Variable Acceleration | 变加速度

📚 Variable Acceleration | 变加速度

In Edexcel A Level Mechanics, many motion problems involve acceleration that is not constant. The standard SUVAT equations fail in these cases. Instead, students must use calculus to link displacement, velocity and acceleration. This article covers differentiation, integration, initial conditions, turning points and the difference between displacement and distance travelled.

在 Edexcel A Level 力学中，许多运动问题的加速度并不是恒定的。此时标准的 SUVAT 公式不再适用，学生必须使用微积分来联系位移、速度和加速度。本文涵盖微分、积分、初始条件、静止时刻以及位移与路程的区别。

1. What Is Variable Acceleration? | 什么是变加速度？

Acceleration is variable when it changes with time t or displacement s. For example, a = 6t − 2 means acceleration increases linearly with time. Under these conditions, equations such as v = u + at and s = ut + ½at² are no longer valid.

当加速度随时间 t 或位移 s 变化时，就称为变加速度。例如 a = 6t − 2 表示加速度随时间线性增大。此时 v = u + at 和 s = ut + ½at² 等公式不再成立。

Calculus provides the exact relationship: velocity is the derivative of displacement, and acceleration is the derivative of velocity.

微积分提供了精确的关系：速度是位移的导数，加速度是速度的导数。

2. Core Definitions and Notation | 核心定义与记号

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