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HKDSE Physics – Position and Movement

HKDSE Physics Core 2
Chapter 1: Position and Movement | 位置與運動

Billy Sir’s Smart Notes: Master Vectors, Kinematics Equations, Motion Graphs, and Free-Falling.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握運動學公式、圖像分析及自由下落。

1. Physical Quantities | 物理量

In physics, quantities are classified into two main categories based on whether direction matters. 在物理學中，物理量根據是否具有方向性分為兩大類。

Scalar (標量) Vector (矢量)
Magnitude (= value + unit) only.
只有量值（數值 + 單位）。		 Magnitude (= value + unit) + Direction.
具有量值（數值 + 單位）及方向。
Examples: temperature (K), time (s), distance (m), volume (m³), mass (kg), speed (m s⁻¹). Examples: force (N), displacement (m), velocity (m s⁻¹), acceleration (m s⁻²).

2. Quantities Related to Motion | 運動相關物理量

📏 Distance vs. Displacement | 距離與位移

  • Distance (travelled): Total length of the path actually gone through. (Scalar) 實際行走路徑的總長度。（標量）
  • Displacement (\(s\)): The straight line distance between the starting point to the ending point. (Vector) 起點到終點的直線距離及方向。（矢量）

🚀 Speed vs. Velocity | 速率與速度

Speed is the rate of change of distance, while velocity is the rate of change of displacement.

$$ v = \frac{\Delta s}{\Delta t} $$
  • Average Velocity: Total displacement / Total time. 總位移 / 總時間。
  • Instantaneous Velocity: Velocity at a specific short period of time. 某一瞬間的速度。

🏎️ Acceleration | 加速度

Acceleration is the rate of change of velocity. It is a vector quantity. 加速度是速度的變化率。它是一個矢量。

$$ a = \frac{\Delta v}{\Delta t} = \frac{v – u}{t} $$
  • Speeding up: Velocity and acceleration are in the same direction. 加速：速度與加速度方向相同。
  • Slowing down (Deceleration): Velocity and acceleration are in opposite directions. 減速：速度與加速度方向相反。
  • Changing direction: Even with a constant speed, changing direction means velocity changes, hence there is acceleration. 改變方向：即使速率不變，方向改變亦代表速度改變，因此具有加速度。

3. Equations of Uniformly Accelerated Motion | 勻加速運動公式

When an object moves along a straight line with a constant acceleration (\(a\)), we can use the four equations of motion. 當物體沿直線作勻加速運動時，可使用以下四條運動學公式。

📐 The Four Equations | 四大公式

$$ v = u + at $$
$$ s = \frac{1}{2}(u + v)t $$
$$ s = ut + \frac{1}{2}at^2 $$
$$ v^2 = u^2 + 2as $$

Variables:

  • \(s\) = Displacement (位移)
  • \(u\) = Initial Velocity (初速度)
  • \(v\) = Final Velocity (末速度)
  • \(a\) = Constant Acceleration (恆定加速度)
  • \(t\) = Time taken (時間)

4. Graphical Representation of Motion | 運動圖像分析

Graph Type (圖像種類) Slope (斜率代表) Area Under Graph (面積代表)
Displacement-time (s-t)
位移-時間圖		 Instantaneous Velocity (\(v = \frac{\Delta s}{\Delta t}\)) N.A.
Velocity-time (v-t)
速度-時間圖		 Acceleration (\(a = \frac{\Delta v}{\Delta t}\)) Change in Displacement (\(\Delta s\))
Acceleration-time (a-t)
加速度-時間圖		 N.A. Change in Velocity (\(\Delta v\))

5. Acceleration due to Gravity | 重力加速度

A free-falling object is falling under the sole influence of gravitational force, meaning air resistance is negligible. 自由下落的物體只受重力影響，忽略空氣阻力。

🌍 Free-Falling Analysis | 自由下落分析

All free-falling objects fall down with the same acceleration, regardless of their mass.

$$ g = 9.81 \text{ m s}^{-2} $$

Direction: Always pointing vertically downwards. 方向永遠垂直向下。

  • When projected upwards, acceleration is still \(9.81 \text{ m s}^{-2}\) downwards.
  • At the maximum height, velocity \(v = 0 \text{ m s}^{-1}\) momentarily, but acceleration \(a = -g\).

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