📚 Forces and Motion | 力与运动
Forces and motion lie at the heart of classical mechanics, describing how objects interact and change their state of rest or movement. This topic is fundamental to Edexcel IGCSE Science, bringing together mathematical descriptions and real-world observations. You will explore key concepts such as vectors, acceleration, graphs of motion, Newton's three laws, momentum, terminal velocity, stopping distances and elastic forces. Understanding these principles not only helps you excel in the exam but also explains everything from vehicle safety to sports performance and space travel.
力与运动是经典力学的核心，描述物体如何相互作用以及如何改变静止或运动状态。这个主题是 Edexcel IGCSE 科学的基础，将数学描述与真实世界的观察结合在一起。你将探索矢量、加速度、运动图像、牛顿三定律、动量、终端速度、制动距离和弹性力等关键概念。理解这些原理不仅能帮助你在考试中取得好成绩，还能解释从车辆安全到运动表现、再到太空旅行中的一切现象。
1. Scalar and Vector Quantities | 标量与矢量
In physics, quantities are divided into scalars and vectors. A scalar quantity has magnitude (size) only, while a vector quantity has both magnitude and direction. Common scalars include distance, speed, mass, time and energy. Vectors include displacement, velocity, acceleration, force and momentum. The distinction is crucial because calculations involving vectors must account for direction. For example, if two forces of 3 N and 4 N act in the same direction, the resultant force is 7 N. If they act at right angles, the resultant is 5 N using Pythagoras' theorem.
在物理学中，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。常见的标量有距离、速率、质量、时间和能量。矢量包括位移、速度、加速度、力和动量。这种区分至关重要，因为涉及矢量的计算必须考虑方向。例如，如果两个力 3 N 和 4 N 作用在同一方向，合力为 7 N。如果它们成直角，则用勾股定理求得合力为 5 N。
| Scalar | Vector |
|---|---|
| distance | displacement |
| speed | velocity |
| mass | weight (force) |
| energy | momentum |
Always remember: "vector = magnitude + direction," and use arrows to represent vectors in diagrams.
请始终记住：“矢量 = 大小 + 方向”，并在示意图中用箭头表示矢量。
2. Speed, Velocity and Acceleration | 速度、速率与加速度
Speed is the distance travelled per unit time and is a scalar. It is calculated using speed = distance ÷ time direction, so it is a vector. Acceleration is the rate of change of velocity and is also a vector. The equation for acceleration is a = (v − u) / t, where v is final velocity, u is initial velocity and t is the time taken. The unit of acceleration is m/s² (metres per second squared). If an object slows down, acceleration is negative – this is often called deceleration or retardation.
速率是单位时间内通过的距离，是一个标量。计算公式为 速率 = 距离 ÷ 时间（v = d / t）。速度是给定方向上的速率，因此是一个矢量。加速度是速度变化的快慢，也是一个矢量。加速度的公式为 a = (v − u) / t，其中 v 是末速度，u 是初速度，t 是所用时间。加速度的单位是 m/s²（米每二次方秒）。如果物体变慢，加速度为负——这通常称为减速。
= 2 m/s². If it then brakes to rest in 4 s, the acceleration is (0 − 30) / 4 = −7.5 m/s².
一辆汽车以 20 m/s 的速度行驶，5 秒内加速到 30 m/s。它的加速度为 (30 − 20) / 5 = 2 m/s²。如果它随后刹车并在 4 秒内停止，则加速度为 (0 − 30) / 4 = −7.5 m/s²。
3. Distance-Time Graphs | 距离-时间图
A distance-time graph plots distance travelled against time. The gradient of the line represents speed. A horizontal line indicates the object is stationary. A straight, sloping line means constant speed. A curved line means changing speed (acceleration or deceleration). To calculate speed at a specific time on a curve, draw a tangent and find its gradient. The steeper the gradient, the higher the speed.
距离-时间图绘制距离随时间的变化关系。线的斜率代表速率。水平线表示物体静止。倾斜直线表示匀速。曲线表示变速（加速或减速）。要计算曲线上某一时刻的速率，可以画一条切线并求其斜率。斜率越陡，速率越大。
In an exam, you may need to interpret graphs: for example, a straight line from the origin shows constant speed, while a plateau shows the object has stopped. Always label axes with units.
在考试中，你可能需要解读图像：例如，从原点出发的直线表示匀速，而一段平台表示物体已停止。务必用单位标注坐标轴。
4. Velocity-Time Graphs | 速度-时间图
A velocity-time graph gives more information than a distance-time graph. The gradient represents acceleration, and the area under the graph represents displacement (distance in a given direction). A horizontal line above the time axis indicates constant velocity; a sloping line indicates constant acceleration. If the line crosses the time axis, the object changes direction. Negative velocity means motion in the opposite direction.
