📚 Forces and Motion | 力与运动
Understanding forces and motion is central to IGCSE CIE Science. This topic connects everyday experiences—like walking, driving, or throwing a ball—with fundamental physics concepts. Students learn to describe motion using graphs and equations, apply Newton’s laws, and explore momentum and turning effects. Mastery of this unit requires both qualitative reasoning and numerical problem-solving skills. Let’s walk through each key area step by step.
理解力与运动是 IGCSE CIE 科学的核心内容。这一主题将步行、驾驶、投球等日常体验与基础物理概念联系起来。学生将学会用图像和方程描述运动，应用牛顿定律，并探索动量和转动效应。掌握本单元既需要定性推理，也需要定量计算的能力。我们逐步梳理每一个关键考点。
1. Scalar and Vector Quantities | 标量与向量
Scalars are quantities that have magnitude only, such as mass (kg), time (s), speed (m/s), and energy (J). Vectors have both magnitude and direction, for example displacement, velocity, acceleration, force, and momentum. When adding vectors, we must consider direction; they can be added tip-to-tail or resolved into perpendicular components. In IGCSE, you are often asked to distinguish between scalars and vectors and to calculate resultant vectors using simple geometry or Pythagoras’ theorem.
标量是只有大小的量，如质量 (kg)、时间 (s)、速率 (m/s) 和能量 (J)。向量既有大小又有方向，例如位移、速度、加速度、力和动量。向量相加时必须考虑方向，可用三角形法则（首尾相接）或正交分解。在 IGCSE 中，常考题要求区分标量与向量，并用简单几何或勾股定理计算合向量。
| Scalars | Vectors |
| distance | displacement |
| speed | velocity |
| mass, energy | force, acceleration |
2. Distance and Displacement | 距离与位移
Distance is the total length of the path travelled, a scalar quantity measured in metres (m). Displacement is the straight-line distance between start and end points in a given direction, so it is a vector. For example, if you walk 4 m east then 3 m south, the distance travelled is 7 m, but the magnitude of displacement is √(4² + 3²) = 5 m in a southeast direction. Displacement can be zero if the object returns to its starting point, while distance is always positive and accumulates.
距离是运动路径的总长度，是标量，单位为米 (m)。位移是起点到终点的直线距离，并带有方向，因此是向量。例如，向东走4米再向南走3米，路程为7米，但位移大小为 √(4² + 3²) = 5米，方向为东南。若物体回到出发点，位移为零，而距离始终为正且不断累加。
3. Speed, Velocity and Acceleration | 速率、速度与加速度
Speed is the rate of change of distance: speed = distance / time. Velocity is the rate of change of displacement: v = Δx / Δt, a vector. The SI unit for both is m/s. Acceleration is the rate of change of velocity: a = Δv / Δt, with unit m/s². If an object slows down, its acceleration is negative (deceleration). In IGCSE problems, you often calculate average speed or use constant acceleration. Remember that an object moving in a circle at constant speed is still accelerating because its direction changes.
速率是距离的变化率：速率 = 距离 / 时间。速度是位移的变化率：v = Δx / Δt，为向量。两者的 SI 单位都是 m/s。加速度是速度的变化率：a = Δv / Δt，单位为 m/s²。若物体减速，则加速度为负（减速度）。IGCSE 题目常考平均速率或匀加速运动。注意，物体以恒定速率做圆周运动时仍有加速度，因为方向在变化。
4. Distance-Time Graphs | 距离-时间图
A distance-time graph plots total distance on the vertical axis against time on the horizontal axis. The gradient of the graph gives the speed: a steeper line means faster speed. A horizontal line indicates the object is stationary. A curved line shows acceleration (changing speed). If the graph is a straight line with constant slope, the speed is constant. Always check that distance can never decrease; if the graph shows a drop, it might be a displacement-time graph instead.
距离-时间图以纵轴表示总路程，横轴表示时间。图的斜率表示速率：斜率越陡，速率越大。水平线表示物体静止。曲线则表示物体在加速（速率变化）。若为斜率不变的直线，则速率恒定。注意距离永远不会减小；若图像下降，那可能是位移-时间图。
5. Speed-Time Graphs | 速度-时间图
In a speed-time graph, speed is on the y-axis, time on the x-axis. The gradient equals acceleration: positive slope means increasing speed, negative slope means deceleration. The area under the graph between two times gives the distance travelled during that interval. A horizontal line represents constant speed. For non-uniform acceleration, the area can be estimated by counting squares. These graphs are very common in IGCSE papers; be prepared to calculate acceleration from the gradient and distance from the area.
在速度-时间图中，纵轴为速度，横轴为时间。斜率等于加速度：正斜率表示速度增加，负斜率表示减速。两时间点之间图线下的面积等于该时间段内的位移（或路程）。水平线表示匀速运动。对于非匀加速运动，可通过数格子估算面积。这类图像是 IGCSE 试卷的常客，务必能根据斜率求加速度、根据面积求距离。
6. Equations of Motion | 运动方程
For uniform acceleration in a straight line, four equations relate initial velocity u, final velocity v, acceleration a, displacement s, and time t:
对于匀加速直线运动，有四个方程联系初速度 u、末速度 v、加速度 a、位移 s 和时间 t：
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
These are used when acceleration is constant. First, identify which three quantities you know, then choose the equation that contains the unknown variable. In IGCSE, you are expected to rearrange these equations competently and use consistent units (e.g., m, s, m/s).
