📚 Mastering Motion and Forces for Edexcel IGCSE Science | 掌握爱德思IGCSE科学中的运动与力
Understanding motion and forces is at the heart of Edexcel IGCSE Science (Double Award / Physics). Whether you are calculating the speed of a car, interpreting a velocity-time graph, or applying Newton’s laws, these concepts form a foundation for analysing the physical world. This article covers key definitions, equations, graph skills and force interactions, all tailored to the IGCSE specification. By mastering these topics, you will build confidence for both multiple-choice questions and long-answer structured problems.
理解运动与力是爱德思 IGCSE 科学（双奖/物理）的核心。无论是计算汽车的速度、解读速度-时间图像，还是应用牛顿定律，这些概念都是分析物理世界的基础。本文涵盖了关键定义、方程、图像技能和力的相互作用，全部针对 IGCSE 考纲。掌握这些主题后，你在面对选择题和结构化长答题时将更有信心。
1. Scalar and Vector Quantities | 标量与矢量
A scalar quantity has only magnitude (size). Examples include distance, speed, mass, energy and temperature. When you say a car has travelled 200 metres, distance is a scalar — the direction is not specified.
标量只有大小。例如距离、速率、质量、能量和温度。当你说汽车行驶了200米时，距离是标量——没有指定方向。
A vector quantity has both magnitude and direction. Displacement, velocity, acceleration, force and momentum are all vectors. For instance, a velocity of 20 m/s east is a vector description because it tells us how fast and in which direction the object is moving.
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。例如，向东20 m/s的速度就是矢量描述，因为它说明了物体运动的快慢和方向。
When adding vectors, you must consider direction. Two forces of 5 N and 5 N acting in the same line can produce a resultant of 10 N or 0 N, depending on whether they act in the same or opposite directions. This distinction is vital for understanding resultant forces later in the topic.
矢量相加时必须考虑方向。两个5 N的力沿同一直线作用，根据它们方向相同还是相反，可以产生10 N或0 N的合力。这一区别对后续理解合力至关重要。
2. Speed and Velocity Calculations | 速度与速率的计算
Speed is the rate of change of distance. The average speed can be calculated using the equation:
v = d / t
where v is speed (m/s), d is distance travelled (m) and t is time taken (s). Note that speed is a scalar — direction is not taken into account.
速率是距离的变化率。平均速率可以用以下方程计算：v = d / t，其中v为速率（m/s），d为行驶距离（m），t为所用时间（s）。请注意速率是标量，不考虑方向。
Velocity is defined as the rate of change of displacement. The equation has the same form: v = Δs / Δt, but here Δs is displacement (a vector) and v is velocity in a specific direction. If a runner completes a 400 m lap and returns to the start, her displacement is zero, so average velocity is 0 m/s, despite an average speed of (400 / t) m/s.
速度定义为位移的变化率。方程形式相同：v = Δs / Δt，但这里的Δs是位移（矢量），v是特定方向上的速度。如果一名跑者完成400米一圈回到起点，她的位移为零，因此平均速度为0 m/s，尽管平均速率可能是(400 / t) m/s。
Be careful to use the correct units: speed and velocity in metres per second (m/s), distance and displacement in metres (m), time in seconds (s). In IGCSE questions, you may also need to convert kilometres per hour (km/h) to m/s by dividing by 3.6.
要注意使用正确的单位：速率和速度以米每秒（m/s）为单位，距离和位移以米（m）为单位，时间以秒（s）为单位。在IGCSE题目中，你可能还需要将千米每小时（km/h）转换为m/s（除以3.6）。
3. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector quantity calculated by:
a = (v – u) / t
where a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s) and t is time (s).
加速度是速度的变化率，是一个矢量，计算公式为：a = (v – u) / t，其中a为加速度（m/s²），v为末速度，u为初速度（m/s），t为时间（s）。
A negative acceleration means the object is decelerating (slowing down) or accelerating in the opposite direction. In everyday language, ‘deceleration’ is used, but in physics we often just say negative acceleration.
负加速度意味着物体正在减速或以相反方向加速。日常用语中使用“减速”，但在物理中我们通常只说负加速度。
Uniform acceleration means a constant acceleration. A free-falling object near the Earth’s surface experiences uniform acceleration due to gravity (g ≈ 9.8 m/s²), neglecting air resistance. In IGCSE calculations, g is sometimes taken as 10 m/s². The equations of motion for uniform acceleration are often applied: v = u + at, s = ut + ½at², and v² = u² + 2as.
匀加速是指加速度恒定。忽略空气阻力时，地球表面附近自由下落的物体会受到由于重力产生的匀加速（g ≈ 9.8 m/s²）。在IGCSE计算中，g有时取10 m/s²。匀加速运动的方程常被应用：v = u + at，s = ut + ½at²，以及 v² = u² + 2as。
4. Distance-Time Graphs | 距离-时间图
A distance-time graph shows how distance changes with time. The slope (gradient) of the line represents speed. A straight diagonal line constant speed; a horizontal line indicates the object is stationary. The steeper the gradient, the greater the speed.
