📚 Movement & Position | 运动与位置
Understanding how objects move is fundamental in physics. This article covers the key concepts of movement and position as outlined in the Edexcel IGCSE Physics syllabus, including scalar and vector quantities, distance, displacement, speed, velocity, acceleration, graphical analysis, and the equations of motion. Mastering these topics will help you solve motion problems and interpret real-world scenarios.
理解物体如何运动是物理学的基础。本文涵盖了 Edexcel IGCSE 物理大纲中运动与位置的核心概念，包括标量和矢量、距离、位移、速率、速度、加速度、图像分析以及运动方程。掌握这些内容将帮助你解决运动问题并解释现实世界的情况。
1. Scalars and Vectors | 标量与矢量
A scalar quantity has only magnitude (size). Examples include distance, speed, mass, time, and energy. No direction is needed to describe a scalar.
标量只有大小（量值）。例如距离、速率、质量、时间和能量。描述标量不需要方向。
A vector quantity has both magnitude and direction. Examples are displacement, velocity, acceleration, force, and momentum. When stating a vector, you must give its direction (e.g., 5 m east).
矢量既有大小也有方向。例如位移、速度、加速度、力和动量。表示矢量时必须指明方向（例如 5 米 向东）。
Understanding the difference is crucial because calculations involving vectors require considering direction, often using positive and negative signs.
理解二者的区别至关重要，因为涉及矢量的计算需要考虑方向，通常使用正负号表示。
2. Distance and Displacement | 距离与位移
Distance is the total length of the path travelled by an object. It is a scalar quantity, always positive, and measured in metres (m).
距离是物体运动路径的总长度。它是一个标量，总是正值，以米（m）为单位。
Displacement is the straight-line distance from the starting point to the finishing point, in a specific direction. It is a vector. For example, if you walk 3 m east and then 4 m west, your total distance is 7 m, but your displacement is 1 m west.
位移是从起点到终点的直线距离，并有特定的方向。它是一个矢量。例如，如果你向东走 3 米，再向西走 4 米，总距离是 7 米，但位移是向西 1 米。
In many exam questions, you must distinguish between the two and use displacement for velocity and acceleration calculations.
在许多考试题目中，你必须区分二者，并在速度和加速度计算中使用位移。
3. Speed and Velocity | 速率与速度
Speed is the rate at which distance is covered. Average speed = total distance ÷ total time. Speed is a scalar.
速率是距离变化的快慢。平均速率 = 总距离 ÷ 总时间。速率是标量。
Velocity is the rate of change of displacement. Average velocity = total displacement ÷ total time. Velocity is a vector and can be positive or negative depending on direction.
速度是位移变化的快慢。平均速度 = 总位移 ÷ 总时间。速度是矢量，根据方向可为正或负。
Instantaneous speed is the speed at a particular moment; a speedometer in a car shows instantaneous speed. Instantaneous velocity includes direction.
瞬时速率是某一特定时刻的速率；汽车的速度表显示瞬时速率。瞬时速度则包含方向。
Units: both speed and velocity are measured in metres per second (m/s).
单位：速率和速度均以米每秒（m/s）为单位。
You can rearrange the formula to find distance or time: distance = speed × time, time = distance ÷ speed.
你可以变换公式求距离或时间：距离 = 速率 × 时间，时间 = 距离 ÷ 速率。
4. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector quantity. The formula is:
加速度是速度变化的快慢。它是一个矢量。公式为：
a = (v – u) / t
where v is final velocity, u is initial velocity, and t is time. Unit: m/s².
其中 v 为末速度，u 为初速度，t 为时间。单位：米每二次方秒（m/s²）。
Positive acceleration means increasing velocity in the positive direction; negative acceleration (deceleration) means decreasing velocity or acceleration in the opposite direction.
正加速度表示在正方向上速度增加；负加速度（减速）表示速度减小或加速度方向相反。
For uniform acceleration, the velocity changes by equal amounts in equal time intervals.
对于匀加速运动，相等时间内速度的变化量相等。
An object moving in a circle at constant speed is constantly accelerating because its direction changes, so velocity changes.
