📚 IGCSE CCEA Physics: Kinematics Key Points | IGCSE CCEA 物理：运动学 考点精讲
Kinematics is the branch of physics that describes motion without considering its causes. In IGCSE CCEA Physics, you need to master concepts such as speed, velocity, acceleration, graphical analysis and the equations of motion. This revision guide breaks down each key topic with clear explanations and examples.
运动学是描述物体运动而不考虑其原因的物理学分支。在 IGCSE CCEA 物理中，你需要掌握速率、速度、加速度、图像分析以及运动方程等概念。本复习指南将逐一解析每个重点内容，并配有清晰的解释和例题。
1. Scalars and Vectors | 标量与矢量
A scalar quantity has only magnitude (size) and no direction. Examples include distance, speed, mass, time and energy.
标量只有大小，没有方向。常见的标量有距离、速率、质量、时间和能量。
A vector quantity has both magnitude and direction. Examples include displacement, velocity, acceleration, force and momentum. Vectors are often represented by arrows; the length shows magnitude, and the arrowhead shows direction.
矢量既有大小又有方向。常见的矢量包括位移、速度、加速度、力和动量。矢量通常用箭头表示；长度表示大小，箭头指向表示方向。
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 and is always positive. Displacement is the straight-line distance from the starting point to the final position, in a specific direction. It is a vector.
距离是物体运动路径的总长度。它是标量，恒为正值。位移是从起点到终点沿直线的长度，并带有特定方向。它是矢量。
| Property | Distance | Displacement |
|---|---|---|
| Type | Scalar | Vector |
| Depends on path? | Yes | No |
| Can it be zero? | Only if no movement | Yes, if start = end |
If you walk 3 m east then 4 m west, the distance is 7 m, but the displacement is 1 m west.
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。
3. Speed and Velocity | 速率与速度
Speed = distance / time. It is a scalar. Average speed = total distance / total time. Velocity = displacement / time. It is a vector. If an object moves in a straight line without turning, the magnitude of velocity equals speed.
速率 = 距离 / 时间。它是标量。平均速率 = 总距离 / 总时间。速度 = 位移 / 时间。它是矢量。如果物体沿直线运动不转向，速度的大小等于速率。
v = s / t
Instantaneous speed is the speed at a particular moment, shown by a speedometer. Instantaneous velocity is the velocity at an instant, including direction.
瞬时速率是某一时刻的速率，由速度表显示。瞬时速度是某一时刻的速度，包括方向。
4. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector. a = (v − u) / t, where v is final velocity, u is initial velocity, t is time taken. Unit: m/s².
加速度是速度的变化率。它是矢量。a = (v − u) / t，其中 v 是末速度，u 是初速度，t 是所用时间。单位：m/s²。
a = (v − u) / t
Deceleration (negative acceleration) means slowing down; the acceleration is opposite to the direction of motion.
减速度（负加速度）表示速度减小；加速度方向与运动方向相反。
5. Equations of Uniformly Accelerated Motion (SUVAT) | 匀加速运动方程 (SUVAT)
For motion with constant acceleration in a straight line, the following variables are used: s – displacement, u – initial velocity, v – final velocity, a – acceleration, t – time. The equations are:
对于匀变速直线运动，使用以下变量：s – 位移，u – 初速度，v – 末速度，a – 加速度，t – 时间。方程如下：
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = (u + v) t / 2
These equations only apply when acceleration is constant. You must ensure the signs (positive/negative) are correct for direction.
这些方程仅适用于加速度恒定的情况。必须确保方向的正负号正确。
6. Using SUVAT – Worked Example | 使用 SUVAT – 例题
A car accelerates from rest at 2 m/s² for 5 seconds. Find the distance travelled.
一辆汽车从静止开始以 2 m/s² 的加速度行驶 5 秒。求行驶的距离。
Known: u = 0, a = 2 m/s², t = 5 s, s = ? Use s = u t + ½ a t². s = 0 + ½ × 2 × 5² = 0.5 × 2 × 25 = 25 m.
