Deducing Acceleration | 推断加速度

📚 Deducing Acceleration | 推断加速度

In CIE A-Level Physics, deducing acceleration means finding the rate of change of velocity from experimental data, graphs, equations or known forces. This skill appears in kinematics, dynamics and circular motion, so you need to understand both the definition and practical methods for obtaining acceleration.

在 CIE A-Level 物理中，推断加速度是指从实验数据、图像、方程或已知力中求出速度的变化率。这一技能出现在运动学、动力学和圆周运动中，因此既要理解加速度的定义，也要掌握获取加速度的实用方法。

1. What Acceleration Means | 加速度的定义

Acceleration is defined as the rate of change of velocity with time. Because velocity is a vector, acceleration is also a vector: it has both magnitude and direction. Average acceleration is given by a = Δv / Δt = (v − u) / t, where u is the initial velocity, v is the final velocity and t is the time taken.

加速度定义为速度随时间的变化率。由于速度是矢量，加速度也是矢量：既有大小也有方向。平均加速度由 a = Δv / Δt = (v − u) / t 给出，其中 u 为初速度，v 为末速度，t 为所用时间。

a = Δv / Δt = (v − u) / t

The SI unit of acceleration is metre per second squared, written m s⁻². In one-dimensional motion, if the positive direction is chosen along the initial velocity, a negative acceleration means the object is slowing down in that direction.

加速度的国际单位是米每二次方秒，写作 m s⁻²。在一维运动中，如果选定初速度方向为正方向，那么负加速度表示物体在该方向上正在减速。

2. Acceleration from Velocity-Time Graphs | 从速度-时间图推断加速度

A velocity-time graph is one of the most direct tools for deducing acceleration. The gradient of a straight-line segment equals the constant acceleration. For a curved line, draw a tangent at the point of interest and use the gradient of that tangent as the instantaneous acceleration.

速度-时间图是推断加速度最直接的工具之一。直线段的斜率等于恒定加速度。如果图像是曲线，则在感兴趣的点处作切线，并用该切线的斜率作为瞬时加速度。

a = gradient = Δv / Δt = (v₂ − v₁) / (t₂ − t₁)

The sign of the gradient gives the direction of acceleration relative to the chosen positive direction. The area under a velocity-time graph gives displacement, but area is not used to deduce acceleration.

斜率的正负给出加速度相对于选定正方向的方向。速度-时间图下的面积给出位移，但面积不能用于推断加速度。

Straight line sloping upwards: constant positive acceleration | 直线向上倾斜：恒定的正加速度
Straight line sloping downwards: constant negative acceleration | 直线向下倾斜：恒定的负加速度
Horizontal line: zero acceleration, constant velocity | 水平线：零加速度，速度恒定
Curved line: changing acceleration; use a tangent | 曲线：加速度在变化；应使用切线

3. Using the SUVAT Equations | 运用匀加速运动方程

For motion with constant acceleration, the SUVAT equations link displacement s, initial velocity u, final velocity v, acceleration a and time t. If three of these quantities are known, you can deduce the others.

对于加速度恒定的运动，SUVAT 方程将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系起来。如果已知其中三个量，就可以求出其他量。

v = u + at

s = ut + ½at²

v² = u² + 2as

s = ½(u + v)t

For example, a trolley starts from rest and travels 0.80 m in 2.0 s under constant acceleration. Using s = ut + ½at² with u = 0 gives a = 2s / t² = 2 × 0.80 / (2.0)² = 0.40 m s⁻².

例如，一辆小车从静止开始，在 2.0 s 内运动 0.80 m，加速度恒定。由 s = ut + ½at²，代入 u = 0 得 a = 2s / t² = 2 × 0.80 / (2.0)² = 0.40 m s⁻²。

Always check that acceleration is constant before applying SUVAT equations. If acceleration changes, use graphs, calculus or numerical methods instead.

使用 SUVAT 方程前必须确认加速度恒定。如果加速度发生变化，应改而使用图像、微积分或数值方法。

4. Ticker-Tape Timers | 利用打点计时器推断加速度

A ticker-tape timer places dots on a tape at equal time intervals. With a 50 Hz supply, the interval between consecutive dots is 1/50 = 0.02 s. You can cut the tape into sections containing equal numbers of intervals and treat each section as a displacement during a known time.

打点计时器在纸带上每隔相等时间打一个点。使用 50 Hz 电源时，相邻点之间的时间间隔为 1/50 = 0.02 s。可以将纸带剪成包含相同间隔数的段，并将每段视为已知时间内的位移。

To deduce acceleration, calculate the average velocity of each section using v = x / t, plot these velocities against the mid-time of each section, and find the gradient of the best-fit line. The gradient is the acceleration.

为推断加速度，先用 v = x / t 计算每段的平均速度，再将这些速度对每段中间时刻作图，并求出最佳拟合线的斜率。该斜率就是加速度。

v = x / t, a = Δv / Δt

This method is useful because it produces a permanent record and shows whether the acceleration was roughly constant throughout the motion.

该方法很有用，因为它留下永久记录，并能显示整个运动过程中加速度是否大致恒定。

5. Photogates and Data Loggers | 光门与数据记录仪

A light gate measures the time for a card of known length to interrupt a light beam. The average speed is the card length divided by the interruption time. Using a double-interrupt card gives an initial and final speed over the two edges, allowing acceleration to be deduced with a = (v − u) / t if the time between edges is known.

光门测量已知长度的挡光片遮挡光束的时间。平均速度等于挡光片长度除以遮挡时间。使用双挡光片可获得两个边缘对应的初速度和末速度，若已知边缘之间的时间，就可用 a = (v − u) / t 求出加速度。

v = L / t, a = (v − u) / t

Motion sensors and data loggers can record displacement and velocity continuously. The software plots velocity-time graphs, and the gradient tool gives the acceleration directly.

运动传感器和数据记录仪可以连续记录位移和速度。软件绘制速度-时间图，其斜率工具可直接给出加速度。

When using light gates, align the card perpendicular to the beam and repeat measurements to reduce random uncertainty. Avoid using very short cards, because the interruption time becomes too small to measure accurately.

使用光门时，挡光片要垂直于光束，并重复测量以减少随机不确定度。避免使用很短的挡光片，因为遮挡时间过短会难以精确测量。

6. Acceleration on a Ramp: Experimental Approach | 斜面实验中的加速度

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Deducing Acceleration | 推断加速度