🚀 位移与路程：走多远 vs 挪了多远🚀 Displacement & Distance: How Far You Ran vs How Far You Moved
接下来几片，我们一起研究「运动」。描述运动的第一步：把「跑了多少」说清楚——可绕操场跑一圈回到起点，这算 400 米，还是 0 米？For the next few leaves we study motion. First job: say exactly how far something went. But after one lap back to the start — is that 400 metres, or zero?
第 1 步：路程——轨迹的总长Step 1: Distance — the whole path
先看最简单的问题：小火箭绕操场跑一整圈，它跑了多远？Start with the simplest question: the rocket runs one full lap — how far did it run?
沿着跑道跑一整圈，虚线轨迹的总长度就是路程。每一步都算数，哪怕最后回到了出发点。路程只看「怎么走的」，不讲方向。Run one full lap and the total length of the dashed path is the distance. Every step counts, even though you end where you began. Distance watches how you moved — not which way.
可是跑回起点时，路程几百米——有没有哪个数其实是 0？But back at the start with hundreds of metres on the path — is any number here actually zero?
第 2 步：位移——只看头尾的直线Step 2: Displacement — the start-to-finish line
从起点到终点拉一条直线箭头，就是位移：它只问「终点离起点多远」，过程怎么绕都不管。图中小狗跑出去 8 米、又折回 3 米：路程 = 8 + 3 = 11 米，位移却是 5 米。要是它正好回到树那里，位移就是 0——谜底揭开：绕圈回到原点，位移 = 0。One straight arrow from start to finish is the displacement: it only asks how far the finish is from the start, no matter how winding the trip. In the picture the dog runs 8 m out, then 3 m back: distance = 8 + 3 = 11 m, yet displacement is 5 m. If it returned exactly to the tree, displacement would be 0 — that solves the lap puzzle: back where you began means zero displacement.
为什么两个数都要用？看看手机导航就懂了。Why keep both numbers? Your phone's navigation shows exactly why.
第 3 步：矢量与标量——有方向和没方向Step 3: Vectors and scalars — with and without direction
位移带方向：往东 5 米和往西 5 米不是一回事——带方向的量叫矢量（vector），只有大小的叫标量（scalar），路程就是标量。导航同时给你两个：弯弯绕绕的路线（路程），和那条直直的绿箭头（位移）。Displacement carries a direction: 5 m east is not 5 m west. A quantity with direction is a vector; one with size only is a scalar — distance is a scalar. Navigation gives you both: the winding route (distance) and the straight green arrow (displacement).
🎮 你来开跑（30 秒）🎮 Your turn: track run (30 seconds)
道理讲完了。按住小火箭在操场上跑，盯住两个数——完成 4 个任务。Theory done. Drag the rocket around the track and watch the two numbers — finish 4 tasks.
一句话记住它：路程数轨迹总长，位移看头到尾的直线；位移带方向是矢量，路程不带方向是标量。Remember it in one line: distance adds up the whole path; displacement is the straight line from start to finish. Displacement is a vector (with direction); distance is a scalar.
路程 = 轨迹总长，每一步都算，没有方向Distance = the whole path length, every step counts, no direction位移 = 起点到终点的直线；绕一圈回到原点就是 0Displacement = the straight line from start to finish; a full loop back home gives 0带方向的量叫矢量（如位移），只有大小的叫标量（如路程）Quantities with direction are vectors (displacement); size-only ones are scalars (distance)
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
Back to tree
