📚 Core Concepts of Space, Time and Motion | 空间、时间与运动核心概念
This article provides a comprehensive review of the core concepts in the IB Physics topic “Space, Time and Motion”, including displacement, velocity, acceleration, uniformly accelerated motion, motion graphs, projectile motion, and relative motion. All definitions and equations follow the IB DP Physics syllabus.
本文系统梳理 IB 物理“空间、时间与运动”主题的核心概念，包括位移、速度、加速度、匀加速运动、运动图像、抛体运动和相对运动。所有定义和公式均依据 IB DP 物理考纲。
1. Fundamental Quantities: Distance and Displacement | 基本量：距离与位移
Distance is a scalar quantity that measures the total length of the path traveled, regardless of direction. Its SI unit is the metre (m).
距离是标量，表示物体运动路径的总长度，与方向无关。其国际单位制单位为米（m）。
Displacement is a vector quantity that measures the change in position of an object. It is defined as the straight-line distance from the initial position to the final position, together with the direction. Its SI unit is also the metre (m).
位移是矢量，表示物体位置的变化。它定义为从初位置指向末位置的有向线段长度，同时包含方向。其国际单位制单位也是米（m）。
- Distance is always positive or zero; displacement can be positive, negative, or zero depending on the chosen coordinate system.
- 距离总是非负的；位移可以为正、为负或为零，取决于所选坐标系。
- If an object returns to its starting point, the displacement is zero, but the distance traveled is not necessarily zero.
- 若物体回到出发点，位移为零，但走过的路程不一定为零。
2. Speed and Velocity | 速率与速度
Speed is a scalar quantity equal to the distance traveled per unit time. The average speed is calculated as total distance divided by total time.
速率是标量，等于单位时间内通过的路程。平均速率等于总路程除以总时间。
average speed = total distance / total time
Velocity is a vector quantity equal to the displacement per unit time. Average velocity is displacement divided by time interval.
速度是矢量，等于单位时间内的位移。平均速度等于位移除以时间间隔。
average velocity = displacement / time interval
Instantaneous velocity is the limit of average velocity as the time interval approaches zero. On a position-time graph, the instantaneous velocity at a point equals the slope of the tangent at that point.
瞬时速度是时间间隔趋于零时平均速度的极限。在位移-时间图像上，某点的瞬时速度等于该点切线的斜率。
3. Acceleration | 加速度
Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, and its SI unit is metres per second squared (m s⁻²).
加速度是速度对时间的变化率。它是矢量，国际单位制单位为米每二次方秒（m s⁻²）。
a = Δv / Δt = (v – u) / t
Here, u is the initial velocity, v is the final velocity, and t is the time interval.
其中，u 为初速度，v 为末速度，t 为时间间隔。
- An object can have a negative acceleration while moving in the positive direction if its speed is decreasing.
- 物体沿正方向运动时，若速度减小，加速度为负。
- An object moving in a circle at constant speed has acceleration because its direction changes continuously.
- 物体做匀速圆周运动时，速度方向不断改变，因此存在加速度。
4. The Equations of Uniformly Accelerated Motion | 匀加速运动方程
For motion with constant acceleration, the following four kinematic equations are used. They apply only when acceleration is constant.
对于加速度恒定的运动，常用以下四个运动学方程。它们仅在加速度为常数时适用。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Here, s is displacement, u is initial velocity, v is final velocity, a is acceleration, and t is time.
其中 s 为位移，u 为初速度，v 为末速度，a 为加速度，t 为时间。
5. Motion Graphs | 运动图像
Interpreting and sketching displacement-time, velocity-time, and acceleration-time graphs is essential in IB Physics.
理解并绘制位移-时间、速度-时间和加速度-时间图像是 IB 物理的基本要求。
| Graph | Slope | Area under graph |
|---|---|---|
| Displacement-time | Velocity | Not meaningful |
| Velocity-time | Acceleration | Displacement |
| Acceleration-time | Jerk (not required) | Change in velocity |
On a velocity-time graph, a straight horizontal line represents constant velocity; a straight sloped line represents constant acceleration.
在速度-时间图像中，水平直线表示匀速运动；倾斜直线表示匀加速运动。
6. Free Fall and Acceleration due to Gravity | 自由落体与重力加速度
Free fall is motion under the influence of gravity only. Near the surface of the Earth, the acceleration due to gravity g is approximately 9.8 m s⁻², directed downward.