距离-时间图展示距离随时间的变化。图线的斜率（梯度）代表速率。一条倾斜的直线表示匀速；水平线表示物体静止。斜率越大，速率越快。
If the graph is curved, the speed is changing (acceleration or deceleration). You can find the instantaneous speed at a point by drawing a tangent and calculating its gradient. The total distance travelled is simply read from the vertical axis.
如果图线是曲线，则速率在变化（加速或减速）。你可以通过在一点作切线并计算其斜率来求瞬时速率。行驶的总距离直接从纵轴读取即可。
IGCSE questions often ask you to describe the motion of different sections of a graph. For example: ‘From 0 to 10 s, the object moved at a constant speed of 5 m/s; from 10 s to 20 s it was stationary; after 20 s it returned to the start at a higher speed.’ Practice linking graph features with verbal descriptions.
IGCSE题目常常要求你描述图像不同区段的运动。例如：“0至10秒，物体以5 m/s的恒定速率运动；10至20秒静止；20秒后以更高速率返回起点。” 练习将图像特征与文字描述联系起来。
5. Velocity-Time Graphs | 速度-时间图
Velocity-time graphs are even more powerful. The gradient gives acceleration, and the area under the graph gives displacement (or distance if direction is constant). A horizontal line represents constant velocity; a sloping straight line represents constant acceleration.
速度-时间图更有用。斜率表示加速度，图线下的面积表示位移（若方向不变，也表示距离）。水平线表示匀速；倾斜直线表示匀加速。
For a velocity-time graph, an area above the time axis indicates positive displacement, while an area below indicates negative displacement (movement in the opposite direction). The total distance travelled is the sum of the magnitudes of all areas, regardless of sign.
对于速度-时间图，时间轴上方的面积表示正位移，下方的面积表示负位移（反方向运动）。总行驶距离是所有面积的绝对值之和，与正负号无关。
Be prepared to calculate acceleration from a gradient: a = (v₂ – v₁) / (t₂ – t₁). Also, you may need to find the area of a triangle, rectangle or trapezium under the graph. For non-uniform acceleration, you may be asked to estimate the area by counting squares.
要会通过斜率计算加速度：a = (v₂ – v₁) / (t₂ – t₁)。此外，你可能需要计算图线下三角形、矩形或梯形的面积。对于非匀加速，可能会要求你通过数格子的方法估算面积。
6. Forces and Free-Body Diagrams | 力与受力分析图
A force is a push or pull acting on an object due to its interaction with another object. Force is a vector quantity measured in newtons (N). Contact forces (friction, tension, normal reaction) require physical touch; non-contact forces (gravity, magnetic, electrostatic) act at a distance.
力是物体与另一物体相互作用时受到的推或拉。力是矢量，单位为牛顿（N）。接触力（摩擦力、张力、法向反作用力）需要物体接触；非接触力（重力、磁力、静电力）可以隔空作用。
Free-body diagrams use arrows to represent all forces acting on a single object. The length of the arrow indicates magnitude, and the direction shows the force direction. Common forces to include: weight (W = mg) acting downwards, normal reaction perpendicular to a surface, friction opposing motion, and driving force or thrust.
受力分析图用箭头表示作用在单个物体上的所有力。箭头的长度表示大小，方向表示力的方向。常见的力有：重力（W = mg, 向下），法向反作用力（垂直于表面），摩擦力（与运动方向相反），以及驱动力或推力。
When forces on an object are balanced, the resultant force is zero, and the object will remain at rest or move with constant velocity (Newton’s first law). If forces are unbalanced, there is a resultant force causing acceleration.
当物体上的力平衡时，合力为零，物体将保持静止或匀速直线运动（牛顿第一定律）。如果力不平衡，则存在合力，引起加速度。
7. Newton’s First Law and Inertia | 牛顿第一定律与惯性
Newton’s first law states: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction, unless acted upon by an unbalanced force. This property of matter is called inertia.
牛顿第一定律指出：任何物体都要保持静止或匀速直线运动状态，直到外力迫使它改变运动状态为止。物体的这一属性称为惯性。
Inertia depends on mass; the greater the mass, the greater the resistance to change in motion. This is why it is harder to push a full trolley than an empty one. The law also explains why passengers lurch forward in a car when it brakes suddenly — their bodies tend to continue moving forward due to inertia.
惯性与质量有关；质量越大，运动状态越难改变。这就是为什么推装满的推车比空推车更费力。该定律也解释了为什么汽车急刹车时乘客会向前冲——由于惯性，他们的身体趋向于继续向前运动。
In IGCSE, you must be able to apply the first law to everyday situations, like the need for seat belts, or the behaviour of a puck on an air table (almost no friction, so it keeps moving with nearly constant velocity). An unbalanced force is needed to start, stop or change the direction of motion.
