SUVAT Equations (Part 1): Uniformly Accelerated Linear Motion | 匀加速直线运动基本公式（一）

📚 SUVAT Equations (Part 1): Uniformly Accelerated Linear Motion | 匀加速直线运动基本公式（一）

Welcome to the TutorHao A-Level Mathematics Revision Series. In this article, we focus on the core equations of uniformly accelerated linear motion, commonly known as the SUVAT equations. These formulas are essential for the Mechanics (Applied Mathematics) component of A-Level Mathematics and appear in nearly every exam paper, either directly or embedded in more complex problems.

欢迎阅读 TutorHao A-Level 数学复习系列。本文将聚焦于匀加速直线运动的核心方程，通常称为 SUVAT 方程。这些公式是 A-Level 数学中力学（应用数学）部分的基础，几乎每份试卷都会直接或间接考查。

The ability to set up and solve SUVAT problems is not just about memorising formulas — it is about building a systematic approach to kinematics. Once you master the three fundamental equations in this article, you will be able to handle a wide variety of motion problems with confidence.

掌握 SUVAT 问题的建立与求解，不仅仅是记住公式——更重要的是建立系统化的运动学解题思路。一旦你熟练掌握本文中的三大基本方程，你将能够自信地处理各类运动问题。

1. What Is Uniformly Accelerated Linear Motion? | 什么是匀加速直线运动？

Uniformly accelerated linear motion is motion along a straight line in which the acceleration remains constant in both magnitude and direction. This means that the velocity of the object changes by the same amount in each equal interval of time. For example, a falling object near the Earth’s surface (ignoring air resistance) experiences a constant acceleration of approximately 9.8 m/s².

匀加速直线运动是指物体沿直线运动，且加速度的大小和方向都保持恒定。这意味着物体在每个相等的时间间隔内速度的变化量相同。例如，忽略空气阻力时，地球表面附近的下落物体受到约 9.8 m/s² 的恒定加速度。

Three important conditions must hold for the SUVAT equations to be valid:

SUVAT 方程成立必须满足三个重要条件：

• The path must be a straight line. 运动路径必须是直线。
• The acceleration must be constant. 加速度必须恒定。
• All quantities must be measured from the same origin and direction. 所有量必须基于同一原点和方向进行测量。

When dealing with such motion, we can describe the complete motion using only five variables: displacement s, initial velocity u, final velocity v, acceleration a, and time t. These five variables form the foundation of the SUVAT notation.

在处理这类运动时，我们仅用五个变量就能完整描述运动：位移 s、初速度 u、末速度 v、加速度 a 和时间 t。这五个变量构成了 SUVAT 记号的基础。

2. The SUVAT Variables and Sign Conventions | SUVAT 变量与符号约定

The five standard variables are summarised in the table below. It is crucial to understand that displacement, velocity and acceleration are vector quantities — they have both magnitude and direction. In one-dimensional motion, direction is represented by positive and negative signs.

下表总结了五个标准变量。务必理解：位移、速度和加速度都是矢量——它们既有大小也有方向。在一维运动中，方向用正负号表示。

A clear sign convention is the single most important habit in kinematics. Before solving any problem, decide which direction is positive. For example, if you choose “upwards is positive”, then a falling object has a negative acceleration (or a negative velocity). Consistency prevents sign errors that can cost several marks.

清晰的符号约定是运动学中最重要的习惯。在解任何题目之前，先确定哪个方向为正。例如，若选取“向上为正”，则下落物体的加速度为负（或速度为负）。保持一致性可以避免因符号错误而失分。

3. The First Formula: v = u + at | 第一个公式：v = u + at

Acceleration is defined as the rate of change of velocity. For constant acceleration, we can write:

加速度定义为速度的变化率。对于恒定加速度，可以写成：

a = (v − u) ÷ t

Multiplying both sides by t and rearranging gives the first SUVAT equation:

两边同时乘以 t 并整理，得到第一个 SUVAT 方程：

v = u + at

This equation tells us that the final velocity is the sum of the initial velocity and the change in velocity caused by the acceleration acting over time t. It is most convenient when we know u, a and t and want to find v. It contains no displacement s, so it cannot directly answer questions about distance.

Published by TutorHao | Mathematics Revision Series | aleveler.com

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