Constant Acceleration Formulae 1 | 匀加速运动公式（一）

📚 Constant Acceleration Formulae 1 | 匀加速运动公式（一）

In Edexcel A Level Mechanics, constant acceleration problems are often the first step into modelling real objects such as cars, balls and falling particles. The key idea is that if acceleration does not change, velocity changes at a steady rate, so the motion can be described by a small set of equations linking displacement, initial velocity, final velocity, acceleration and time.

在 Edexcel A Level 力学中，匀加速运动问题通常是大家第一次把汽车、小球和下落物体等真实对象抽象为数学模型。核心思想是：如果加速度保持不变，速度就会均匀变化，因此运动可以用一组联系位移、初速度、末速度、加速度和时间的方程来描述。

1. The SUVAT Variables | 五个运动变量

In these problems there are five standard quantities: s is displacement measured in metres, u is initial velocity in m s⁻¹, v is final velocity in m s⁻¹, a is acceleration in m s⁻², and t is time in seconds. These are often called the SUVAT variables.

在这些问题中有五个标准物理量：s 是位移（米），u 是初速度（m s⁻¹），v 是末速度（m s⁻¹），a 是加速度（m s⁻²），t 是时间（秒）。它们通常被称为 SUVAT 变量。

Displacement is a vector, so its direction matters just as much as its size. Velocity and acceleration are also vectors, which means a positive or negative sign must be chosen consistently for every quantity in a calculation.

位移是矢量，因此方向与大小同样重要。速度和加速度也是矢量，这意味着在计算中每个量的正负号都必须保持一致。

Time is the only scalar quantity in the set. You should always write the units clearly, because Edexcel examiners expect correct SI units in final answers and in any working that is used for substitution.

时间是这组量中唯一的标量。你应当始终把单位写清楚，因为 Edexcel 考官希望在最终答案和用于代入的步骤中看到正确的国际单位。

2. The Four Constant Acceleration Equations | 四个匀加速运动公式

The four equations below are valid only when acceleration is constant. They must not be used for motion where acceleration changes, such as a particle moving along a curved path or a car with a continually varying driving force.

下面四个方程仅在加速度恒定时成立。加速度变化的运动不能使用它们，例如做曲线运动的质点或驱动力不断变化的汽车。

v = u + at

s = ½(u + v)t

s = ut + ½at²

v² = u² + 2as

These four equations are often remembered by the variables they contain. Each one omits exactly one SUVAT quantity, which is very useful when you are deciding which formula to use.

这四个公式通常按它们包含的变量来记忆。每一个公式都恰好省略一个 SUVAT 量，这在决定使用哪个公式时非常有用。

The velocity-displacement equation without t is particularly important in stopping-distance and maximum-height questions, because time is often not mentioned.

不含 t 的速度-位移方程在刹车距离和最大高度问题中尤其重要，因为这类题目通常不会提到时间。

3. Deriving v = u + at | 推导速度-时间公式

Since acceleration is the rate of change of velocity, for constant acceleration we can write a = (v – u) / t. Rearranging this definition gives the first equation.

由于加速度是速度的变化率，当加速度恒定时可以写成 a = (v − u) ÷ t。整理这个定义就得到第一个方程。

a = (v − u) / t

v = u + at

This equation shows that final velocity is the initial velocity plus the extra velocity gained by accelerating at a constant rate for t seconds. If acceleration is negative, the final velocity is smaller than the initial velocity.

该公式表明，末速度等于初速度加上以恒定加速度运动 t 秒所增加的速度。如果加速度为负，末速度就会小于初速度。

In a velocity-time graph, this equation represents a straight line with gradient a and vertical intercept u. The gradient being constant is exactly what is meant by constant acceleration.

在速度-时间图中，这个方程表示一条斜率为 a、纵截距为 u 的直线。斜率恒定正是匀加速运动的含义。

4. Deriving the Displacement Equations | 位移公式推导

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