Class 11 · Chapter 3
Kinematics
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
Kinematics Short Notes
2 min read
Condensed revision points for Kinematics — for quick recall before exams, not a substitute for the full notes.
Core Definitions
- Distance: scalar, total path length, never decreases.
- Displacement: vector, shortest path from start to end.
- Distance ≥ |Displacement| always.
- Speed = distance/time (scalar). Velocity = displacement/time (vector).
- Acceleration = rate of change of velocity; can act to speed up, slow down, or change direction.
Equations of Motion (constant a only)
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- Distance in nth second: sₙ = u + (a/2)(2n − 1)
Motion Under Gravity
- Dropped from rest: u = 0, a = +g (downward positive).
- Thrown upward: a = −g during rise and fall; time up = time down = u/g.
- Max height: H = u²/2g. Total time of flight (up + down to same level): T = 2u/g.
- Speed of projection = speed on return to the same point.
Ground-to-Ground Projectile
- Horizontal velocity (u cosθ) stays constant throughout flight.
- Vertical velocity changes under gravity: vy = u sinθ − gt.
- Time of flight: T = 2u sinθ/g
- Max height: H = u² sin²θ/2g
- Range: R = u² sin2θ/g — maximum at θ = 45°.
- Same speed, complementary angles (θ and 90°−θ) → equal range, different height and time of flight.
Horizontal Projection from Height h
- Time to land: t = √(2h/g) — depends only on h, not on launch speed.
- Range: R = u√(2h/g)
- Landing speed: v = √(u² + 2gh)
Relative Velocity
- v_AB = v_A − v_B (always subtract as vectors, not magnitudes).
- Same direction → relative speed = difference of speeds.
- Opposite direction → relative speed = sum of speeds.
- Rain-man / river-boat: draw vector diagram, subtract velocities, then resolve angle.
River-Boat — Two Goals, Two Headings
- Shortest path (reach point directly opposite): angle upstream so sinθ = v_river/v_boat. Takes longer.
- Shortest time: head straight across (θ = 0 to bank). Drift occurs, but crossing time = width/v_boat is minimum.
Common Exam Traps
- Equations of motion apply ONLY for constant acceleration — check before using them.
- Distance ≠ displacement unless motion is one-directional in a straight line.
- At the top of a vertical throw, velocity = 0 but acceleration ≠ 0 (still g, downward).
- Speed can never be negative; velocity can be.
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