速度-时间图比距离-时间图提供更多信息。斜率表示加速度，图像下方的面积表示位移（给定方向上的距离）。时间轴上方的水平线表示恒定速度；斜线表示恒定加速度。如果线穿过时间轴，则物体改变了方向。负速度表示向相反方向运动。
gradient is 2 m/s², and the area (a triangle) gives the displacement: ½ × 10 × 20 = 100 m.
例如，一辆车从静止开始匀加速，10 秒内达到 20 m/s。速度-时间图是从 (0,0) 到 (10,20) 的直线。斜率为 2 m/s²，面积（三角形）给出位移：½ × 10 × 20 = 100 m。
5. Equations of Motion | 运动方程
For uniform acceleration in a straight line, there are four useful equations of motion (SUVAT):
对于匀加速直线运动，有四个有用的运动方程（SUVAT）：
- v = u + at
- s = ½ (u + v) t
- s = ut + ½ at²
- v² = u² + 2as
uantities are in consistent SI units. Choose the equation that includes the unknown you need and the known values you have. These equations only apply when acceleration is constant.
其中 s = 位移，u = 初速度，v = 末速度，a = 加速度，t = 时间。必须确保所有量使用一致的 SI 单位。选择包含未知量和你已知值的方程。这些方程只适用于加速度恒定的情况。
. Find the distance travelled: using s = ut + ½ at² = (2)(6) + ½(0.5)(36) = 12 + 9 = 21 m.
示例：一个自行车手从 2 m/s 开始以 0.5 m/s² 加速 6 秒。求行驶距离：使用 s = ut + ½ at² = (2)(6) + ½(0.5)(36) = 12 + 9 = 21 m。
6. Newton's First Law and Inertia | 牛顿第一定律与惯性
Newton's first law states that an object remains at rest or in uniform motion in a straight line unless acted upon by an external resultant force. This property is called inertia – the tendency of an object to resist changes in its motion. The more mass an object has, the greater its inertia, so it requires a larger force to change its velocity.
牛顿第一定律指出，除非受到合外力的作用，否则物体将保持静止或匀速直线运动状态。这种性质称为惯性——物体抵抗其运动状态变化的趋势。物体的质量越大，其惯性越大，因此需要更大的力来改变其速度。
A passenger in a car lurches forward when the car brakes suddenly because their body continues moving forward due to inertia while the car slows down. Seat belts provide the unbalanced force needed to stop the passenger.
汽车突然刹车时，车内的乘客会向前冲，这是因为惯性使他们的身体继续向前运动，而汽车在减速。安全带提供阻止乘客所需的非平衡力。
7. Newton's Second Law: F=ma | 牛顿第二定律：F=ma
Newton's second law explains the relationship between force, mass and acceleration. It is often written as 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. This equation tells us that the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass. Therefore, a larger force produces a larger acceleration, while a larger mass leads to a smaller acceleration for the same force.
牛顿第二定律解释了力、质量和加速度之间的关系。常写作 F = m × a，其中 F 是合力，单位牛顿 (N)；m 是质量，单位千克 (kg)；a 是加速度，单位 m/s²。这个等式告诉我们，物体的加速度与合外力成正比，与质量成反比。因此，力越大，加速度越大；而对于同样的力，质量越大，加速度越小。
5 m/s². Always be careful to use the resultant force, not just one of many forces acting.
如果一个 50 N 的力作用在质量为 10 kg 的小车上，加速度 a = F/m = 50/10 = 5 m/s²。要始终注意使用合外力，而不仅仅是众多作用力中的一个。
8. Newton's Third Law | 牛顿第三定律
Newton's third law states: "When object A exerts a force on object B, object B exerts an equal and opposite force on object A." These forces are called action and reaction pairs. They are always of the same type, equal in magnitude but opposite in direction, and act on two different bodies. Because they act on different objects, they do not cancel each other out.
牛顿第三定律指出：“当物体 A 对物体 B 施加一个力时，物体 B 也对物体 A 施加一个大小相等、方向相反的力。”这些力称为作用力与反作用力对。它们总是同种性质的力，大小相等、方向相反，并分别作用在两个不同物体上。由于作用在不同的物体上，它们不会相互抵消。
In rocket propulsion, the rocket pushes exhaust gases downwards (action); the gases push the rocket upwards (reaction). In walking, your foot pushes backwards on the ground, and the ground pushes you forwards.