自由落体是仅受重力作用的运动。在地球表面附近，重力加速度 g 约为 9.8 m s⁻²，方向竖直向下。
For an object released from rest, the displacement after time t is given by:
对于从静止释放的物体，经过时间 t 后的位移为：
s = ½gt²
Air resistance is usually neglected in ideal free-fall analysis. Real downward motion near the surface may reach terminal velocity when air resistance balances gravity.
在理想的自由落体分析中通常忽略空气阻力。实际下落过程中，当空气阻力与重力平衡时，物体将达到终端速度。
7. Projectile Motion | 抛体运动
Projectile motion is a two-dimensional motion under constant acceleration due to gravity, with the horizontal and vertical components of motion independent.
抛体运动是在重力加速度恒定下的二维运动，水平方向与竖直方向的运动彼此独立。
The horizontal component of velocity remains constant (ignoring air resistance), and the vertical component accelerates at g downward.
水平分速度保持不变（忽略空气阻力），竖直分速度以 g 向下加速。
Horizontal: x = uₓt
Vertical: y = u_y t – ½gt²
- The time of flight is determined by the vertical motion alone.
- 飞行时间仅由竖直方向运动决定。
- The maximum height occurs when the vertical velocity becomes zero.
- 当竖直分速度为零时，物体达到最大高度。
- For a symmetrical projectile launched and landing at the same height, the range is maximum for a launch angle of 45°.
- 对于从同一高度抛出并落回的对称抛体，射程在抛射角为 45° 时最大。
8. Relative Motion | 相对运动
Relative velocity is the velocity of one object as observed from another moving reference frame. For two objects A and B moving with velocities vₐ and v_b relative to a fixed frame, the velocity of A relative to B is:
相对速度是从另一个运动参考系观察到的物体速度。设物体 A、B 相对于固定参考系的速度分别为 vₐ 和 v_b，则 A 相对于 B 的速度为：
vₐ_b = vₐ – v_b
This vector subtraction must be performed component by component when motion is not along a single line.
当运动不沿同一直线时，需要按分量进行矢量相减。
In two dimensions, relative velocity problems often involve boats crossing rivers or aircraft flying in wind. The resultant velocity is the vector sum of the object’s velocity in still water/air and the current/wind velocity.
在二维问题中，相对运动常见于船渡河或飞机在风中飞行。合速度是物体在静水/静空气中的速度与水流/风速的矢量和。
9. Scalars and Vectors | 标量与矢量
A scalar quantity has magnitude only, such as mass, time, speed, distance, and energy. A vector quantity has magnitude and direction, such as displacement, velocity, acceleration, and force.
标量只有大小，如质量、时间、速率、距离和能量。矢量既有大小又有方向，如位移、速度、加速度和力。
Vector addition can be done graphically using the tip-to-tail method or analytically using components. The sum of two vectors is called the resultant vector.
矢量的合成可以用首尾相连的图形法，也可以用分量解析法。两个矢量的合矢量称为合矢量（或矢量和）。
R = √(Rₓ² + R_y²), θ = tan⁻¹(R_y / Rₓ)
Here, Rₓ and R_y are the components of the resultant vector along the x and y axes, and θ is the angle relative to the x-axis.
其中 Rₓ 和 R_y 为合矢量在 x 轴和 y 轴上的分量，θ 为合矢量与 x 轴的夹角。
10. Common Pitfalls and Exam Tips | 常见误区与应试建议
Many students confuse speed and velocity, especially when an object changes direction. Always check whether the problem asks for distance or displacement.
许多学生容易混淆速率与速度，尤其在物体改变方向时。务必看清题目要求的是路程还是位移。
When using the kinematic equations, define a positive direction and keep signs consistent. The acceleration due to gravity is often taken as -9.8 m s⁻² when the upward direction is chosen as positive.
应用运动学方程时，先规定正方向并保持符号一致。若取竖直向上为正方向，重力加速度通常为 -9.8 m s⁻²。
- Always state the direction of vector quantities when giving final answers.
- 在最终答案中，矢量量必须说明方向。
- Check units carefully: velocity in m s⁻¹, acceleration in m s⁻².
- 注意单位：速度为 m s⁻¹，加速度为 m s⁻²。
- Draw a clear diagram for projectile and relative motion problems.
- 对于抛体运动和相对运动问题，先画出清晰示意图。
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