📚 Understanding Motion | 理解运动
Motion is one of the most fundamental topics in CIE A-Level Physics. To describe how objects move, you need precise quantities such as displacement, velocity and acceleration, and you need to interpret graphs and equations that link these quantities together.
运动是 CIE A-Level 物理中最基础的主题之一。要描述物体如何运动，你需要使用位移、速度和加速度等精确物理量，并且需要解读把它们联系起来的图像与方程。
1. Scalars and Vectors in Motion | 运动中的标量与矢量
In physics, quantities are divided into scalars and vectors. A scalar has magnitude only, while a vector has both magnitude and direction.
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。
Distance and speed are scalars. Displacement and velocity are vectors. The direction of a vector is essential when combining or resolving motions.
路程和速率是标量。位移和速度是矢量。矢量的方向在合成或分解运动时至关重要。
In one-dimensional motion, vector direction is often shown by a positive or negative sign. For example, if moving to the right is positive, then moving to the left is negative.
在一维运动中，矢量方向通常用正号或负号表示。例如，若取向右为正，则向左运动为负。
2. Displacement, Distance, Speed and Velocity | 位移、路程、速率与速度
Displacement s is defined as the change in position of an object from a chosen origin. It can be positive or negative depending on direction.
位移 s 定义为物体相对于选定原点的位置变化。根据方向，它可以是正值或负值。
Distance is the total length of the path travelled, so it is always positive and never decreases. Displacement, by contrast, can be zero even when distance is not.
路程是物体经过路径的总长度，因此它总是正值，并且不会减少。相比之下，即使路程不为零，位移也可能为零。
Average speed is total distance divided by total time. Average velocity is total displacement divided by total time.
平均速率等于总路程除以总时间。平均速度等于总位移除以总时间。
average speed = total distance ÷ total time; average velocity = total displacement ÷ total time
平均速率 = 总路程 ÷ 总时间；平均速度 = 总位移 ÷ 总时间
Instantaneous velocity is the velocity at one specific moment. It is found from the gradient of a displacement-time graph at that point.
瞬时速度是某一特定时刻的速度。它可由位移-时间图在该点的斜率求得。
3. Acceleration and Its Sign | 加速度及其正负
Acceleration a is the rate of change of velocity. It is a vector, so its sign depends on the chosen positive direction.
加速度 a 是速度的变化率。它是矢量，因此其正负取决于选定的正方向。
a = Δv ÷ Δt = (v − u) ÷ t
加速度 = 速度变化量 ÷ 时间
The SI unit of acceleration is metre per second squared, written m s⁻² or m/s². This means the velocity changes by a certain number of metres per second every second.
加速度的国际单位是米每二次方秒，写作 m s⁻² 或 m/s²。这意味着速度每秒改变一定的米每秒。
If an object slows down, the acceleration is in the opposite direction to its velocity. This is often called deceleration or retardation, but CIE usually treats it as negative acceleration.
如果物体减速，加速度与速度方向相反。这通常称为减速或 retardation，但 CIE 通常将其视为负加速度。
You must check directions carefully: a negative acceleration does not always mean slowing down. If velocity is also negative, a negative acceleration can mean speeding up in the negative direction.
你必须仔细判断方向：负加速度并不总是表示减速。如果速度也为负，那么负加速度可能表示沿负方向加速。
4. Graphs of Motion: Displacement-Time Graphs | 运动图像：位移-时间图
On a displacement-time graph, the gradient gives velocity. A straight line means constant velocity; a curved line means changing velocity, so acceleration is present.
在位移-时间图上，斜率表示速度。直线代表匀速；曲线代表速度变化，因此存在加速度。
A horizontal line indicates the object is stationary. A positive gradient means motion in the positive direction; a negative gradient means motion in the negative direction.
水平线表示物体静止。正斜率表示沿正方向运动；负斜率表示沿负方向运动。
For a curved graph, the gradient of a chord gives average velocity over an interval, while the gradient of a tangent at a point gives instantaneous velocity.
对于曲线图像，割线的斜率给出某段时间内的平均速度，而某点切线的斜率给出瞬时速度。
5. Velocity-Time and Acceleration-Time Graphs | 速度-时间图与加速度-时间图
On a velocity-time graph, the gradient gives acceleration and the area under the graph gives displacement.
在速度-时间图上，斜率表示加速度，图线下的面积表示位移。
A horizontal line on a velocity-time graph indicates constant velocity. A straight sloping line indicates constant acceleration. The area above the time axis is positive displacement, and the area below is negative displacement.
