📚 IB CCEA Physics: Kinematics | IB CCEA 物理：运动学考点精讲
Kinematics is the branch of physics that describes the motion of objects without considering the causes of that motion. For IB CCEA Physics students, mastering kinematics means understanding displacement, velocity, acceleration, and the graphical and algebraic tools used to analyse one- and two-dimensional motion. This article provides a focused revision guide covering all core concepts, common pitfalls, and exam-ready strategies.
运动学是物理学的分支，描述物体的运动，而不涉及引起运动的力。对 IB 和 CCEA 物理课程的学生来说，掌握运动学意味着必须深刻理解位移、速度、加速度，以及用来分析一维和二维运动的图像与代数工具。本文是一篇考点精讲，涵盖了所有核心概念、常见错误和实用的应试技巧。
1. Scalars and Vectors | 标量与矢量
In kinematics, we must distinguish between scalar quantities, which have magnitude only, and vector quantities, which have both magnitude and direction. Distance and speed are scalars; displacement and velocity are vectors. When solving problems, always treat vector quantities with their direction in mind – choose a positive direction and stick to it.
在运动学中，必须区别标量和矢量。标量只有大小，如路程和速率；矢量既有大小又有方向，如位移和速度。解题时，必须始终考虑矢量的方向——先选定一个正方向，并在整个计算中保持统一。
2. Displacement, Velocity and Acceleration | 位移、速度与加速度
Displacement is the straight-line distance in a given direction from the initial to the final position. Average velocity is the displacement divided by the time taken, while instantaneous velocity is the gradient of the displacement–time graph at a point. Acceleration is the rate of change of velocity, and it can be positive (speeding up in the chosen positive direction) or negative (slowing down or speeding up in the negative direction).
位移是从初位置到末位置的直线距离，并带有方向。平均速度等于位移除以所用时间，而瞬时速度则是位移-时间图在某一点的斜率。加速度是速度的变化率，它可以是正值（沿选定的正方向加速），也可以是负值（减速，或者沿负方向加速）。
3. Equations of Motion (SUVAT) | 运动方程 (SUVAT)
For uniformly accelerated motion along a straight line, four key equations link the variables s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time). They are used when acceleration is constant. The equations are:
对于匀加速直线运动，有四个关键方程将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系在一起。前提是加速度保持不变。这些方程是：
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
When applying these equations, list the known quantities and the one you need to find, then select the equation that does not involve the unwanted variable. Always check that the units are consistent, e.g., m, s, m/s, m/s².
应用这些方程时，先列出已知量和待求量，然后选出不含不需要变量在内的方程。一定要确保单位一致，例如位移用米、时间用秒、速度用米/秒、加速度用米/秒²。
4. Free Fall under Gravity | 重力作用下的自由落体
Near the Earth’s surface, all objects fall with a constant acceleration due to gravity, g = 9.81 m/s² (approximately 9.8 m/s²), directed downwards. The SUVAT equations apply directly if we set a = g and take downward as positive, or a = –g if upward is positive. In free fall questions, remember that an object thrown upwards has zero velocity at its highest point, but its acceleration is still g downwards.
在地球表面附近，所有物体都以恒定的重力加速度 g = 9.81 m/s²（约 9.8 m/s²）下落，方向竖直向下。如果取向下为正方向，则 a = g；若取向上为正，则 a = –g，SUVAT方程可直接使用。在自由落体问题中，记得向上抛出的物体在最高点速度为零，但加速度仍为向下的 g。
5. Projectile Motion | 抛体运动
Projectile motion is analysed by splitting the motion into independent horizontal and vertical components. The horizontal velocity remains constant (assuming no air resistance), while the vertical motion is uniformly accelerated with a = g downwards. The time of flight is determined entirely by the vertical motion. Use trigonometric functions to resolve the initial velocity: ux = u cos θ, uy = u sin θ. Treat the two components separately, then recombine to find the final velocity or displacement.
抛体运动通过将运动分解为互相独立的水平和竖直分量来分析。水平速度保持不变（忽略空气阻力），而竖直方向做加速度为向下的 g 的匀加速运动。飞行时间完全由竖直运动决定。运用三角函数分解初速度：uₓ = u cos θ，uᵧ = u sin θ。分别处理这两个分量，然后再合起来求末速度或位移。
6. Displacement–Time Graphs | 位移-时间图
A displacement–time (s–t) graph shows how displacement changes with time. The gradient of the graph gives the velocity. A straight, sloping line indicates constant velocity; a horizontal line means the object is stationary. A curved line reveals changing velocity, and the instantaneous velocity at any point is found by drawing a tangent and calculating its slope.
位移-时间图(s-t图)展示了位移随时间的变化情况。图中线的斜率表示速度。一条倾斜的直线表示匀速运动；水平线表示物体静止。曲线则表明速度在变化，任意点的瞬时速度可通过作切线并计算其斜率求得。
7. Velocity–Time Graphs | 速度-时间图
On a velocity–time (v–t) graph, the gradient represents acceleration and the area under the graph between two times gives the displacement. A straight, sloping line means constant acceleration; a horizontal line means constant velocity. A negative gradient indicates deceleration. When the line crosses the time axis, the object changes direction.
在速度-时间图(v-t图)中，斜率代表加速度，图线与时间轴之间围成的面积代表位移。一条倾斜直线表示匀加速运动；水平线表示匀速运动。斜率为负表示减速。当图线穿过时间轴时，物体运动方向改变。
8. Acceleration–Time Graphs | 加速度-时间图
An acceleration–time (a–t) graph is less commonly used but very useful. The area under the a–t graph gives the change in velocity over that time interval. A horizontal line at a = constant shows uniformly accelerated motion, while a line at zero indicates constant velocity. Sudden jumps in acceleration are usually approximated in exam problems.
加速度-时间图(a-t图)虽然不常用，但很有价值。a-t图下的面积代表对应时间段内速度的变化量。一条水平的直线（a = 常数）表示匀加速运动；加速度为零的直线则表示匀速运动。考试题目中，加速度的突变通常会被理想化处理。
9. Relative Motion | 相对运动
Relative velocity considers how two objects are moving with respect to each other. If object A moves at velocity vA and object B moves at vB, the velocity of A relative to B is vA – vB. This vector subtraction is key in problems where two objects are observed from different reference frames. Always draw vector diagrams to avoid sign errors.
相对速度描述的是两个物体彼此之间的运动关系。若物体 A 的速度为 vA，物体 B 的速度为 vB，则 A 相对于 B 的速度为 vA – vB。这种矢量减法在涉及不同参考系的问题中至关重要。一定要画矢量图，避免正负号错误。
10. Common Mistakes and Exam Tips | 常见错误与应试技巧
One common mistake is mixing up distance and displacement or speed and velocity. Another is forgetting that acceleration can be negative even when an object is moving forward – it simply means the object is slowing down. Always check the sign convention in SUVAT problems, and remember that ‘g’ is always a magnitude, so its direction must be assigned by you. In projectile motion, the vertical component of velocity at maximum height is zero, but the acceleration is still g. Practise interpreting graphs and extracting gradients and areas quickly, as these are frequently tested.
常见错误之一是混淆路程与位移，或速率与速度。另一个错误是忘记加速度可以为负值，即便物体仍在向前运动——负号仅仅代表减速。在 SUVAT 问题中一定要核对正负号规定，并记住‘g’只是大小，方向需要自行指定。在抛体运动中，最高点的竖直速度分量为零，但加速度仍为 g。多加练习图像题的解读，快速求出斜率和面积，因为这些是高频考点。
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