在火箭推进中，火箭向下推排气（作用力）；气体向上推火箭（反作用力）。走路时，你的脚向后推地面，地面向前推你。
9. Terminal Velocity | 终端速度
When an object falls through a fluid (liquid or gas), it experiences two opposing forces: weight (downwards) and drag (upwards). Initially, weight is greater, and the object accelerates. As speed increases, drag increases. Eventually, drag equals weight, the resultant force becomes zero, and the object stops accelerating. It continues to fall at a constant speed called terminal velocity. A graph of velocity against time for a skydiver shows acceleration, then a curve levelling off to terminal speed, then a sharp drop when the parachute opens, followed by a new lower terminal velocity.
当物体在流体（液体或气体）中下落时，会受到两个相反的力：重力（向下）和阻力（向上）。起初，重力大于阻力，物体加速。随着速度增大，阻力也增大。最终，阻力等于重力，合外力为零，物体停止加速。它将以恒定的速度下落，这个速度称为终端速度。跳伞者的速度-时间图像先显示加速，然后曲线趋于一条水平线（终端速度），开伞后速度急剧下降，接着达到一个新的较低的终端速度。
Factors affecting terminal velocity include the object's mass, cross-sectional area and the fluid's density. This concept explains why a feather falls more slowly than a stone in air.
影响终端速度的因素包括物体的质量、横截面积和流体的密度。这个概念解释了为什么在空气中羽毛比石头下落得慢。
10. Stopping Distances | 制动距离
The total stopping distance of a vehicle is the sum of the thinking distance and the braking distance. Thinking distance is the distance travelled during the driver's reaction time (before the brakes are applied). Braking distance is the distance travelled while the brakes are applied and the vehicle decelerates to a stop. Reaction time can be affected by tiredness, alcohol, drugs and distractions. Braking distance increases with vehicle speed, poor tyre condition, wet or icy roads and worn brakes.
车辆的总制动距离是思考距离与刹车距离之和。思考距离是驾驶员反应时间内（在踩刹车之前）行驶的距离。刹车距离是踩下刹车后车辆减速至停止所行驶的距离。反应时间会受到疲劳、酒精、药物和分心的影响。刹车距离会随着车速提高、轮胎状况不佳、路面湿滑或结冰以及刹车磨损而增加。
Remember: doubling the speed roughly quadruples the braking distance because kinetic energy depends on v². This is a key safety lesson.
记住：速度加倍，刹车距离大约变为原来的四倍，因为动能依赖于 v²。这是一个重要的安全提示。
11. Momentum | 动量
Momentum (p) is a vector quantity defined as the product of mass and velocity: p = m × v. The unit is kg m/s. In a closed system, the total momentum before a collision or explosion equals the total momentum afterwards – this is the principle of conservation of momentum. It is used to analyse collisions and recoil problems. For example, when a stationary cannon fires a cannonball, the total momentum before firing is zero. Afterwards, the forward momentum of the cannonball is exactly balanced by the backward momentum (recoil) of the cannon.
动量 (p) 是一个矢量，定义为质量与速度的乘积：p = m × v。单位是 kg m/s。在封闭系统中，碰撞或爆炸前的总动量等于碰撞后的总动量——这就是动量守恒原理。它用于分析碰撞和反冲问题。例如，当一门静止的大炮发射炮弹时，发射前总动量为零。发射后，炮弹的前向动量正好被大炮的后向动量（后坐力）抵消。
is explains the importance of airbags and crumple zones, which increase the time over which momentum changes, thus reducing the force.
力也可以与动量的变化率联系起来：F = (mv − mu) / t。这解释了安全气囊和碰撞缓冲区的重要性，它们延长了动量变化的时间，从而减小了冲击力。
12. Hooke's Law and Forces in Springs | 胡克定律与弹簧中的力
Hooke's law describes the behaviour of many elastic materials, such as springs. It states that the extension (x) is directly proportional to the applied force (F), provided the elastic limit is not exceeded: F = k × x, where k is the spring constant (N/m). A graph of force against extension is a straight line through the origin up to the limit of proportionality. Beyond the elastic limit, the material deforms plastically and will not return to its original length when the force is removed.
胡克定律描述了许多弹性材料（如弹簧）的行为。它指出，只要不超过弹性限度，伸长量 (x) 与施加的力 (F) 成正比：F = k × x，其中 k 是劲度系数（N/m）。力-伸长量图像在比例限度内是一条过原点的直线。超过弹性限度后，材料发生塑性形变，撤去力后无法恢复原长。
energy is released when the spring returns to shape, as in a catapult or a mechanical toy.
拉伸弹簧所做的功（弹性势能）由 E = ½ F x 或 ½ k x² 计算。当弹簧恢复原状时，储存的能量会被释放，就像弹弓或机械玩具中那样。
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