📚 Vertical Motion Under Gravity | 重力作用下的竖直运动分析
Vertical motion under gravity is one of the most fundamental topics in A-level Mechanics, forming the bridge between kinematics and dynamics. When an object moves vertically near the Earth’s surface, it experiences a constant acceleration due to gravity, which allows us to apply the standard equations of motion with a fixed acceleration value. Mastery of this topic is essential for success in both AS and A2 Mechanics papers.
重力作用下的竖直运动是 A-level 力学中最基础的课题之一，它连接了运动学与动力学。当物体在地球表面附近做竖直运动时，会受到恒定的重力加速度，这使我们能够运用恒定加速度下的标准运动学方程。掌握这一课题对 AS 和 A2 力学考试都至关重要。
1. The Equations of Motion | 运动学方程
For any object moving with constant acceleration, we use the SUVAT equations. In vertical motion, the acceleration a is replaced by g (or -g depending on the chosen sign convention). These four equations are the foundation of all problems in this topic.
对于任何做匀加速运动的物体，我们使用 SUVAT 方程组。在竖直运动中，加速度 a 被替换为 g（或 -g，取决于所选符号约定）。这四组方程是该课题所有问题的基础。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Here, u is the initial velocity (m/s), v is the final velocity (m/s), a is the acceleration (m/s²), t is the time (s), and s is the displacement (m). All quantities except time are vectors, so direction must be specified at every stage of the solution.
其中，u 是初速度（m/s），v 是末速度（m/s），a 是加速度（m/s²），t 是时间（s），s 是位移（m）。除时间外所有量均为矢量，因此解题的每一步都必须标明方向。
2. Sign Convention | 符号约定
The single most important decision in solving vertical motion problems is choosing a positive direction. The two common conventions are upward positive or downward positive. Once chosen, you must remain consistent throughout the entire problem; changing direction midway is one of the most frequent causes of incorrect answers in examinations.
解决竖直运动问题时最关键的决定是选择正方向。常见的有两种约定：向上为正或向下为正。一旦选定，整个问题中必须始终保持一致；中途改变方向是考试中出现错误答案的最常见原因之一。
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Upward positive: The acceleration due to gravity acts
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