force and mass. A common trap is forgetting the word “resultant” and substituting a single individual force into the formula. Always draw a free-body diagram first, identify every force acting on the object, and then calculate the resultant.

六、牛顿第三定律：作用力与反作用力 | Newton’s Third Law: Action and Reaction Pairs

牛顿第三定律指出：每一个作用力都有一个大小相等、方向相反的反作用力，且作用在不同的物体上。例如，当你站在地面上时，你对地面施加一个向下的力，地面同时对你施加一个大小相等、方向向上的支持力。这两个力大小相等、方向相反，但分别作用在地面和你的身体上。

Newton’s third law states that for every action force there is an equal and opposite reaction force, acting on a different object. For example, when you stand on the ground, you push down on the ground, and the ground pushes back up on you with an equal force in the opposite direction. The two forces are equal and opposite, but one acts on the ground and the other on your body.

判断一对力是否是”作用力与反作用力”，关键看两点：一是大小相等、方向相反、在同一直线上；二是作用在两个不同的物体上。如果两个力作用在同一个物体上，它们就是平衡力而不是作用力与反作用力。考题经常给出两个力，让你判断它们属于哪一种关系。

To decide whether two forces form an action-reaction pair, check two things: they must be equal in magnitude, opposite in direction and along the same line, and they must act on two different objects. If two forces act on the same object, they are balanced forces, not an action-reaction pair. Exam questions often present two forces and ask you to judge which relationship they belong to.

火箭升空是牛顿第三定律的经典例子：火箭向下喷出高温气体，气体对火箭施加一个向上的反作用力，推动火箭上升。需要注意的是，火箭并不需要空气来”推”，因此它可以在真空中飞行，这与很多人凭直觉认为”火箭靠推空气上升”的理解不同。

A rocket launch is a classic example of Newton’s third law: the rocket pushes hot gas downward, and the gas pushes back on the rocket with an upward reaction force that drives it upward. Importantly, the rocket does not need air to push against, which is why it can fly in a vacuum. This differs from the common intuition that a rocket rises by pushing against the air.

七、动量：质量与速度的乘积 | Momentum: The Product of Mass and Velocity

动量是描述物体”运动量”的物理量，定义为质量与速度的乘积：p = mv。动量的单位是千克米每秒（kg m/s），它是一个矢量，方向与速度相同。一个质量很大的物体即使速度很慢，也可以有很大的动量；同样，一个质量很小的物体如果速度极快，动量也可以很大。

Momentum is the quantity that describes an object’s “quantity of motion”, defined as mass multiplied by velocity: p = mv. Its unit is kilogram metres per second (kg m/s), and it is a vector whose direction matches the velocity. A very massive object can have large momentum even at low speed; likewise a light object moving extremely fast can also have large momentum.

动量的变化与冲量有关：冲量等于力乘以作用时间，也等于动量的变化量。这意味着，要改变物体的动量，既可以施加很大的力作用很短的时间，也可以施加较小的力作用较长的时间。这就是汽车安全气囊和安全带的原理：延长碰撞时间，减小作用在人体上的力。

Changes in momentum are linked to impulse: impulse equals force multiplied by time, and it also equals the change in momentum. This means that to change an object’s momentum we can either apply a large force for a short time, or a smaller force for a longer time. This is the principle behind car airbags and seatbelts: by lengthening the collision time they reduce the force acting on the body.

在 IGCSE 考试中，动量相关题目通常要求你计算物体的动量、比较两个物体的动量，或用冲量解释安全装置的作用。记住动量的单位 kg m/s 与冲量的单位 N s 实际上是等价的，因为 1 N = 1 kg m/s²。

In the IGCSE exam, momentum questions usually ask you to calculate an object’s momentum, compare the momentum of two objects, or use impulse to explain how safety devices work. Remember that the momentum unit kg m/s and the impulse unit N s are actually equivalent, because 1 N = 1 kg m/s².

八、动量守恒：碰撞与爆炸 | Conservation of Momentum: Collisions and Explosions

在没有外力作用的封闭系统中，总动量保持不变，这就是动量守恒定律。它适用于碰撞和爆炸两种情况。碰撞前所有物体的总动量等于碰撞后的总动量。利用这一守恒关系，我们可以在已知一部分速度的情况下，求出碰撞后未知的速度。

In a closed system with no external forces, total momentum is conserved; this is the law of conservation of momentum. It applies to both collisions and explosions. The total momentum of all objects before the collision equals the total momentum after. Using this conservation relationship, we can find an unknown velocity after a collision when some of the velocities are known.

碰撞分为弹性碰撞和非弹性碰撞。弹性碰撞中，动能和动量都守恒（例如理想气体分子之间的碰撞）；非弹性碰撞中，只有动量守恒，部分动能转化为热能、声能等（例如两辆汽车相撞）。IGCSE 考试通常只要求动量守恒的计算，不要求区分能量的细节。

Collisions are classified as elastic or inelastic. In an elastic collision both kinetic energy and momentum are conserved (as in collisions between ideal gas molecules); in an inelastic collision only momentum is conserved and some kinetic energy is converted into heat, sound and so on (as when two cars crash). IGCSE questions usually require only momentum-conservation calculations, not the fine details of energy.

爆炸是动量守恒的另一种应用。静止的物体（总动量为零）爆炸后分成几块向不同方向飞散，各块的动量之和仍然为零。例如，一门大炮发射炮弹时，炮弹向前飞去，炮身向后反冲（后坐力），两者的动量大小相等、方向相反。

Explosions are another application of momentum conservation. When a stationary object (total momentum zero) explodes into fragments flying in different directions, the vector sum of the fragments’ momenta is still zero. For example, when a cannon fires a shell, the shell flies forward and the cannon recoils backward, with the two momenta equal in magnitude and opposite in direction.

