A2 Physics: Kinematics Key Points | A2 物理：运动学考点精讲

📚 A2 Physics: Kinematics Key Points | A2 物理：运动学考点精讲

In A2 Physics, kinematics extends beyond simple constant acceleration to encompass projectile motion, relative velocity, graphical analysis, and circular motion. Mastering these concepts is essential for solving complex exam questions and understanding the broader principles of mechanics. This article highlights the key points you must know for success in your examinations.

在 A2 物理中，运动学超越了简单的匀加速直线运动，扩展到抛体运动、相对速度、图像分析以及圆周运动。掌握这些概念对于解决复杂的考试题目以及理解力学更广泛的原理至关重要。本文重点梳理了你在考试中必须掌握的核心考点。

1. Scalars and Vectors in Kinematics | 运动学中的标量与矢量

In kinematics, quantities are classified as scalars or vectors. Scalars have magnitude only (e.g., speed, distance, time). Vectors have both magnitude and direction (e.g., displacement, velocity, acceleration). Using vector notation correctly and resolving vectors into perpendicular components is crucial for solving two-dimensional motion problems.

在运动学中，物理量分为标量和矢量。标量仅具有大小（如速率、路程、时间）。矢量既有大小又有方向（如位移、速度、加速度）。正确使用矢量符号并将矢量分解为垂直分量，对于解决二维运动问题至关重要。

Examples:

Scalar: speed v (e.g., 30 m/s)
Vector: velocity v (e.g., 30 m/s due east)

例子：

标量：速率 v (例如 30 m/s)
矢量：速度 v (例如 30 m/s 向东)

2. Displacement, Velocity and Acceleration | 位移、速度与加速度

Displacement s is a vector representing the change in position. Velocity v is the rate of change of displacement, and acceleration a is the rate of change of velocity. Average velocity is defined as Δs/Δt, while instantaneous velocity is the gradient of the displacement-time graph.

位移 s 是表示位置变化的矢量。速度 v 是位移的变化率，加速度 a 是速度的变化率。平均速度定义为 Δs/Δt，而瞬时速度是位移-时间图像的斜率。

Key formulas: v_avg = Δs / Δt; a = Δv / Δt. Vector directions are determined by sign conventions or bearings.

关键公式：v_avg = Δs / Δt；a = Δv / Δt。矢量方向由符号规定或方位角决定。

3. SUVAT Equations of Motion | SUVAT 运动方程

For motion with constant acceleration in a straight line, five quantities are linked: s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time). The four SUVAT equations are essential:

对于匀加速直线运动，五个量相互关联：s (位移), u (初速度), v (末速度), a (加速度), t (时间)。四个 SUVAT 方程至关重要：

v = u + at

s = ut + ½at²

s = vt − ½at²

v² = u² + 2as

These equations apply only when acceleration is constant. Always define a positive direction and substitute values with appropriate signs. Negative values indicate opposite direction.

这些方程仅适用于加速度恒定的情况。务必规定正方向，并代入带有正确符号的值。负值表示相反方向。

4. Free Fall Motion | 自由落体运动

An object falling freely under gravity experiences constant acceleration g = 9.81 m/s² downward (ignoring air resistance). The SUVAT equations can be used with a = ±g depending on the chosen positive direction. For an object dropped from rest, u = 0, and the equations simplify.

物体仅在重力作用下自由下落时，加速度恒为向下的 g = 9.81 m/s² (忽略空气阻力)。根据所选的正方向，可使用 a = ±g 代入 SUVAT 方程。对于从静止释放的物体，初速度 u = 0，方程可以简化。

Displacement after time t: s = ½gt². Velocity after falling height h: v² = 2gh.

时间 t 后的位移：s = ½gt²。下落高度 h 后的速度：v² = 2gh。

5. Projectile Motion: Components | 抛体运动：分量分解

Projectile motion involves two independent perpendicular motions: constant horizontal velocity (a_x = 0) and constant vertical acceleration (a_y = g downward). The initial velocity u must be resolved into horizontal and vertical components using trigonometry.

