📚 IB Physics: Core Concepts of Space, Time and Motion | IB物理：空间、时间与运动核心概念梳理
Physics is the study of the fundamental principles that govern the universe. In the IB Physics syllabus, the topic of Space, Time and Motion forms the foundation for all other areas. This article provides a concise and exam-focused review of the key ideas every IB candidate should master.
物理学是研究宇宙基本规律的学科。在IB物理课程中，空间、时间与运动这一主题是所有其他知识领域的基础。本文将为每一位IB考生提供一份重点突出、紧扣考纲的核心概念梳理。
1. Fundamental Concepts of Motion | 运动的基本概念
Distance is a scalar quantity that measures the total length of the path travelled. Displacement is a vector quantity that measures the straight-line distance from the initial to the final position, together with its direction.
路程是标量，表示物体运动轨迹的总长度。位移是矢量，表示从初位置到末位置的有向直线距离，包含大小和方向。
Speed is the rate of change of distance, while velocity is the rate of change of displacement. Speed is always positive, but velocity can be positive or negative depending on the chosen direction.
速率是路程随时间的变化率，而速度是位移随时间的变化率。速率始终为正，而速度的正负取决于所选取的方向。
Acceleration is the rate of change of velocity. It is a vector quantity. Deceleration is simply acceleration acting in the opposite direction to the velocity.
加速度是速度随时间的变化率，是一个矢量。减速本质上是加速度方向与速度方向相反的情形。
- Distance: a scalar, measured in metres (m).
- 路程：标量，单位为米（m）。
- Displacement: a vector, measured in metres with direction.
- 位移：矢量，单位为米，并具有方向。
- Speed: ( text{scalar} = frac{text{distance}}{text{time}} ) — but write as speed = distance ÷ time.
- 速率：标量，等于路程除以时间。
- Velocity: vector ( v = frac{Delta s}{Delta t} ).
- 速度：矢量 ( v = Δs / Δt )。
- Acceleration: vector ( a = frac{Delta v}{Delta t} ).
- 加速度：矢量 ( a = Δv / Δt )。
2. Uniformly Accelerated Motion | 匀加速直线运动
For an object moving in a straight line with constant acceleration, the following kinematic equations apply. These are sometimes called the SUVAT equations because they use the symbols ( s, u, v, a, t ).
当物体沿直线做匀加速运动时，以下运动学公式适用。这些公式常被称为SUVAT公式，因为它们涉及 ( s, u, v, a, t ) 五个符号。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
In these equations, ( u ) is the initial velocity, ( v ) is the final velocity, ( a ) is the constant acceleration, ( t ) is the time, and ( s ) is the displacement.
在这些公式中，( u ) 表示初速度，( v ) 表示末速度，( a ) 表示恒定加速度，( t ) 表示时间，( s ) 表示位移。
When an object is released from rest, ( u = 0 ). When an object reaches its maximum height, ( v = 0 ). Choosing the correct equation based on the known and unknown variables is a critical exam skill.
当物体从静止释放时，( u = 0 )。当物体到达最高点时，( v = 0 )。根据已知量和未知量选择正确的公式是一项关键的应试技能。
3. Motion Graphs | 运动图像
Graphical analysis is essential in IB Physics. Three types of graphs are commonly used: displacement-time, velocity-time, and acceleration-time graphs.
图像分析在IB物理中至关重要。常用图像有三种：位移-时间图像、速度-时间图像和加速度-时间图像。
In a displacement-time graph, the gradient represents the velocity. A straight line means uniform velocity, and a horizontal line means the object is at rest. The slope of the tangent at any point gives the instantaneous velocity.
在位移-时间图像中，斜率表示速度。直线表示匀速运动，水平线表示物体静止。某点的切线斜率表示该时刻的瞬时速度。
In a velocity-time graph, the gradient represents the acceleration, and the area under the graph represents the displacement. In an acceleration-time graph, the area under the graph represents the change in velocity.
在速度-时间图像中，斜率表示加速度，图线与时间轴围成的面积表示位移。在加速度-时间图像中，图线与时间轴围成的面积表示速度的变化量。
| Graph type | Gradient | Area |
| 图像类型 | 斜率 | 面积 |
| displacement-time | velocity 速度 | not usually used 通常不使用 |
| velocity-time | acceleration 加速度 | displacement 位移 |
| acceleration-time | not usually used 通常不使用 | change in velocity 速度变化量 |
4. Projectile Motion | 抛体运动
Projectile motion is the motion of an object thrown into the air and subject only to gravity. The horizontal and vertical components of motion are independent of each other.
抛体运动是指物体被抛入空中后仅受重力作用的运动。水平的运动与竖直方向的运动彼此独立。
Horizontally, there is no acceleration (ignoring air resistance), so the horizontal velocity remains constant. Vertically, the acceleration is constant and equal to the gravitational acceleration ( g = 9.8 text{ m s⁻²} ).
水平方向上没有加速度（忽略空气阻力），因此水平速度保持不变。竖直方向上加速度恒定，等于重力加速度 ( g = 9.8 text{ m s⁻²} )。
For an object launched horizontally with initial speed ( u ), the time to hit the ground depends only on the vertical height, not on the horizontal speed.
