Special cases:
θ = 0° → W = Fs (maximum positive)
θ = 90° → W = 0 (no work)
θ = 180° → W = –Fs (negative work)

Work by variable force: W = ∫ F·dx (area under F-x graph)

Kinetic Energy (KE): K = ½ mv²

Potential Energy (PE): U = mgh (gravitational), U = ½ kx² (spring)

Work-Energy Theorem: W_net = ΔK = K_f – K_i

🎢 Example: Free fall

mgh + ½ mv² = constant. At height h, v = √(2g(H–h)).

🔧 Spring-mass system

½ mv² + ½ kx² = ½ kA² (amplitude A).

Unit: Watt (W) = J/s. 1 hp = 746 W

Efficiency: η = (output power)/(input power) × 100%

💡 NEET TIPS & SHORTCUTS

• Work done by gravity is independent of path: W_g = –ΔU = –mgΔh.
• Work done by spring force: W_spring = –½ k(x₂² – x₁²).
• For variable force, use integration or area under F-x.
• In collisions, kinetic energy may not be conserved, but momentum always is.

⚠️ COMMON MISTAKES

• Confusing work done by friction with change in kinetic energy (friction always does negative work).
• Using conservation of energy when non‑conservative forces are present.
• Not using the correct sign for work done by a force.
• Assuming power = force × speed always – only valid when force and velocity are in same direction.

Work (constant force): W = Fs cosθ

Kinetic energy: K = ½ mv²

Gravitational PE: U = mgh

Spring PE: U = ½ kx²

Power: P = Fv (if F∥v)

Work-energy theorem: W_net = ΔK