📚 From moving to stationary | 从运动到静止
In physics, studying an object that transitions from moving to stationary is a fundamental exercise in dynamics. Whether it's a car braking, a block sliding to a halt, or a ball rolling to a stop, the principles of kinematics, forces, energy, and momentum all converge to describe the process. Understanding these principles is crucial for A-Level Physics under the CIE syllabus, as it integrates multiple topics and prepares students for real-world applications such as road safety and mechanical design.
在物理学中，研究一个从运动到静止的物体是动力学的基础练习。无论是汽车刹车、滑块停下来，还是球滚动至停止，运动学、力、能量和动量的原理都汇聚在一起描述这个过程。理解这些原理对CIE A-Level物理至关重要，因为它整合了多个主题，并为道路安全和机械设计等实际应用做好准备。
1. Understanding 'From Moving to Stationary' | 理解“从运动到静止”
When we say an object goes "from moving to stationary," we mean its initial velocity u is greater than zero and its final velocity v becomes zero. This change requires a net force acting opposite to the direction of motion, producing a deceleration (negative acceleration). Such scenarios are abundant: a train stopping at a station, a falling object hitting the ground, or a sliding coin coming to rest due to friction.
当我们说物体“从运动到静止”时，意味着它的初速度 u 大于零，末速度 v 变为零。这一变化需要一个与运动方向相反的净力，产生减速度（负加速度）。这样的情景比比皆是：列车在车站停下、下落的物体击中地面、或者硬币因摩擦而停止滑动。
The stopping process can be analysed using the equations of uniformly accelerated motion, provided the deceleration is constant. However, not all stopping is uniform: in many cases the resistive force, and hence the deceleration, may vary with speed or time.
如果减速度是恒定的，可以用匀加速运动方程来分析停止过程。但并非所有停止都是均匀的：在许多情况下，阻力及其产生的减速度可能随速度或时间变化。
2. Kinematic Equations for Uniform Deceleration | 匀减速运动的运动学方程
For motion with constant acceleration (or deceleration), four kinematic equations link displacement s, initial velocity u, final velocity v, acceleration a, and time t. When an object decelerates, a is negative. The most directly relevant equation for stopping is:
对于匀加速度（或匀减速度）运动，有四个运动学方程联系位移 s、初速度 u、末速度 v、加速度 a 和时间 t。当物体减速时，a 为负值。关于停止最直接的方程是：
v² = u² + 2as
s = −u²/(2a). Since a is negative, s is positive. The other equations are equally useful:
令 v = 0 得到停止距离 s = −u²/(2a)。因为 a 为负，s 为正。其他方程同样有用：
v = u + at | s = ut + ½at² | s = ½(u + v)t
These equations allow us to calculate, for example, the time taken to stop or the deceleration from a known stopping distance. They assume constant resultant force and neglect air resistance unless it is constant.
这些方程使我们能计算，例如停止所需的时间或由已知停止距离求出减速度。它们假设合外力恒定，并且忽略空气阻力，除非阻力也是恒定的。
3. Newton’s Second Law and Decelerating Force | 牛顿第二定律与减速力
According to Newton' leration opposes velocity, the force is a decelerating force. For a car of mass 1200 kg slowing at 6 m s⁻², the net decelerating force has magnitude 7200 N acting backwards.
根据牛顿第二定律，物体所受的合力 F 等于质量 m 乘以加速度 a：F = ma。如果加速度与速度方向相反，该力就是减速力。对于一辆质量 1200 kg、以 6 m s⁻² 减速的汽车，净减速力的大小为 7200 N，方向向后。
This force can originate from friction, applied brakes, or other resistive forces. When multiple forces act, the vector sum determines the direction of deceleration. As long as the resultant is opposite to motion, the object slows down.
这个力可以来自摩擦、制动器施加的力或其他阻力。当多个力作用时，矢量和决定减速的方向。只要合力的方向与运动相反，物体就会减速。
4. Friction as a Decelerating Force | 摩擦力作为减速力
Friction is a common decelerating force. For a sliding block on a rough surface, kinetic friction fk s opposes motion, providing a deceleration a = −μ_k g (if N = mg on a horizontal surface).
摩擦力是一种常见的减速力。对于在粗糙表面上滑动的物块，动摩擦力 fk = μ_k N，其中 μ_k 为动摩擦系数，N 为法向接触力。该摩擦力总是阻碍运动，产生的减速度 a = −μ_k g（在水平面上 N = mg 时）。
ing distance s = u²/(2 μ_k g), showing that higher initial speed dramatically increases stopping distance (quadratic dependence).
