📚 IGCSE AQA Physics: Kinematics Key Points | IGCSE AQA 物理：运动学考点精讲
Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. In the AQA IGCSE Physics specification, you are expected to confidently distinguish between scalar and vector quantities, interpret distance and displacement, speed and velocity, and calculate acceleration. You will also use the equations of uniformly accelerated motion (often called SUVAT equations) and analyse motion graphs. A clear understanding of free fall near the Earth’s surface completes this topic.
运动学是描述物体运动而不探究引起运动之力的物理学分支。在 AQA IGCSE 物理大纲中，你需要熟练区分标量与矢量，理解路程和位移、速率和速度，并能计算加速度。你还需要运用匀加速运动方程（常称 SUVAT 方程）并分析运动图像。掌握地球表面附近的自由落体也是这一主题的重要内容。
1. Scalars and Vectors | 标量与矢量
A scalar quantity has magnitude (size) only. Common examples include distance, speed, mass, time and energy. Scalars are added or subtracted using ordinary arithmetic.
标量只有大小（数值）。常见的例子包括路程、速率、质量、时间和能量。标量的加减使用普通算术。
A vector quantity has both magnitude and direction. Displacement, velocity, acceleration, force and momentum are all vectors. When adding vectors, you must consider their directions – for example, by drawing a scale diagram or using tip-to-tail addition.
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。合成矢量时，必须考虑它们的方向——例如通过绘制比例图或使用首尾相接法。
| Scalar quantities (标量) | Vector quantities (矢量) |
|---|---|
| Distance (路程) | Displacement (位移) |
| Speed (速率) | Velocity (速度) |
| Mass (质量) | Weight (重力) |
| Time (时间) | Acceleration (加速度) |
Table: Common scalar and vector pairs – you must learn these distinctions.
表：常见的标量-矢量对应——你必须记住这些区分。
2. Distance and Displacement | 路程与位移
Distance is the total length of the path travelled by an object. It is a scalar and is always positive. Displacement is the straight-line distance from the starting point to the finishing point, together with the direction. It is a vector and can be positive, negative or zero.
路程是物体经过路径的总长度，是标量且总为正值。位移是从起点指向终点的直线距离并带有方向，是矢量，可以为正、负或零。
Imagine a runner completing one full lap of a 400 m track. The distance covered is 400 m, but the displacement is zero because she returns to the start. This distinction is frequently tested in IGCSE questions.
想象一名跑步者在 400 m 的跑道上跑完一整圈。走过的路程是 400 m，但位移为零，因为她回到了起点。这一区别在 IGCSE 考题中经常出现。
When calculating displacement, remember to state both the magnitude and the direction, for example ‘100 m east’.
计算位移时，记得同时写出大小和方向，例如“向东 100 m”。
3. Speed and Velocity | 速率与速度
Speed is the rate at which distance is covered. It is a scalar quantity. The average speed can be calculated using:
速率是路程随时间的变化率，是标量。平均速率可用下式计算：
average speed = total distance ÷ total time
Velocity is the rate of change of displacement. It is a vector. The average velocity is:
速度是位移的变化率，是矢量。平均速度为：
average velocity = total displacement ÷ total time
Constant speed in a straight line means constant velocity. However, if an object moves at constant speed but changes direction (e.g. going around a roundabout at steady speed), its velocity is changing because the direction changes. This links directly to the idea of acceleration.
沿直线以恒定速率运动意味着速度恒定。然而，如果物体以恒定速率运动但方向改变（如以稳定速率绕转盘运动），则其速度改变，因为方向在变。这直接与加速度的概念相联系。
4. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector quantity. An object accelerates if its speed changes, or if its direction changes, or both. The equation for average acceleration is:
加速度是速度的变化率，是矢量。如果物体的速率改变，或方向改变，或两者同时改变，物体就在加速。平均加速度的方程为：
a = (v – u) ÷ t
where v is final velocity, u is initial velocity and t is time taken. The unit of acceleration is metres per second squared (m s⁻²).
其中 v 是末速度，u 是初速度，t 是经历的时间。加速度的单位是米每二次方秒（m s⁻²）。
Negative acceleration (deceleration) means the object is slowing down. In one-dimensional motion, if we choose a positive direction, deceleration is indicated by a negative value of a. Always pay attention to the sign convention in calculations.
负加速度（减速）意味着物体在减慢。在一维运动中，若我们选定一个正方向，减速就表示为 a 取负值。计算时务必留意正负号规定。
5. Equations of Uniform Acceleration (SUVAT) | 匀加速运动方程
When acceleration is constant, you can use the following four equations, often remembered by the letters SUVAT: s – displacement, u – initial velocity, v – final velocity, a – acceleration, t – time.
当加速度恒定时，可以运用以下四个方程，常记作 SUVAT：s – 位移，u – 初速度，v – 末速度，a – 加速度，t – 时间。
(1) v = u + at
(2) s = ut + ½at²
(3) v² = u² + 2as
(4) s = ½(u + v)t
When solving problems, first list the quantities you know and the quantity you need to find. Then pick the equation that contains these five variables. Ensure all quantities are in SI units (metres, seconds, m s⁻¹ etc.) before substituting.
解题时，先列出已知量和待求量。然后选择包含这五个量的方程。代入前，确保所有量都使用国际单位制（米、秒、米/秒等）。
A common trick: if the object starts from rest, u = 0. If it comes to rest, v = 0. For a freely falling object dropped from rest, u = 0 and a = g = 9.8 m s⁻² (downwards).