九、末速度：重力与空气阻力的平衡 | Terminal Velocity: When Gravity Meets Air Resistance

当一个物体从高空下落时，它受到两个力：向下的重力和向上的空气阻力。空气阻力随速度增大而增大。物体刚下落时速度很小，空气阻力也很小，合力向下，物体加速下落。随着速度增大，空气阻力逐渐增大，直到与重力大小相等，合力变为零，物体不再加速，而以恒定速度下落。这个恒定的速度就是末速度（terminal velocity）。

When an object falls through the air, two forces act on it: weight downward and air resistance upward. Air resistance increases with speed. At the start the speed is small so air resistance is small, the resultant force is downward and the object accelerates. As speed grows, air resistance grows until it equals the weight; the resultant becomes zero and the object stops accelerating, falling at constant speed. This constant speed is called terminal velocity.

跳伞运动员是末速度的经典例子。跳伞员刚从飞机跳出时加速下落；随着速度增加，空气阻力增大，最终达到第一个末速度。当打开降落伞后，空气阻力突然大增，向上的合力使跳伞员减速，直到达到一个更小的末速度，安全着陆。

A skydiver is a classic example of terminal velocity. Just after leaving the plane the skydiver accelerates; as speed increases, air resistance grows until a first terminal velocity is reached. When the parachute opens, air resistance suddenly increases greatly, producing an upward resultant that slows the skydiver until a much smaller terminal velocity is reached for a safe landing.

末速度的大小取决于物体的重量、形状和表面积。重量越大、形状越流线型、表面积越小，末速度越大。这也是为什么一颗雨滴会很快达到较小的末速度，而流线型的赛车比平板车受到的空气阻力更小。

The size of the terminal velocity depends on the object’s weight, shape and surface area. A greater weight, a more streamlined shape and a smaller surface area all give a larger terminal velocity. This is why a raindrop reaches a relatively small terminal velocity quickly, while a streamlined racing car experiences far less air resistance than a flat van.

十、停车距离：反应距离与刹车距离 | Stopping Distance: Thinking Distance Plus Braking Distance

汽车的停车距离由两部分组成：反应距离（司机看到危险到踩下刹车之间汽车走过的距离）和刹车距离（刹车开始到汽车完全停下之间走过的距离）。停车距离 = 反应距离 + 刹车距离。反应时间一般约为 0.7 秒，反应距离等于速度乘以反应时间。

A car’s stopping distance has two parts: thinking distance (the distance travelled between the driver seeing a hazard and applying the brakes) and braking distance (the distance travelled from braking to coming to rest). Stopping distance = thinking distance + braking distance. Reaction time is typically about 0.7 s, and thinking distance equals speed multiplied by reaction time.

影响反应距离的因素包括：车速（越快反应距离越长）、司机的反应时间（疲劳、饮酒、服药、分心都会延长反应时间）。影响刹车距离的因素包括：车速、道路状况（湿滑或结冰会增加刹车距离）、轮胎和刹车片状况等。要注意，车速加倍时，刹车距离大约变为原来的四倍。

Factors affecting thinking distance include speed (higher speed means a longer thinking distance) and the driver’s reaction time (tiredness, alcohol, drugs and distraction all lengthen it). Factors affecting braking distance include speed, road conditions (wet or icy roads increase braking distance), and the condition of tyres and brakes. Note that doubling the speed roughly quadruples the braking distance.

考试中这类题目通常要求你解释某个因素如何影响停车距离，或根据数据表格判断司机的状态。回答时要明确说明该因素影响的是反应距离、刹车距离，还是两者都影响，并解释背后的物理原因，而不是只笼统地说”距离变长”。

Exam questions on this topic usually ask you to explain how a factor affects stopping distance, or to judge a driver’s state from a data table. When answering, state clearly whether the factor affects thinking distance, braking distance, or both, and explain the physical reason behind it rather than just saying “the distance gets longer”.

Summary | 总结

力与运动这一单元以”矢量”概念为起点，逐步建立起描述运动（速率、速度、加速度、运动图像）和解释运动（牛顿三大定律、动量、动量守恒）的完整体系。牛顿第一定律说明物体为何保持原有状态，第二定律用 F = ma 把力与加速度定量地联系起来，第三定律揭示力的相互作用本质。动量 p = mv 及其守恒定律让我们能够分析碰撞与爆炸，而末速度与停车距离则把这些原理应用到真实的日常生活与交通安全中。

Starting from the idea of vectors, the forces-and-motion unit gradually builds a complete system for describing motion (speed, velocity, acceleration and motion graphs) and explaining it (Newton’s three laws, momentum and its conservation). Newton’s first law explains why objects keep their state, the second law uses F = ma to link force and acceleration quantitatively, and the third law reveals the mutual nature of forces. Momentum p = mv and its conservation let us analyse collisions and explosions, while terminal velocity and stopping distance apply these principles to real everyday life and road safety.

复习这一单元时，建议把重点放在四个方面：熟练使用 F = ma、a = (v – u) ÷ t 和 p = mv 这三个核心公式；能够读懂并画出速度-时间图像，从斜率求加速度、从面积求位移；用动量守恒解决一维碰撞与爆炸问题；以及用牛顿定律和力的平衡解释日常现象。掌握了这些，你就能从容应对爱德思 IGCSE 物理中几乎所有力与运动的考题。

When revising this unit, focus on four areas: using the three core equations F = ma, a = (v – u) ÷ t and p = mv fluently; reading and drawing velocity-time graphs to find acceleration from the gradient and displacement from the area; using momentum conservation to solve one-dimensional collision and explosion problems; and explaining everyday phenomena with Newton’s laws and force balance. Once you master these, you can confidently handle almost every forces-and-motion question in Edexcel IGCSE Physics.

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