Grade: IB | Subject: Physics | Board: Cambridge | Topic: 1 Motion
Introduction / 引言
Motion is the most fundamental concept in classical physics. It describes how objects change their position over time, and forms the foundation upon which Newton’s laws, energy, momentum, and virtually all of mechanics are built. For IB Physics students, mastering the topic of motion is not just about memorising equations — it is about developing an intuitive understanding of how and why things move the way they do.
运动是经典物理学中最基本的概念。它描述了物体如何随时间改变位置，构成了牛顿定律、能量、动量以及几乎所有力学内容的基础。对于 IB 物理学生来说，掌握运动这一章节不仅仅是记住公式，更是要建立起对物体运动方式的直觉理解。
本文深入探讨剑桥 IB 物理教学大纲所要求的运动学内容，涵盖位移、速度、加速度、图像分析、运动方程、抛体运动以及学生常见误区。
Scalar vs Vector Quantities / 标量与矢量
One of the first distinctions every physics student must internalise is the difference between scalar and vector quantities. Distance and speed are scalars — they have magnitude only. Displacement and velocity are vectors — they have both magnitude and direction.
每个物理学生必须内化的第一个区别就是标量和矢量。距离和速率是标量（只有大小），位移和速度是矢量（既有大小又有方向）。
| Quantity | Type | SI Unit |
|---|---|---|
| Distance (距离) | Scalar | m |
| Displacement (位移) | Vector | m |
| Speed (速率) | Scalar | m/s |
| Velocity (速度) | Vector | m/s |
| Acceleration (加速度) | Vector | m/s^2 |
A classic exam question: A runner completes one lap of a 400 m track. What is the distance travelled and the displacement? Distance = 400 m, displacement = 0 (back to start).
经典考题：跑步者绕 400 米跑道跑一圈，路程和位移各是多少？路程 = 400 m，位移 = 0（回到起点）。
Distance, Displacement, Speed, and Velocity / 路程、位移、速率和速度
Distance (d) / 路程
Total length of path travelled. Always positive scalar. / 物体所经路径总长度，始终为正标量。
Displacement (s) / 位移
Straight-line distance from start to end, with direction. Vector. / 起点到终点的直线距离及方向，矢量。s = v x t (constant velocity)
Speed (v) / 速率
Rate at which distance is covered: v = d / t / 路程的变化率
Velocity (v) / 速度
Rate of change of displacement: v = change in s / change in t / 位移的变化率
Acceleration / 加速度
Rate of change of velocity. Vector: a = change in v / change in t = (v – u) / t
加速度是速度的变化率，矢量。a = 加速度, v = 末速度, u = 初速度, t = 时间
Misconception: acceleration does not always mean speeding up. It can mean slowing down or changing direction (e.g., circular motion).
常见误解：加速度不只是加速。它也可以表示减速，或匀速改变方向（如圆周运动）。
Graphs of Motion / 运动图像
Displacement-Time Graphs / 位移-时间图像
- Gradient = velocity / 斜率 = 速度
- Straight line = constant velocity / 直线 = 匀速
- Curve = acceleration / 曲线 = 加速
- Horizontal = stationary / 水平 = 静止
Velocity-Time Graphs / 速度-时间图像
- Gradient = acceleration / 斜率 = 加速度
- Area under graph = displacement / 面积 = 位移
- Horizontal = constant velocity / 水平 = 匀速
- Sloping line = constant acceleration / 斜线 = 匀加速
Acceleration-Time Graphs / 加速度-时间图像
- Area under graph = change in velocity / 面积 = 速度变化量
- Horizontal = constant acceleration / 水平 = 匀加速
- Zero = constant velocity / 零 = 匀速
SUVAT Equations / SUVAT 运动方程
For uniform (constant) acceleration. Variables:
匀加速运动的五个方程。变量：
- s = displacement / 位移 (m)
- u = initial velocity / 初速度 (m/s)
- v = final velocity / 末速度 (m/s)
- a = acceleration / 加速度 (m/s^2)
- t = time / 时间 (s)
| # | Equation | Missing |
|---|---|---|
| 1 | v = u + at | s |
| 2 | s = (u + v)t / 2 | a |
| 3 | s = ut + (1/2)at^2 | v |
| 4 | s = vt – (1/2)at^2 | u |
| 5 | v^2 = u^2 + 2as | t |
Method: 1) List knowns 2) Identify unknown 3) Choose equation (missing the variable you do not need) 4) Solve 5) Check units and reasonableness.