常见技巧：若物体从静止开始运动，u = 0。若物体停下，v = 0。对于从静止释放的自由落体，u = 0 且 a = g = 9.8 m s⁻²（向下）。
6. Velocity–Time Graphs | 速度–时间图像
A velocity–time (v–t) graph plots velocity on the vertical axis and time on the horizontal axis. Its features allow you to extract a wealth of information.
速度–时间（v–t）图像将速度置于纵轴，时间置于横轴。通过图像特征可解读大量信息。
- The gradient (slope) of the line gives the acceleration.
- 一条线的斜率（倾斜度）表示加速度。
- A horizontal line indicates constant velocity (zero acceleration).
- 水平线表示恒定速度（加速度为零）。
- A straight sloping line shows constant acceleration. An upward slope is positive acceleration; a downward slope is deceleration (negative acceleration).
- 倾斜的直线表示匀加速。向上倾斜为正加速度，向下倾斜为减速（负加速度）。
- The area under the graph (between the line and the time axis) represents the displacement. For irregular shapes, you may need to count squares or split the area into triangles and rectangles.
- 图像之下（线与时间轴之间）的面积代表位移。对于不规则图形，可能需要数格或将其分割为三角形和矩形。
Curved lines on a v–t graph indicate changing acceleration (non-uniform). For IGCSE, you are mainly expected to interpret straight-line segments and calculate areas.
v–t 图上的曲线表示加速度在变化（非匀加速）。在 IGCSE 阶段，主要要求解读直线段并计算面积。
7. Displacement–Time Graphs | 位移–时间图像
On a displacement–time (s–t) graph, the gradient gives the velocity. A straight, sloping line means constant velocity. A horizontal line indicates the object is stationary (velocity = 0).
在位移–时间（s–t）图像上，斜率表示速度。一条倾斜的直线意味着速度恒定。水平线表示物体静止（速度为零）。
A curved line on an s–t graph means the velocity is changing: if the curve gets steeper, the object is accelerating; if it becomes less steep, the object is decelerating. You can find the instantaneous velocity by drawing a tangent to the curve and calculating its gradient.
s–t 图上的曲线意味着速度在变化：曲线变陡表示物体在加速；曲线变缓表示物体在减速。可以通过在曲线上作切线并计算其斜率来求瞬时速度。
Be careful: the s–t graph does not directly show acceleration. That information must be inferred from how the slope changes.
注意：s–t 图并不直接显示加速度，必须通过斜率的变化来推断。
8. Free Fall and Acceleration due to Gravity | 自由落体与重力加速度
Near the Earth’s surface, all objects fall freely with the same acceleration due to gravity, g, provided air resistance is negligible. For IGCSE, g is usually taken as 9.8 m s⁻², though you might also use 10 m s⁻² if the question directs.
在地表附近，只要空气阻力可忽略，所有物体自由下落时都具有相同的重力加速度 g。IGCSE 中 g 通常取 9.8 m s⁻²，如果题目要求，也可取 10 m s⁻²。
For an object dropped from rest: u = 0, a = g. The downward direction is often taken as positive. The equations of motion apply exactly as before. For an object thrown upwards, the initial velocity is positive, but a = –g (decelerating on the way up).
对于从静止释放的物体：u = 0, a = g。通常取向下为正方向。运动方程完全适用。对于向上抛出的物体，初速度向上为正，而 a = –g（上升过程中减速）。
At the highest point of a vertically thrown object, the velocity is momentarily zero, but the acceleration is still g downwards. This is a common misconception.
在竖直上抛物体的最高点，速度瞬间为零，但加速度仍为向下的 g。这是一个常见的误解。
The famous demonstration of a feather and a coin falling together in a vacuum shows that without air resistance, all objects fall at the same rate, regardless of mass.
著名的真空管中羽毛和硬币同时下落的演示表明，在没有空气阻力的情况下，所有物体无论质量大小，都以相同速率下落。
9. Common Mistakes and Exam Tips | 常见错误与应试技巧
Confusing distance with displacement and speed with velocity is the most frequent error. Always check whether direction matters – if it does, use vector quantities.
混淆路程与位移、速率与速度是最常见的错误。务必检查方向是否重要——如果需要考虑方向，就应使用矢量。
When using the SUVAT equations, forgetting to use consistent signs for direction leads to incorrect answers. Define your positive direction at the start and stick to it.
使用 SUVAT 方程时，忘记对方向使用一致的符号会导致错误答案。一开始就定义正方向并贯彻始终。
In motion graphs, students often mistake the height of a v–t line for displacement; remember, displacement is the area under the line. Likewise, a flat line on an s–t graph does not mean the object has stopped moving forward – it may mean the object is stationary relative to the origin, but if velocity is zero, it is indeed not moving.
在运动图像中，学生常误将 v–t 图线的高度当作位移；请记住，位移是线下面积。同样，s–t 图中的水平线意味着物体相对于原点静止，此时速度为零，物体确实没有运动。
Always show your formula, substitution and final answer with correct units. AQA expects clear working for calculation questions. For graph questions, draw large tangents and show your gradient calculation clearly.
在计算题中，始终写出公式、代入过程和最终答案，并带上正确单位。AQA 评分要求计算清晰。对于图像题，画出足够大的切线并清楚地展示斜率计算过程。
Finally, in free-fall problems, never assume the object stops accelerating at the peak – the acceleration due to gravity is constant throughout the entire flight.
最后，在自由落体问题中，切勿认为物体在最高点就不再加速——重力加速度在整个飞行过程中都是恒定的。
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