Part of ME-02 — Kinematics

Mind Map — Kinematics

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KINEMATICS
├── 1. Basic Quantities
│   ├── Scalars: distance, speed, time, mass
│   └── Vectors: displacement, velocity, acceleration
│       ├── Resolution: Ax = Acosθ, Ay = Asinθ
│       ├── Dot product: AB cosθ → scalar
│       └── Cross product: AB sinθ → vector (⊥)
│
├── 2. Equations of Motion (constant a)
│   ├── v = u + at  [omits s]
│   ├── s = ut + ½$at^{2}$  [omits v]
│   ├── $v^{2}$ = $u^{2}$ + 2as  [omits t]
│   └── sₙ = u + a(2n−1)/2  [nth second]
│
├── 3. Graphical Analysis
│   ├── x-t graph
│   │   ├── Slope → instantaneous velocity
│   │   └── Parabola → uniform acceleration
│   └── v-t graph
│       ├── Slope → acceleration
│       └── Area → displacement
│
├── 4. Projectile Motion
│   ├── Horizontal: constant velocity u cosθ
│   ├── Vertical: SUVAT with a = −g
│   ├── T = 2u sinθ / g
│   ├── H = $u^{2}$s$in^{2}$θ / 2g
│   ├── R = $u^{2}$sin2θ / g  [max at 45°]
│   └── Complementary angles → same R, different H
│
└── 5. Circular Motion
    ├── Speed: constant
    ├── Velocity: direction changing
    ├── ω = v/r  [rad/s]
    └── aₒ = $v^{2}$/r = ω^{2}r  [toward centre]

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