在冰面（低 μ_k）上滑动的物体比在混凝土（高 μ_k）上需要更长时间停下来。利用 a = −μ_k g 代入运动学方程可得停止距离 s = u²/(2 μ_k g)，表明较高的初速度会大幅增加停止距离（平方关系）。
5. Energy Transformation: Kinetic to Thermal | 能量转换：动能转化为热能
A moving object possesses kinetic energy Ek sferred. The work done by the decelerating force equals the change in kinetic energy (work–energy theorem): W = F d cos180° = −F d = ½m(v² − u²).
运动物体具有动能 Ek = ½mu²。要使其停下，这部分能量必须被耗散或转移。减速力做的功等于动能的变化量（动能定理）：W = F d cos180° = −F d = ½m(v² − u²)。
ning the force removes ½mu² of energy from the object. This energy is primarily converted into thermal energy, raising the temperature of the brakes, tyres, and road surface. In a car, braking transforms ordered kinetic energy into disordered internal energy, illustrating the principle of energy conservation.
因为 v = 0，做功为 −½mu²，意味着该力从物体移走了 ½mu² 的能量。这部分能量主要转化为热能，使刹车片、轮胎和路面升温。在汽车中，制动将有序的动能转化为无序的内能，体现了能量守恒原理。
6. Braking and Stopping Distances | 刹车距离与停止距离
topping distance is the sum of the thinking distance (distance travelled during the driver' u × reaction time; braking distance = u²/(2a), with a being the magnitude of deceleration.
在道路安全中，总停止距离为反应距离（在驾驶员反应时间内行驶的距离）与刹车距离（制动期间行驶的距离）之和。反应距离 = u × 反应时间；刹车距离 = u²/(2a)，其中 a 是减速度的大小。
Factors affecting thinking distance include fatigue, alcohol, and distractions. Braking distance depends on speed squared, road conditions (friction coefficient), tyre conditions, and brake quality. Typical data are summarised below (assume reaction time 0.7 s, deceleration 6.5 m s⁻²):
影响反应距离的因素包括疲劳、酒精和注意力分散。刹车距离取决于速度的平方、路面状况（摩擦系数）、轮胎状况和制动质量。以下是一些典型数据（假设反应时间 0.7 s，减速度 6.5 m s⁻²）：
| Initial speed u / m s⁻¹ | Thinking distance / m | Braking distance / m | Total stopping distance / m |
|---|---|---|---|
| 13.4 (30 mph) | 9.4 | 13.8 | 23.2 |
| 22.4 (50 mph) | 15.7 | 38.6 | 54.3 |
| 31.3 (70 mph) | 21.9 | 75.4 | 97.3 |
The quadratic relationship for braking distance underscores the danger of high speeds: doubling the speed quadruples the braking distance.
刹车距离与速度的平方关系突显了高速驾驶的危险：速度加倍，刹车距离变为四倍。
7. Momentum and Impulse during Deceleration | 减速过程中的动量与冲量
in momentum: J = F Δt = Δp. Therefore, a greater stopping time Δt reduces the average force experienced.
动量 p = mv。物体从 u 减速到 0 时，动量变化量 Δp = m(v − u) = −mu。净力提供的冲量 J 等于动量的变化量：J = F Δt = Δp。因此，较大的停止时间 Δt 会减小平均受力。
This principle is applied in car safety features: airbags and crumple zones extend the collision time, reducing the force on occupants. Similarly, when catching a fast cricket ball, a fielder moves their hands backward to increase the stopping time, thereby feeling a smaller force.
这一原理应用于汽车安全装置：安全气囊和溃缩区延长碰撞时间，减小乘员受力。同样，接住快速飞来的板球时，守场员向后移动双手以增加停止时间，从而感受较小的力。
8. Work Done by Decelerating Forces | 减速力做的功
is negative work reduces the kinetic energy. For a constant force, the graph of F against distance gives a rectangle area equal to the work done. If force varies (e.g., air resistance proportional to speed²), the area under the curve still represents work.
减速力在位移 d 上做的功为 W = F d cos θ。由于 θ = 180°，cos180° = −1，所以 W = −F d。这个负功减小了动能。对于恒力，F – 距离图给出矩形面积等于所做的功。如果力是变化的（如空气阻力与速度平方成正比），曲线下的面积仍然表示功。
ing distance d is given by 5000 × d = 200 000 J, so d = 40 m. This illustrates the direct energy method, often simpler than kinematic equations when forces are constant.
