Distance (scalar): total path length.
Displacement (vector): shortest distance from initial to final position.

Speed = distance/time (scalar)
Velocity = displacement/time (vector)
Average vs Instantaneous: v_avg = Δx/Δt, v_inst = dx/dt

Acceleration = dv/dt = d²x/dt²

🧠 Derivations (graphical)

From a-t graph: area → change in velocity.

From v-t graph: slope = a, area = displacement.

Displacement in nth second: s_n = u + ½a(2n-1)

For a body dropped from height h:
Time to hit ground: t = √(2h/g)
Final velocity: v = √(2gh)

For upward projection: max height = u²/(2g), time of flight = 2u/g

💡 NEET TIPS & SHORTCUTS

• If acceleration is zero → constant velocity → v-t graph horizontal.
• For average speed when particle moves with speeds v₁, v₂ for equal time: avg speed = (v₁+v₂)/2.
• For equal distances: avg speed = 2v₁v₂/(v₁+v₂).
• Area under v-t gives displacement; area above axis positive, below negative.
• In free fall, initial velocity zero if dropped, not if thrown.

⚠️ COMMON MISTAKES

• Confusing distance with displacement in velocity definition.
• Using v = u + at when acceleration is not constant.
• Sign convention: upward positive, downward negative – be consistent.
• Taking g as positive always – use sign according to direction.

v_avg = Δx/Δt

a_avg = Δv/Δt

v_inst = dx/dt

s_nth = u + ½a(2n-1)

For free fall: v = gt, h = ½gt²