已知：u = 0，a = 2 m/s²，t = 5 s，s = ?。使用公式 s = u t + ½ a t²。s = 0 + ½ × 2 × 5² = 0.5 × 2 × 25 = 25 m。
7. 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) represents speed. A straight horizontal line means the object is stationary. A straight sloping line means constant speed. A curved line indicates changing speed (acceleration or deceleration).
距离-时间图将距离标在 y 轴，时间标在 x 轴。斜率表示速率。水平直线表示物体静止。倾斜直线表示匀速运动。曲线表示速率在变化（加速或减速）。
To find the speed at a point, draw a tangent to the curve and calculate its gradient.
要找到某一点的速率，可画出曲线的切线并计算其斜率。
8. 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 acceleration. A horizontal line means constant velocity (zero acceleration). A sloping straight line means constant acceleration. The area under the graph represents the displacement travelled.
速度-时间图中 y 轴为速度，x 轴为时间。斜率表示加速度。水平线表示速度恒定（零加速度）。倾斜直线表示匀加速度。图线下方的面积表示位移。
For a graph with a positive slope, acceleration is positive; a negative slope indicates deceleration. When the graph crosses the time axis, the object changes direction.
斜率为正，表示正向加速度；斜率为负，表示减速。当图线穿过时间轴时，物体改变运动方向。
9. Free Fall and Gravity | 自由落体与重力加速度
Near the Earth’s surface, all objects fall with the same acceleration due to gravity, g = 9.8 m/s² (often rounded to 10 m/s² in CCEA questions) if air resistance is negligible. This acceleration is constant.
在地球表面附近，如果空气阻力忽略不计，所有物体以相同的重力加速度 g = 9.8 m/s²（在 CCEA 考试中常取 10 m/s²）下落。该加速度恒定。
Free fall means the only force acting is gravity. Use SUVAT equations with a = g (take downward as positive, or careful with signs).
自由落体意味着只受重力作用。使用 SUVAT 方程，a = g（规定向下为正，或注意符号）。
For an object thrown upwards, acceleration is still g downwards. At the highest point, velocity = 0, but acceleration = g.
对于上抛物体，加速度仍为向下的 g。在最高点，速度为零，但加速度仍为 g。
10. Projectile Motion Basics | 抛体运动基础
A projectile is an object launched into the air, moving under gravity. The horizontal and vertical motions are independent. Horizontally, velocity is constant (ignoring air resistance). Vertically, the object accelerates downwards at g.
抛体是发射到空中、在重力作用下运动的物体。水平和竖直运动是独立的。水平方向速度恒定（忽略空气阻力）。竖直方向物体以加速度 g 向下运动。
For a horizontally launched projectile, initial vertical velocity u_y = 0. Use s_y = ½ g t² to find time of flight. Horizontal range = horizontal velocity × time.
对于水平抛出的物体，初速度竖直分量 u_y = 0。使用 s_y = ½ g t² 求飞行时间。水平射程 = 水平速度 × 时间。
11. Common Mistakes and Tips | 常见错误与技巧
Mixing up distance and displacement, or speed and velocity: always check if direction matters. Forgeting to square time in s = ut + ½ at². Using the wrong sign for acceleration (e.g., negative for deceleration or downward motion). Not converting units (cm to m, minutes to seconds).
混淆距离与位移、或速率与速度：务必检查方向是否相关。在 s = ut + ½ at² 中忘记给时间平方。加速度符号用错（例如减速或向下运动时未取负）。未转换单位（厘米转米，分钟转秒）。
For graphs, misreading the area under velocity-time graph as distance; it gives displacement, and total distance requires summing absolute areas if direction changes.
对于图像，将速度-时间图下方面积误读为距离；它给出的是位移，如果方向改变，总距离需各项绝对值之和。
Always write down the known SUVAT variables before choosing an equation. Label units clearly.
在选用方程前，先写出已知的 SUVAT 变量。明确标注单位。
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