抛体运动包含两个相互独立的垂直运动：水平方向匀速运动 (a_x = 0) 和竖直方向匀加速运动 (a_y = g 向下)。必须利用三角函数将初速度 u 分解为水平和竖直分量。

If launch angle θ from horizontal: u_x = u cosθ, u_y = u sinθ.

若发射角 θ 相对于水平面，则 u_x = u cosθ，u_y = u sinθ。

6. Projectile Motion: Equations and Range | 抛体运动方程与射程

Horizontal motion: x = u_x t (since no horizontal acceleration). Vertical motion: use SUVAT with a_y = −g (or +g depending on positive direction). The time of flight, maximum height, and horizontal range are derived from these.

水平运动：x = u_x t (因水平方向无加速度)。竖直运动：使用 SUVAT，其中 a_y = −g (或 +g 取决于正方向)。飞行时间、最大高度和水平射程均由此导出。

T = (2u_y)/g

H = u_y²/(2g)

R = (u² sin 2θ)/g

Time of flight T = (2u_y)/g (for symmetrical trajectory on level ground). Maximum height H = u_y²/(2g). Range R = (u² sin 2θ)/g.

飞行时间 T = (2u_y)/g (对于水平地面上的对称轨迹)。最大高度 H = u_y²/(2g)。射程 R = (u² sin 2θ)/g。

7. Motion Graphs | 运动图像

Graphs provide a powerful way to analyse motion. Key graphs are displacement-time (s-t), velocity-time (v-t), and acceleration-time (a-t). The gradient and area under these graphs yield important kinematic quantities.

图像是分析运动的有力工具。关键的图像有位移-时间 (s-t) 图、速度-时间 (v-t) 图和加速度-时间 (a-t) 图。这些图像的斜率和面积可以给出重要的运动学量。

s-t graph: gradient = velocity
v-t graph: gradient = acceleration, area under graph = displacement
a-t graph: area under graph = change in velocity

s-t 图：斜率 = 速度
v-t 图：斜率 = 加速度，图下面积 = 位移
a-t 图：图下面积 = 速度变化量

8. Relative Velocity | 相对速度

Relative velocity is the velocity of one object as observed from another moving object. It is the vector difference of the two velocities. For two objects A and B, velocity of A relative to B: v_AB = v_A − v_B.

相对速度是指从另一个运动的物体上观察到的某一物体的速度。它是两个速度的矢量差。对于物体 A 和 B，A 相对于 B 的速度为：v_AB = v_A − v_B。

This concept is essential for solving problems involving moving walkways, boats crossing rivers, and wind affecting aircraft motion.

这一概念对于解决涉及移动式走廊、船只过河以及风对飞机运动影响的问题至关重要。

9. Circular Motion: Angular Velocity and Period | 圆周运动：角速度与周期

When an object moves in a circle at constant speed, its direction changes continuously, so it experiences acceleration. Angular displacement θ (rad), angular velocity ω (rad/s), and period T are key descriptors. ω = Δθ/Δt; for uniform circular motion, ω = 2π/T.

当物体以恒定速率做圆周运动时，其方向不断变化，因此具有加速度。角位移 θ (弧度)、角速度 ω (弧度/秒) 和周期 T 是关键描述量。ω = Δθ/Δt；对于匀速圆周运动，ω = 2π/T。

Relationship between linear speed v and angular velocity: v = ωr, where r is the radius of the circle.

线速度 v 与角速度的关系：v = ωr，其中 r 是圆的半径。

10. Centripetal Acceleration | 向心加速度

An object in uniform circular motion has centripetal acceleration directed towards the centre of the circle. The magnitude is given by a_c = v²/r or a_c = ω²r. Although the speed is constant, the velocity vector changes, causing this acceleration.

做匀速圆周运动的物体具有指向圆心的向心加速度。其大小为 a_c = v²/r 或 a_c = ω²r。尽管速率恒定，但速度矢量变化，从而产生此加速度。

Centripetal acceleration is always perpendicular to velocity. For non-uniform circular motion, a tangential acceleration also exists.

向心加速度始终垂直于速度。对于非匀速圆周运动，还存在切向加速度。

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A2 Physics: Kinematics Key Points | A2 物理：运动学 考点精讲