这些方程仅在加速度恒定时适用。先确定已知哪三个物理量，然后选择包含未知量的方程。IGCSE 要求能熟练变形并使用一致的单位（如 m、s、m/s）。
7. Free Fall and Acceleration due to Gravity | 自由落体与重力加速度
All objects near the Earth’s surface fall with the same acceleration due to gravity, g ≈ 9.8 m/s², if air resistance is negligible. This acceleration acts downward, toward the centre of the Earth. In free fall, the equations of motion apply with a = g. An object thrown upward has initial velocity upward, but acceleration is still downward, so it decelerates until reaching the highest point (v = 0), then accelerates downward. Falling objects reach a terminal velocity when air resistance equals weight, resulting in no net force and zero acceleration.
若空气阻力可忽略，地球表面附近的所有物体都以相同的重力加速度 g ≈ 9.8 m/s² 下落。加速度方向向下，指向地心。自由落体中，运动方程里的 a 取 g。向上抛出的物体初速度向上，但加速度仍向下，因此先减速至最高点（v = 0），然后加速下落。当空气阻力与重力相等时，物体达到终极速度，合力为零，加速度为零。
8. Newton’s First Law of Motion | 牛顿第一运动定律
An object remains at rest or moves with constant velocity unless acted upon by a resultant external force. This law introduces the concept of inertia—the tendency of an object to resist changes in its motion. Mass is a measure of inertia; a larger mass requires a larger force to change its velocity. Balanced forces produce no change in motion. If the resultant force is zero, the object either stays still or continues moving at a steady speed in a straight line.
物体在不受外力（或合外力为零）时，将保持静止或匀速直线运动状态。这一定律引入了惯性的概念——物体抵抗运动状态改变的特性。质量是惯性的量度；质量越大，改变其速度所需的力就越大。平衡力不会改变运动状态。若合外力为零，物体要么静止，要么做匀速直线运动。
9. Newton’s Second Law | 牛顿第二定律
The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. This is summarised by the equation:
物体的加速度与所受合外力成正比，与其质量成反比。可用方程概括：
F = ma
where F is the resultant force (N), m is mass (kg), and a is acceleration (m/s²). This law means a larger force produces a larger acceleration, and a larger mass gives a smaller acceleration for the same force. The unit of force, the newton (N), is defined as the force needed to accelerate 1 kg by 1 m/s². When solving problems, always determine the net force before using F = ma.
其中 F 是合外力 (N)，m 为质量 (kg)，a 是加速度 (m/s²)。该定律表明，力越大加速度越大；相同力下质量越大加速度越小。力的单位牛顿 (N) 定义为使 1 kg 物体产生 1 m/s² 加速度所需的力。解题时务必先求出合外力，再使用 F = ma。
10. Newton’s Third Law | 牛顿第三定律
For every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B simultaneously exerts a force of the same magnitude but opposite direction on object A. These two forces act on different bodies and are of the same type. For example, when you push against a wall, the wall pushes back on you. A rocket propels forward by expelling exhaust gases backward—the gas pushes the rocket forward. In static situations, the normal contact force and weight are not an action-reaction pair because they act on the same object.
每一个作用力都有一个大小相等、方向相反的反作用力。若物体 A 对物体 B 施加一个力，则 B 同时对 A 施加大小相等、方向相反的力。这两个力作用在不同物体上，且属于同种性质的力。例如，你推墙时，墙也推你。火箭向后喷射燃气，燃气反推火箭前进。在静态问题中，支持力和重力不是一对作用力与反作用力，因为它们作用在同一物体上。
11. Momentum and Impulse | 动量与冲量
Momentum (p) is the product of mass and velocity: p = mv. It is a vector quantity with unit kg m/s. Impulse is the change in momentum, equal to the applied force multiplied by the time for which it acts: impulse = F × Δt = Δp. In collisions, the total momentum before equals the total momentum after, provided no external forces act (principle of conservation of momentum). IGCSE often asks for calculations involving explosions, collisions, and recoil, where the initial total momentum is zero.
动量 (p) 是质量与速度的乘积：p = mv。它是向量，单位为 kg m/s。冲量是动量的变化量，等于力与其作用时间的乘积：冲量 = F × Δt = Δp。碰撞中，若没有外力作用，总动量守恒（动量守恒原理）。IGCSE 常考爆炸、碰撞和反冲问题，这类情景初总动量常为零。
12. Turning Effect (Moments) | 转动效应（力矩）
The moment of a force about a pivot is the product of the force and the perpendicular distance from the pivot to the line of action of the force:
力对支点的力矩等于力乘以支点到力作用线的垂直距离：
M = F × d
where M is the moment (Nm), F is the force (N), and d is the perpendicular distance (m). For an object in equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments (principle of moments). This is used to analyse levers, seesaws, and crane arms. If a force’s line of action passes through the pivot, its moment is zero. Always identify the pivot and measure perpendicular distances.
其中 M 是力矩 (Nm)，F 是力 (N)，d 是垂直距离 (m)。处于平衡状态的物体，对任意支点的顺时针力矩之和等于逆时针力矩之和（力矩原理）。这一原理常用来分析杠杆、跷跷板和起重机臂。若力的作用线通过支点，则力矩为零。解题时务必明确支点并测量垂直距离。
Published by TutorHao | IGCSE CIE Science Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导