➡️ 位移计算器（匀加速运动四种公式）Displacement Calculator (Constant Acceleration, Four Equations)

使用说明与常见问题How-to & FAQ

「位移计算器（匀加速运动四种公式）」是什么？What is the Displacement Calculator (Constant Acceleration, Four Equations) tool?

匀加速直线运动的位移：由初速度、加速度和时间 (s = v₀t + ½at²)；由初速度、末速度和时间 (s = (v₀ + v)t/2)；由初速度、末速度和加速度 (s = (v² − v₀²)/2a)；或由末速度、加速度和时间。同时补齐其余未知量。本地处理。Displacement under constant acceleration from initial velocity, acceleration and time (s = v₀t + ½at²), from initial and final velocity and time (s = (v₀ + v)t/2), from both velocities and acceleration (s = (v² − v₀²)/2a), or from final velocity, acceleration and time, filling in the other unknowns too. Processed locally.

如何使用「位移计算器（匀加速运动四种公式）」？How do I use the Displacement Calculator (Constant Acceleration, Four Equations) tool?

在「位移计算器（匀加速运动四种公式）」中，填写「已知」、「初速度 v₀ (m/s)」、「末速度 v (m/s)」、「加速度 a (m/s²)」、「时间 t (s)」等参数，结果会随输入实时计算并显示在下方。In the Displacement Calculator (Constant Acceleration, Four Equations): Fill in "Known", "Initial velocity v₀ (m/s)", "Final velocity v (m/s)", "Acceleration a (m/s²)", "Time t (s)"; results are recalculated instantly as you type.

四个公式分别是什么？What are the four equations?

s = v₀t + ½at²；s = (v₀ + v)t ÷ 2；v² = v₀² + 2as；s = vt − ½at²。再配合 v = v₀ + at，就能由任意三个已知量求出其余量。s = v₀t + ½at², s = (v₀ + v)t / 2, v² = v₀² + 2as and s = vt − ½at². Together with v = v₀ + at, any three knowns give the rest.

位移和路程有什么区别？How is displacement different from distance?

位移是从起点到终点的有向距离，可以为负；路程是实际走过的总长度。物体中途掉头时两者不同。Displacement is the signed straight-line change from start to finish and can be negative; distance is the total length travelled. They differ if the object turns back.

单位要统一吗？Do the units need to match?

需要。本页使用米、秒、m/s、m/s²。若用 km/h，请先除以 3.6 换成 m/s。Yes. This page uses metres, seconds, m/s and m/s². Divide km/h by 3.6 to get m/s first.

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

例如在「位移计算器（匀加速运动四种公式）」中填 已知 = v₀、a、t，初速度 v₀ (m/s) = 0，加速度 a (m/s²) = 2，时间 t (s) = 5，结果区显示：位移 s：25 m；初速度 v₀：0 m/s；末速度 v：10 m/s；加速度 a：2 m/s²；时间 t：5 s；平均速度：5 m/s；ℹ 位移有方向，取正负号；速度方向改变时，路程可能大于位移的绝对值。For example, entering Initial velocity v₀ (m/s) = 0, Acceleration a (m/s²) = 2, Time t (s) = 5 in the Displacement Calculator (Constant Acceleration, Four Equations) gives: Displacement s: 25 m; Initial velocity v₀: 0 m/s; Final velocity v: 10 m/s; Acceleration a: 2 m/s²; Time t: 5 s; Average velocity: 5 m/s; ℹ Displacement has a sign; if the motion reverses, the distance travelled can exceed its size.

哪些输入会被检查？Which inputs are validated?

「位移计算器（匀加速运动四种公式）」会检查这些输入——「初速度 v₀ (m/s)」、「末速度 v (m/s)」、「加速度 a (m/s²)」、「时间 t (s)」：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 Displacement Calculator (Constant Acceleration, Four Equations) checks its inputs — "Initial velocity v₀ (m/s)", "Final velocity v (m/s)", "Acceleration a (m/s²)", "Time t (s)": 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?

「位移计算器（匀加速运动四种公式）」的设置：「已知」可选 v₀、a、t、v₀、v、t、v₀、v、a、v、a、t（默认 v₀、a、t）；「初速度 v₀ (m/s)」默认 0；「末速度 v (m/s)」默认 10；「加速度 a (m/s²)」默认 2；「时间 t (s)」默认 5。每次生成结果都按当前设置处理。Settings in the Displacement Calculator (Constant Acceleration, Four Equations) — "Known": 4 choices; "Initial velocity v₀ (m/s)" default 0; "Final velocity v (m/s)" default 10; "Acceleration a (m/s²)" default 2; "Time t (s)" default 5. 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?

「位移计算器（匀加速运动四种公式）」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 Displacement Calculator (Constant Acceleration, Four Equations) 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.

「位移计算器（匀加速运动四种公式）」免费吗？需要注册吗？Is the Displacement Calculator (Constant Acceleration, Four Equations) free? Do I need an account?

「位移计算器（匀加速运动四种公式）」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 Displacement Calculator (Constant Acceleration, Four Equations) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.