对于以初速度 ( u ) 水平抛出的物体，落地时间只取决于下落高度，而与水平速度无关。
Time of flight: ( t = sqrt{frac{2h}{g}} )
落地时间：( t = √2h / g )
For a projectile launched at an angle, the maximum height and range depend on the launch angle. Maximum range occurs at ( 45circ ) when there is no air resistance.
对于以某一角度抛出的物体，最大高度和射程取决于抛射角。若无空气阻力，射程最大时的抛射角为 ( 45° )。
5. Uniform Circular Motion | 匀速圆周运动
Uniform circular motion occurs when an object moves in a circle at constant speed. Although the speed is constant, the velocity is continuously changing because the direction changes.
匀速圆周运动是指物体以恒定速率沿圆周运动。虽然速率恒定，但由于方向不断变化，速度却在持续改变。
In uniform circular motion, the acceleration is always directed towards the centre of the circle. This is called centripetal acceleration.
在匀速圆周运动中，加速度始终指向圆心，称为向心加速度。
( a = frac{v²}{r} = omega² r )
( a = v² / r = omega² r )
The period ( T ) is the time for one complete revolution. The frequency ( f ) is the number of revolutions per second. They satisfy ( T = 1/f ).
周期 ( T ) 是完成一次完整圆周运动所需的时间。频率 ( f ) 是每秒转过的圈数。二者满足 ( T = 1/f )。
For an object moving in a circle of radius ( r ) with speed ( v ), the angular speed is ( omega = v / r ). The centripetal force required is ( F = mv² / r ).
对于半径为 ( r )、速度为 ( v ) 的圆周运动，角速度为 ( omega = v / r )。所需的向心力为 ( F = mv² / r )。
6. Newton's Laws of Motion | 牛顿运动定律
Newton's laws connect the concept of force with the motion of objects. The first law states that an object remains at rest or moves in a straight line at constant velocity unless acted upon by an unbalanced external force.
牛顿运动定律将力的概念与物体的运动联系起来。第一定律指出，物体在不受合外力作用时，将保持静止或匀速直线运动状态。
The second law states that the net force acting on an object is equal to the rate of change of momentum, commonly written as ( F = ma ).
第二定律指出，物体所受的合力等于其动量的变化率，通常写作 ( F = ma )。
The third law states that every action has an equal and opposite reaction. Forces always occur in pairs acting on different objects, so they do not cancel each other out.
第三定律指出，每一个作用力都有一个大小相等、方向相反的反作用力。力总是成对出现，且分別作用在不同物体上，因此不能互相抵消。
- First law: law of inertia, relates to balanced forces.
- 第一定律：惯性定律，涉及平衡力。
- Second law: ( Ftext{net} = ma ), relates force to acceleration.
- 第二定律：( Ftext{net} = ma )，将力与加速度联系起来。
- Third law: action-reaction pairs act on different bodies.
- 第三定律：作用力与反作用力作用在不同物体上。
7. Momentum and Impulse | 动量与冲量
Momentum ( p ) is the product of mass and velocity, ( p = mv ). It is a vector quantity with the same direction as the velocity.
动量 ( p ) 是质量与速度的乘积，( p = mv )。动量是矢量，方向与速度方向相同。
Impulse ( J ) is the product of the net force and the time interval over which it acts, ( J = F Delta t ). Impulse is equal to the change in momentum of the object.
冲量 ( J ) 是合外力与其作用时间的乘积，( J = F Δt )。冲量等于物体动量的变化量。
( F Delta t = Delta p = m Delta v )
( F Δt = Δp = m Δv )
This relationship explains why airbags and crumple zones in cars are important: they extend the collision time, reducing the average force experienced by passengers.
这一关系解释了汽车安全气囊和防撞缓冲区的重要性：它们延长了碰撞时间，从而减小乘客所受的平均冲击力。
8. Work, Energy and Power | 功、能量与功率
Work ( W ) is done when a force causes a displacement. The equation is ( W = F s cos theta ), where ( theta ) is the angle between the force and the displacement.
当力使物体发生位移时，力对物体做功。公式为 ( W = F s cos θ )，其中 ( θ ) 是力与位移之间的夹角。
Energy is the capacity to do work. Kinetic energy is the energy of an object due to its motion, given by ( Ek = ½mv² ). Potential energy is the energy stored due to position, with gravitational potential energy ( Ep = mgh ).
能量是做功的本领。动能是物体由于运动而具有的能量，( Ek = ½mv² )。势能是由于位置而储存的能量，重力势能 ( Ep = mgh )。
The principle of conservation of mechanical energy states that, in the absence of friction, the total mechanical energy (kinetic plus potential) remains constant.
机械能守恒定律指出，在无摩擦的情况下，总机械能（动能加势能）保持不变。
Power ( P ) is the rate of doing work or transferring energy, ( P = W / t ). The SI unit of power is the watt (W), where one watt equals one joule per second.