速度-时间图上的水平线表示匀速。倾斜直线表示匀加速。时间轴以上的面积表示正位移，以下的面积表示负位移。
If the acceleration is not constant, the velocity-time graph is curved. The gradient at a point still gives instantaneous acceleration, and the total area still gives total displacement.
如果加速度不是恒定的，速度-时间图就是曲线。某点的斜率仍给出瞬时加速度，总面积仍给出总位移。
On an acceleration-time graph, the area under the line gives the change in velocity between two times.
在加速度-时间图上，图线下的面积表示两个时刻之间速度的变化量。
6. The SUVAT Equations | SUVAT 方程
For motion in a straight line with constant acceleration, four equations link displacement s, initial velocity u, final velocity v, acceleration a and time t.
对于匀加速直线运动，四个方程联系位移 s、初速度 u、末速度 v、加速度 a 和时间 t。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = (u + v)t ÷ 2
These equations only apply when acceleration is constant and motion is along a straight line. You must use a consistent set of units, usually metres, seconds and metres per second.
这些方程仅适用于加速度恒定且运动沿直线的情况。你必须使用一套一致的单位，通常是米、秒和米每秒。
Choose the equation that includes the quantity you want to find and excludes the quantity you do not need. Always write down the known values and check signs before substituting.
选择包含待求量、不包含无用量的方程。在代入之前，务必写下已知量并检查符号。
7. Deriving the Equations of Motion | 运动方程推导
The first equation comes directly from the definition of acceleration: a = (v − u) ÷ t, so v = u + at.
第一个方程直接来自加速度的定义：a = (v − u) ÷ t，因此 v = u + at。
The displacement equation can be derived from the area under a velocity-time graph. For constant acceleration, the area is a trapezium of parallel sides u and v and height t.
位移方程可由速度-时间图下的面积推导。匀加速时，该面积是上下底为 u 和 v、高为 t 的梯形。
s = average velocity × t = (u + v)t ÷ 2
位移 = 平均速度 × 时间
Substituting v = u + at into s = (u + v)t ÷ 2 gives s = ut + ½at². Combining this with v = u + at to eliminate t gives v² = u² + 2as.
将 v = u + at 代入 s = (u + v)t ÷ 2 得到 s = ut + ½at²。将此式与 v = u + at 联立消去 t，得到 v² = u² + 2as。
Understanding the derivations helps you remember which physical idea each equation expresses, so you can apply them correctly under exam pressure.
理解推导过程有助于记住每个方程表达的物理含义，从而在考试压力下正确应用。
8. Free Fall under Gravity | 重力作用下的自由落体
Near the Earth’s surface, all objects in free fall accelerate downwards at approximately 9.81 m s⁻², denoted g. Air resistance is ignored in ideal free fall.
在地球表面附近，所有自由落体物体以约 9.81 m s⁻² 的加速度下落，记作 g。理想自由落体忽略空气阻力。
If upward is chosen as positive, then a = −g = −9.81 m s⁻². If downward is chosen as positive, then a = +g = +9.81 m s⁻². Consistency of signs is essential.
如果取向上为正，则 a = −g = −9.81 m s⁻²。如果取向下为正，则 a = +g = +9.81 m s⁻²。符号的一致性至关重要。
An object thrown upward comes to rest momentarily at its highest point, but its acceleration is still g downward at that instant. Velocity changes sign while acceleration remains constant.
向上抛出的物体在最高点瞬时静止，但此刻加速度仍为向下的 g。速度改变符号，而加速度保持恒定。
It is often useful to split a vertical motion into an upward journey and a downward journey, or to treat the whole flight as one continuous SUVAT process.
通常可以把竖直运动分成上升过程和下降过程，或者把整个飞行当作一个连续的 SUVAT 过程来处理。
9. Projectile Motion | 抛体运动
Projectile motion can be analysed by resolving into independent horizontal and vertical components. The horizontal motion has constant velocity because ax = 0. The vertical motion has constant acceleration ay = g downward.
抛体运动可以通过分解为独立的水平和竖直分量来分析。水平方向因 ax = 0 而做匀速运动；竖直方向因 ay = g 向下而做匀加速运动。
The horizontal and vertical components are linked only by time t. Use SUVAT equations separately in each direction.
水平和竖直分量仅通过时间 t 联系。分别对每个方向使用 SUVAT 方程。
If a projectile is launched horizontally, its initial vertical velocity is zero. Its vertical displacement after time t is s = ½gt², while its horizontal displacement is x = ut.
如果抛体水平抛出，其初始竖直速度为零。经过时间 t 后，竖直位移为 s =
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