在IGCSE中，你必须能将第一定律应用于日常情境，如安全带的作用，或气垫桌上冰球的行为（几乎无摩擦，因此它保持接近匀速的运动）。需要一个非平衡力才能启动、停止或改变运动方向。
8. Newton’s Second Law: F = ma | 牛顿第二定律 F = ma
Newton’s second law relates resultant force, mass and acceleration:
F = m × a
where F is resultant force (N), m is mass (kg) and a is acceleration (m/s²). This equation shows that for a fixed mass, acceleration is directly proportional to resultant force. It also shows that for a fixed force, acceleration is inversely proportional to mass.
牛顿第二定律将合力、质量和加速度联系起来：F = m × a，其中F为合力（N），m为质量（kg），a为加速度（m/s²）。该方程表明，对于固定质量，加速度与合力成正比；对于固定力，加速度与质量成反比。
The resultant force must be used in the equation. If you push a box with 10 N to the right, and friction is 4 N to the left, then F_resultant = 10 N – 4 N = 6 N. This resultant determines the acceleration. You will often need to resolve forces and calculate the net force first.
公式中必须使用合力。如果你用10 N向右推箱子，摩擦力向左为4 N，则合力 = 10 N – 4 N = 6 N。这个合力决定加速度。你通常需要先分解力并计算净力。
Weight is a common application: W = mg, where W is weight (N), m is mass (kg) and g is gravitational field strength (N/kg or m/s²). The mass of an object is constant, but its weight can change depending on the gravitational field.
重力是一个常见应用：W = mg，其中W为重力（N），m为质量（kg），g为引力场强度（N/kg或m/s²）。物体的质量是恒定的，但其重量会因引力场不同而改变。
9. Newton’s Third Law: Action-Reaction | 牛顿第三定律：作用与反作用
Newton’s third law states: When object A exerts a force on object B, object B simultaneously exerts an equal and opposite force on object A. These two forces are often called an action-reaction pair. They are equal in magnitude, opposite in direction, and act on different bodies.
牛顿第三定律指出：当物体A对物体B施加力时，物体B同时会对物体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。它们大小相等、方向相反，并作用在不同物体上。
A classic example is the rocket engine. The rocket pushes exhaust gases downwards (action), and the gases push the rocket upwards (reaction). It is a common misconception that the two forces cancel out; they do not, because they act on different objects — the rocket and the exhaust gases.
一个经典例子是火箭发动机。火箭向下推出发动机废气（作用），而废气向上推动火箭（反作用）。常见的误解是这两个力相互抵消；事实并非如此，因为它们作用在不同物体上——火箭和废气。
Walking is another example: your foot pushes back on the ground, and the ground pushes you forward. In IGCSE, you must identify action-reaction pairs correctly and realise they never act on the same object. This is tested with diagrams of colliding objects or a book resting on a table (the book pushes down on the table; the table pushes up on the book).
走路也是一个例子：你的脚向后推地面，地面向前推你。在IGCSE中，你必须正确识别作用力与反作用力对，并意识到它们从不作用在同一物体上。这一知识点常通过碰撞物体的示意图，或桌子上静止的书（书压桌子，桌子支撑书）来考查。
10. Stopping Distance and Safety | 制动距离与安全
The stopping distance of a vehicle is made up of two parts: thinking distance (the distance travelled during the driver’s reaction time) and braking distance (the distance travelled under the braking force). Total stopping distance = thinking distance + braking distance.
车辆的停车距离由两部分组成：反应距离（驾驶员反应时间内行驶的距离）和制动距离（在制动力作用下行驶的距离）。总停车距离 = 反应距离 + 制动距离。
Thinking distance is affected by factors such as driver tiredness, alcohol, drugs, and distractions. Braking distance is influenced by vehicle speed, mass, condition of tyres and brakes, and road surface (icy, wet). At higher speeds, braking distance increases dramatically because the kinetic energy to be dissipated is proportional to v².
反应距离受驾驶员疲劳、酒精、药物和注意力分散等因素的影响。制动距离则受车速、车辆质量、轮胎和刹车状况以及路面情况（结冰、潮湿）的影响。速度较高时，制动距离急剧增加，因为需要耗散的动能与v²成正比。
This section often links to energy: work done by brakes = force × braking distance, and the work done equals the initial kinetic energy (½mv²). This is why doubling the speed roughly quadruples the braking distance. Safety features such as air bags, crumple zones and seat belts increase the time over which the occupant decelerates, reducing the force experienced (impulse = change in momentum = force × time).
此部分常与能量联系：刹车所做的功 = 力 × 制动距离，且所做的功等于初始动能（½mv²）。这就是为什么速度加倍，制动距离大约变为原来四倍。安全气囊、防撞褶皱区和安全带等安全设施延长了乘员减速的时间，从而减小了受力（冲量 = 动量变化 = 力 × 时间）。
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