功率 ( P ) 是做功或能量转化的快慢，( P = W / t )。功率的国际单位是瓦特（W），一瓦特等于每秒一焦耳。
9. Conservation of Energy | 能量守恒定律
Energy cannot be created or destroyed, only converted from one form to another. This is the law of conservation of energy, one of the most fundamental principles in physics.
能量既不会凭空产生，也不会凭空消失，只能从一种形式转化为另一种形式。这就是能量守恒定律，是物理学中最基本的原理之一。
In a closed system, the total energy before an event equals the total energy after the event. For a ball thrown upwards, kinetic energy is converted into gravitational potential energy, and then back again as it falls.
在封闭系统中，事件发生前的总能量等于事件发生后的总能量。例如竖直上抛的小球，动能转化为重力势能，下落时又转化回动能。
In practical problems, friction dissipates energy as heat and sound, so mechanical energy alone is not conserved. However, the total energy of the system remains conserved.
在实际问题中，摩擦力会使能量以热和声音的形式耗散，因此机械能本身并不守恒。但系统的总能量仍然守恒。
When solving energy problems, identify all forms of energy at the initial and final states, then set the total initial energy equal to the total final energy plus any energy lost to the surroundings.
解决能量问题时，应先识别初态和末态的所有能量形式，然后令初态总能量等于末态总能量加上损失到环境的能量。
10. Conservation of Linear Momentum | 动量守恒定律
In an isolated system, the total linear momentum remains constant. This is the law of conservation of linear momentum, which holds even when kinetic energy is not conserved, such as in inelastic collisions.
在孤立系统中，总动量保持不变。这就是动量守恒定律。即使在动能不守恒的非弹性碰撞中，动量守恒仍然成立。
For a collision between two objects A and B:
对于A、B两个物体之间的碰撞：
( mA uA + mB uB = mA vA + mB vB )
( mA uA + mB uB = mA vA + mB vB )
In an elastic collision, both momentum and kinetic energy are conserved. In a perfectly inelastic collision, the two objects stick together after the collision, and kinetic energy is not conserved.
在弹性碰撞中，动量和动能均守恒。在完全非弹性碰撞中，两个物体碰撞后粘在一起运动，动能不再守恒。
When analysing explosions, the total momentum before the event is zero, so the momenta of the fragments must add to zero. This explains the recoil of a gun or the separation stages of a rocket.
分析爆炸过程时，爆炸前总动量为零，因此各碎片的动量之和也为零。这解释了枪支的后座力或火箭分级分离的现象。
11. Forces and Free-Body Diagrams | 力与受力分析图
A free-body diagram shows all the forces acting on a single object as vectors. Drawing these diagrams is an essential skill for solving mechanics problems.
受力分析图将作用在单个物体上的所有力用矢量表示出来。绘制受力分析图是解决力学问题的关键技能。
Common forces include weight ( W = mg ), normal force, friction, tension, and applied forces. In equilibrium, the vector sum of all forces is zero.
常见力包括重力 ( W = mg )、支持力、摩擦力、张力和施加的外力。在平衡状态下，所有力的矢量和为零。
For an object on an inclined plane, the weight component parallel to the plane is ( mg sin theta ), and the component perpendicular to the plane is ( mg cos theta ).
对于斜面上的物体，重力沿斜面方向的分量为 ( mg sin θ )，垂直斜面方向的分量为 ( mg cos θ )。
- Identify the object of interest and isolate it.
- 明确研究对象并将其隔离出来。
- Draw all external forces, not forces the object exerts on others.
- 画出所有外力，不包括物体对其他物体施加的力。
- Resolve forces into perpendicular components when useful.
- 需要时可将力分解为相互垂直的分量。
- Apply Newton's second law separately in each direction.
- 在各自方向上分别应用牛顿第二定律。
12. Exam Tips and Common Pitfalls | 考试技巧与常见误区
One common mistake is confusing mass and weight. Mass is a scalar quantity measured in kilograms, while weight is a force measured in newtons. Weight changes with gravitational field strength, but mass does not.
常见误区之一是混淆质量与重量。质量是标量，单位为千克；重量是力，单位为牛顿。重量随重力场强度变化，而质量不变。
Another common error is forgetting that velocity is a vector. A change in direction without a change in speed still means the velocity is changing, and therefore acceleration is non-zero.
另一个常见错误是忘记速度是矢量。即使速率不变，只要方向改变，速度也在改变，因此加速度不为零。
When using graphs, check the axes first. A displacement-time graph looks similar to a velocity-time graph, but the interpretations are completely different.
使用图像时务必先看清坐标轴。位移-时间图像与速度-时间图像看起来相似，但解读方法完全不同。
Always use the correct sign convention and significant figures. State units clearly for every numerical answer. In IB examinations, data booklet equations should be quoted before substitution.
始终使用正确的正负号约定和有效数字。每个数值答案都要写明单位。在IB考试中，代入数值前应先引用公式书中的公式。
Finally, remember that the study of space, time and motion is not just about memorising equations. It builds conceptual understanding that underpins fields, waves, electromagnetism and quantum physics.
最后请记住，空间、时间与运动的学习不仅仅在于记忆公式。它构建了理解场、波、电磁学和量子物理所必需的概念基础。
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