Components: uₓ = u cosθ, uᵧ = u sinθ

Time of flight (T): T = 2u sinθ / g

Max height (H): H = u² sin²θ / (2g)

Range (R): R = u² sin2θ / g

Initial velocity horizontal: uₓ = u, uᵧ = 0

Time to hit ground: t = √(2h/g)

Horizontal range: R = u × t = u √(2h/g)

Velocity at time t: v = √(u² + g²t²)

Angular displacement: Δθ (radians)

Angular velocity: ω = Δθ/Δt = v/r (rad/s)

Centripetal acceleration: a_c = v²/r = ω²r

Centripetal force: F_c = mv²/r = mω²r

Velocity of A w.r.t B: v_AB = v_A – v_B

River-boat problems: v_boat/ground = v_boat/water + v_water/ground

Minimum time to cross river: drift = (v_river × width) / v_boat (perpendicular crossing)

💡 NEET TIPS & SHORTCUTS

• In projectile, velocity at any time: v = √(uₓ² + (uᵧ – gt)²)
• Angle of projection for max range: 45° (sin90=1).
• For same range, two angles: θ and 90°–θ, and time of flight differ: T₁ = 2u sinθ/g, T₂ = 2u cosθ/g.
• In UCM, a_c is constant in magnitude but direction changes → not uniform acceleration.
• For a particle moving in a circle with constant speed, no tangential acceleration, only radial.

⚠️ COMMON MISTAKES

• Taking vertical acceleration as zero in projectile – it's always g downwards.
• Confusing centripetal force with centrifugal (fictitious).
• For river crossing, not resolving velocity components correctly.
• Using range formula for horizontal projection directly.

Projectile: T = 2u sinθ/g, H = u² sin²θ/2g, R = u² sin2θ/g

Horizontal projection: t = √(2h/g), R = u√(2h/g)

UCM: a_c = v²/r = ω²r, F_c = mv²/r

Relative velocity: v_AB = v_A – v_B