考虑一辆质量 1000 kg、初速度 20 m s⁻¹ 的汽车，其动能为 ½ × 1000 × 20² = 200 000 J。若制动力恒为 5000 N，刹车距离 d 由 5000 × d = 200 000 J 得出，因此 d = 40 m。这说明了直接使用能量方法，在力恒定时常比运动学方程更简便。
9. Real-World Example: Car Braking | 实例：汽车刹车
Modern car braking systems convert kinetic energy into heat via hydraulic disc brakes. The driver applies force to the brake pedal, which is amplified and transmitted to brake pads clamping onto discs. The friction between pads and discs provides a torque that decelerates the wheels and, through tyre–road friction, the entire vehicle.
现代汽车制动系统通过液压盘式制动器将动能转化为热量。驾驶员踩下制动踏板，力被放大并传递到夹紧制动盘的刹车片。刹车片与制动盘之间的摩擦产生转矩，使车轮减速，并通过轮胎与路面的摩擦使整个车辆减速。
Anti-lock Braking System (ABS) prevents wheel lock-up during hard braking. When wheels lock, kinetic friction becomes sliding friction, reducing deceleration and steering control. ABS rapidly modulates brake pressure to maintain static friction between tyre and road at the threshold, optimising deceleration and maintaining steerability.
防抱死制动系统（ABS）防止在紧急制动时车轮抱死。当车轮抱死时，滚动摩擦变为滑动摩擦，降低了减速度和转向控制能力。ABS 快速调节制动压力，使轮胎与路面保持在静摩擦的临界状态，从而既最大化减速度，又保持转向能力。
10. Experimental Determination of Deceleration | 实验测定减速度
d runway stops momentarily; its deceleration can be calculated from v² = u² + 2as using data from light gates. Alternatively, a ticker tape timer records dots at equal time intervals; the decreasing spacing between dots indicates deceleration, and a velocity–time graph yields the gradient a.
在实验室中，可以使用运动传感器、光门或打点计时器测量减速度。例如，一辆小车沿倾斜跑道向上滚动会瞬间停下；它的减速度可以利用光门数据从 v² = u² + 2as 中算出。或者，打点计时器以相等时间间隔记录点迹；点间距减小表明减速，速度–时间图的斜率即为加速度 a。
on with a motion sensor. The deceleration a = −μ_k g allows μ_k to be found. Such practical work reinforces the link between Newton’s laws, friction, and kinematics.
一个测定物块与表面间摩擦系数的实验可以给物块一个初始推动，并用运动传感器记录其减速度。由 a = −μ_k g 可求得 μ_k。这样的实践强化了牛顿定律、摩擦和运动学之间的联系。
11. Safety Features and the Impulse–Momentum Relationship | 安全装置与冲量–动量关系
In a collision, bringing an occupant to rest involves a large momentum change over a very short time if no safety features are present. By increasing the stopping time, the average force is reduced. Crumple zones at the front and rear of a car deform plastically, increasing collision time. Airbags provide a cushioning effect, further extending the time of deceleration for the occupant’s torso and head.
在碰撞中，如果没有安全装置，乘员在极短时间内停下来会涉及很大的动量变化。通过增加停止时间，可以减小平均作用力。汽车前后部的溃缩区通过塑性变形延长碰撞时间。安全气囊提供缓冲效果，进一步延长乘员躯干和头部的减速时间。
0 kg passenger’s speed changes from 15 m s⁻¹ to 0 in 0.1 s without an airbag, the average force is about 10 500 N. With an airbag stretching the time to 0.3 s, the force drops to around 3500 N, significantly reducing injury risk.
乘客受到的力可用 F = Δp / Δt 估算。如果一名 70 kg 的乘客在 0.1 s 内速度从 15 m s⁻¹ 减至 0，没有气囊时平均力约为 10 500 N。使用气囊将时间延长至 0.3 s，力降为约 3500 N，大大降低了受伤风险。
12. Summary and Key Takeaways | 总结与关键要点
Bringing an object from moving to stationary involves a decelerating force that does negative work, converting kinetic energy into other forms, primarily heat. The kinematic equations for uniform acceleration are essential tools for calculating stopping distances and times. Newton’s second law links the deceleration to the net force, while the impulse–momentum theorem explains how extending stopping time reduces impact forces.
使物体从运动到静止涉及一个做负功的减速力，将动能转化为其他形式，主要是热能。匀加速运动方程是计算停止距离和时间的基本工具。牛顿第二定律将减速度与净力联系起来，而冲量–动量定理则解释了延长停止时间如何减小撞击力。
Understanding these principles has direct real-world implications in vehicle safety, sports, and engineering design. For CIE A-Level Physics, mastering the interplay between motion, forces, energy, and momentum in stopping scenarios is crucial for problem-solving and practical applications.
理解这些原理对车辆安全、运动和工程设计有着直接的现实意义。对 CIE A-Level 物理而言，掌握停止情景中运动、力、能量和动量之间的相互作用，对解题和实际应用至关重要。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图