物体以恒定速率做圆周运动时，虽然速度的大小不变，但方向时刻变化，因此它一直在加速。
5. Distance-Time Graphs | 距离-时间图
A distance-time graph plots distance on the y-axis and time on the x-axis. The gradient (slope) of the line represents speed.
距离-时间图以距离为 y 轴，时间为 x 轴。线的斜率表示速率。
A straight, sloping line indicates constant speed. A horizontal line means the object is stationary. A curved line shows changing speed (acceleration or deceleration).
一条倾斜的直线表示匀速运动。水平线表示物体静止。曲线表示速率在变化（加速或减速）。
To find the speed at a specific time on a curve, draw a tangent and calculate its gradient.
要在曲线上求某一时刻的速率，可以画一条切线，计算其斜率。
The steeper the gradient, the higher the speed. The direction of the slope does not indicate direction of motion, only how distance increases.
斜率越陡，速率越大。斜率的方向不表示运动方向，只反映距离如何增加。
6. Velocity-Time Graphs | 速度-时间图
A velocity-time graph has velocity on the y-axis and time on the x-axis. The gradient gives the acceleration.
速度-时间图以速度为 y 轴，时间为 x 轴。斜率表示加速度。
The area under the graph between two times represents the displacement (or distance if direction is not considered) travelled in that interval.
图线下某时间段内的面积表示该段时间内的位移（若不考虑方向则为距离）。
A horizontal line indicates constant velocity (zero acceleration). A sloping straight line shows constant acceleration. A curve shows changing acceleration.
水平线表示匀速运动（加速度为零）。倾斜直线表示匀加速运动。曲线表示加速度在变化。
To calculate distance from a v-t graph, find the area: for a rectangle, area = base × height; for a triangle, area = ½ × base × height. Break complex shapes into rectangles and triangles.
利用 v-t 图计算距离时，可求面积：矩形面积 = 底×高；三角形面积 = ½×底×高。将复杂图形分解为矩形和三角形。
Velocity can be negative, meaning motion in the opposite direction. The area above the time axis is positive displacement; area below is negative.
速度可为负值，表示反方向运动。时间轴上方面积为正位移；下方面积为负位移。
The table below compares distance-time and velocity-time graphs:
下表对比了距离-时间图和速度-时间图：
| Feature | Distance-Time Graph | Velocity-Time Graph |
|---|---|---|
| Gradient | Speed | Acceleration |
| Area under graph | No physical meaning | Displacement (distance) |
| Horizontal line | Stationary | Constant velocity |
| Straight sloping line | Constant speed | Constant acceleration |
7. Equations of Motion (SUVAT) | 运动方程
For motion with constant acceleration in a straight line, we use the SUVAT equations, where s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time.
对于直线上的匀加速运动，我们使用 SUVAT 方程，其中 s 为位移，u 为初速度，v 为末速度，a 为加速度，t 为时间。
1. v = u + a t
2. s = u t + ½ a t²
3. v² = u² + 2 a s
4. s = (u + v) t / 2
You must choose the equation that contains the quantities you know and the one you want to find. Always check the sign convention: usually, upward or rightward is taken as positive.
必须选择包含已知量和待求量的方程。始终检查正负号规则：通常取向上或向右为正方向。
Tip: Write down the known variables and the unknown one before selecting the equation.
提示：在选择方程之前，先列出已知变量和未知变量。
- v = u + at (no s)
- s = ut + ½at² (no v)
- v² = u² + 2as (no t)
- s = (u+v)t/2 (no a)
Keep these forms handy for quick recall.
牢记这些形式以快速应用。
8. Free Fall | 自由落体
Free fall is motion under the influence of gravity only, with negligible air resistance. The acceleration due to gravity, g, is approximately 9.8 m/s² on Earth (often rounded to 10 m/s² in IGCSE calculations).
自由落体是仅在重力作用下的运动，空气阻力可忽略。重力加速度 g 在地球上约为 9.8 m/s²（IGCSE 计算中通常取 10 m/s²）。
All objects in free fall, regardless of mass, accelerate at the same rate if air resistance is ignored.
若忽略空气阻力，所有自由落体的物体无论质量大小，加速度都相同。
You can apply the SUVAT equations to free fall by replacing a with g (or -g depending on
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