📐 加速度大小（矢量）Magnitude of Acceleration

使用说明与常见问题How-to & FAQ

「加速度大小（矢量）」是什么？What is the Magnitude of Acceleration tool?

三维加速度矢量的大小 |a| = √(aₓ² + aᵧ² + aᵤ²)；也可用初速度、末速度和时间计算平均加速度。本地处理。Magnitude of a 3-D acceleration vector |a| = √(aₓ² + aᵧ² + aᵤ²); or the average acceleration from initial and final velocity and time. Processed locally.

如何使用「加速度大小（矢量）」？How do I use the Magnitude of Acceleration tool?

填写加速度的三个分量 aₓ、aᵧ、aᵤ，即可得到大小 |a| = √(aₓ² + aᵧ² + aᵤ²)；也可以填写初速度、末速度和时间求平均加速度。结果会随输入实时更新。Enter the components aₓ, aᵧ and aᵤ to get the magnitude |a| = √(aₓ² + aᵧ² + aᵤ²), or fill in the initial speed, final speed and time for the average acceleration. The result updates as you type.

向心加速度？Centripetal?

匀速圆周运动 a = v² / r，方向指向圆心。For uniform circular motion a = v² / r toward the centre.

能举个计算实例吗？Can you show a worked example?

例如在「加速度大小（矢量）」中填 aₓ m/s² = 3，aᵧ m/s² = 4，aᵤ m/s² = 12，结果区显示：加速度大小：13 m/s²；g（约 9.80665）：1.3256 gFor example, entering aₓ m/s² = 3, aᵧ m/s² = 4, aᵤ m/s² = 12 in the Magnitude of Acceleration gives: Magnitude: 13 m/s²; g (≈ 9.80665): 1.3256 g

哪些输入会被检查？Which inputs are validated?

「加速度大小（矢量）」会检查这些输入——「aₓ m/s²」、「aᵧ m/s²」、「aᵤ m/s²」：必须填写；「初速度 m/s（可选）」、「末速度 m/s（可选）」：不能为负数；「时间 s（可选）」：可留空；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Magnitude of Acceleration checks its inputs — "aₓ m/s²", "aᵧ m/s²", "aᵤ m/s²": required; "Initial speed m/s (optional)", "Final speed m/s (optional)": cannot be negative; "Time s (optional)": optional; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「加速度大小（矢量）」的设置：「aₓ m/s²」默认 3；「aᵧ m/s²」默认 4；「aᵤ m/s²」默认 12；「初速度 m/s（可选）」可留空；「末速度 m/s（可选）」可留空；「时间 s（可选）」可留空。每次生成结果都按当前设置处理。Settings in the Magnitude of Acceleration — "aₓ m/s²" default 3; "aᵧ m/s²" default 4; "aᵤ m/s²" default 12; "Initial speed m/s (optional)" optional; "Final speed m/s (optional)" optional; "Time s (optional)" optional. The result always uses the current settings.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「加速度大小（矢量）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Magnitude of Acceleration uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「加速度大小（矢量）」免费吗？需要注册吗？Is the Magnitude of Acceleration free? Do I need an account?

「加速度大小（矢量）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Magnitude of Acceleration is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.