方法：列出已知量，确定未知量，选方程（避开不需要的变量），代入求解，检查单位和合理性。
Free Fall / 自由落体
Special case: acceleration = g = 9.81 m/s^2 downward.
特例：加速度 = g = 9.81 m/s^2，方向向下。
Define positive direction carefully. Upward positive means a = -g. Downward positive means a = +g.
仔细定义正方向。向上为正则 a = -g；向下为正则 a = +g。
Classic problem: Ball thrown upward at 20 m/s. Max height? Time to return? (Use symmetry: time up = time down, ignoring air resistance.)
经典问题：球以 20 m/s 上抛。最大高度？返回时间？（利用对称性：上升时间 = 下降时间，忽略空气阻力。）
Projectile Motion / 抛体运动
Horizontal and vertical motions are independent. Time links them.
水平和竖直运动相互独立，时间连接两者。
Resolving initial velocity / 分解初速度：
v_x = v0 cos(theta) (horizontal) / 水平
v_y0 = v0 sin(theta) (vertical initial) / 竖直初始
Key formulas / 关键公式：
- Time of flight / 飞行时间: T = (2 v0 sin theta) / g
- Maximum height / 最大高度: H = (v0 sin theta)^2 / (2g)
- Range / 射程: R = (v0^2 sin 2theta) / g
- Optimal angle for max range / 最大射程角度: 45 degrees
Relative Motion / 相对运动
v_A_rel_B = v_A – v_B. Important for frames of reference and later momentum/collision analysis.
物体 A 相对 B 的速度 = v_A – v_B。对参考系理解及后续动量/碰撞分析很重要。
Common Mistakes / 常见错误
- Distance vs Displacement: Return journey has zero displacement but non-zero distance. / 往返位移为零，路程不为零。
- Sign conventions: Always define positive direction consistently. / 始终定义正方向并保持一致。
- Negative acceleration: An object moving upward and slowing has a = -g. / 向上减速的物体 a = -g。
- Graph confusion: v-t slope = acceleration, v-t area = displacement. Do not mix them up! / v-t 斜率 = 加速度，面积 = 位移，别搞混！
- Wrong SUVAT equation: Check missing variable before choosing. / 选方程前先确认缺失变量。
Practice Problems / 练习题
Problem 1
A car accelerates from rest to 25 m/s in 10 s. Find acceleration and distance.
汽车从静止加速到 25 m/s，用时 10 s。求加速度和行驶距离。
Solution: u=0, v=25, t=10. a = (25-0)/10 = 2.5 m/s^2. s = (0+25) x 10 / 2 = 125 m.
Problem 2
A stone is thrown horizontally at 20 m/s from a 45 m cliff. Find time to hit water and horizontal distance.
石头从 45 m 悬崖以 20 m/s 水平抛出。求落地时间和水平距离。
Solution: Vertical: s=45, u_y=0, a=9.81. Using s = ut + (1/2)at^2: 45 = (1/2) x 9.81 x t^2, so t = sqrt(90/9.81) = 3.03 s. Horizontal: s_x = 20 x 3.03 = 60.6 m.
Summary / 总结
Motion is foundational to all of mechanics. Master SUVAT equations, graphical analysis, and sign conventions. These skills carry through Newton laws, energy, momentum, and beyond. Physics is about understanding how the Universe works — and motion is where that understanding begins.
运动是所有力学的基础。掌握 SUVAT 方程、图像分析和符号约定。这些技能贯穿牛顿定律、能量、动量及更远。物理是关于理解宇宙如何运作——运动正是这种理解的起点。
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