📚 Mastering SUVAT Equations and Projectile Motion for Edexcel Physics | 精通 Edexcel 物理中的运动学方程与抛体运动
For Edexcel A Level Physics, mechanics forms the foundation of Unit 1, and the SUVAT equations are among the most frequently assessed tools. They describe uniformly accelerated motion in a straight line, and when combined with vector resolution, they allow you to solve projectile motion problems with confidence. This article breaks down the key definitions, derivations, sign conventions, and exam technique you need.
在 Edexcel A Level 物理中，力学是 Unit 1 的基础，而 SUVAT 方程是考试中最常考查的工具之一。它们描述直线上的匀加速运动，结合矢量分解后，能够帮助你自信地解决抛体运动问题。本文将分解关键定义、推导、符号规则和考试技巧。
1. The SUVAT Variables | SUVAT 变量
SUVAT stands for five quantities: displacement s, initial velocity u, final velocity v, acceleration a, and time t. All five must be measured in SI units: metres (m), metres per second (m s⁻¹), metres per second squared (m s⁻²), and seconds (s).
SUVAT 代表五个物理量：位移 s、初速度 u、末速度 v、加速度 a 和时间 t。五个量必须使用国际单位制：米（m）、米每秒（m s⁻¹）、米每二次方秒（m s⁻²）和秒（s）。
In Edexcel questions, displacement is a vector, so a chosen positive direction must be applied consistently to u, v, a and s. If an object changes direction, s can be negative or less than the total distance travelled.
在 Edexcel 考题中，位移是矢量，因此必须规定正方向，并对 u、v、a 和 s 始终沿用该方向。若物体改变运动方向，位移可能为负或小于总路程。
2. Deriving the Four SUVAT Equations | 四个 SUVAT 方程的推导
From the definitions of acceleration and average velocity, four equations are obtained for constant acceleration:
由加速度和平均速度的定义，可得到匀加速运动的四个方程：
v = u + at
s = (u + v)t / 2
s = ut + ½ at²
v² = u² + 2as
third is found by substituting v from the first into the second. The fourth eliminates t.
第一式由 a = (v − u)/t 整理得到；第二式利用平均速度乘时间；第三式将第一式代入第二式消去 v；第四式消去 t 得到。
You are not required to derive them in every Edexcel paper, but knowing how they connect helps you avoid using the wrong one.
并非每份 Edexcel 试卷都要求推导，但理解它们之间的联系有助于避免用错公式。
3. Choosing the Right Equation | 选择正确的方程
Each SUVAT equation omits one variable. Choose the equation that does not contain the quantity you are not given and not asked to find.
每个 SUVAT 方程都少一个变量。选择不包含“未给出且未要求求的物理量”的方程。
| Equation | Missing quantity |
|---|---|
| v = u + at | s |
| s = (u + v)t / 2 | a |
| s = ut + ½ at² | v |
| v² = u² + 2as | t |
question gives u, a, t and asks for v, use v = u + at because it excludes displacement s.
例如，若题目给出 u、a、t 并求 v，应使用 v = u + at，因为该方程不含位移 s。
Many Edexcel candidates lose marks by forcing a formula with too many unknowns. Always write down the given quantities and the target variable first.
许多 Edexcel 考生因强行套用含未知量过多的公式而失分。应先列出已知量和待求量。
4. Vertical Motion Under Gravity | 重力作用下的竖直运动
For free fall near Earth' oose upwards as positive, then a = −9.81 m s⁻²; if downwards is positive, a = +9.81 m s⁻².
在地球表面附近自由下落时，加速度为向下 g = 9.81 m s⁻²。若取向上为正，则 a = −9.81 m s⁻²；若取向下为正，则 a = +9.81 m s⁻²。
Sign errors are the most common mistake in Edexcel mechanics. Always state your positive direction at the start of a solution and keep it unchanged for displacement, velocity and acceleration.
符号错误是 Edexcel 力学中最常见的失分点。解题开始时应明确正方向，并在位移、速度和加速度中始终保持不变。
A ball thrown straight upwards returns to the same level with the same speed but opposite velocity. At the highest point, its instantaneous velocity is zero, but its acceleration is still g downwards.
竖直上抛的球回到同一高度时，速度大小相同但方向相反。在最高点，瞬时速度为零，但加速度仍为向下的 g。
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