Equation of Kinematics – Complete Notes, Revision, Important Questions & Downloads
The equations of kinematics are the computational core of NEET Chapter 2 (Motion In One Dimension). Two subtopics are covered: Motion with Zero Acceleration (uniform velocity, s = ut, v = u = constant) and Motion with Constant Acceleration (the five SUVAT equations: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u+v)t; and the nth-second distance formula sₙ = u + (a/2)(2n−1)). NEET tests these equations in two main ways: (1) direct substitution with two unknowns given three known values; (2) multi-step problems combining two or more equations, such as finding when two projectiles meet. The equations of kinematics are foundational for Projectile Motion, Circular Motion, and every mechanics module in NEET. Mastery of the five equations and their three conditions (constant acceleration, straight-line motion, known symbol assignments) is mandatory.
NEET Weightage — Equation of Kinematics
Motion In One Dimension (Chapter 2)| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 2 | 8 | |
| 2023 | 2 | 8 | |
| 2022 | 2 | 8 | |
| 2021 | 2 | 8 | |
| 2020 | 2 | 8 | |
| 2019 | 2 | 8 | |
| 6-Year Total (2019–2024) | 8–15 | 32–60 |
The nth-second formula sₙ = u + (a/2)(2n−1): n is the serial number of the second (1st second, 2nd second, etc.). sₙ is the displacement in the nth second only — not total displacement from start. Common NEET trap: treating sₙ as total displacement.
Stopping distance: when final velocity v = 0, use v² = u² + 2as → s = u²/(2|a|). This is a direct NEET pattern for braking problems.
Exam Strategy — Equation of Kinematics in NEET
Memorise all five SUVAT equations and the three conditions for validity The five equations: (1) v = u + at. (2) s = ut + ½at². (3) v² = u² + 2as. (4) s = ½(u+v)t. (5) sₙ = u + (a/2)(2n−1). Three conditions for validity: (A) Acceleration is constant in both magnitude and direction. (B) Motion is in a straight line (one dimension). (C) Symbols: u = initial velocity, v = final velocity, a = acceleration (constant), s = displacement, t = time, n = serial number of the second. For uniform velocity (a = 0): use v = u, s = ut.
Identify the three known quantities and select the right equation List the five symbols: u, v, a, s, t, n. Identify which are given, which is unknown. Each equation uses exactly four of these (except equation 5 which uses u, a, n, and gives sₙ). Select the equation that contains your three knowns and one unknown. Example: given u, a, t; need s → use equation 2 (s = ut + ½at²). Given u, v, s; need a → use equation 3 (v² = u² + 2as, rearrange for a).
Apply the correct sign convention consistently Choose a positive direction at the start of the problem. Displacements, velocities, and accelerations in this direction are positive; opposite direction is negative. For a ball thrown upward: if upward is positive, u > 0, a = −g = −9.8 (or −10) m/s², s > 0 while going up, s < 0 after it passes the initial point going down. Retardation means acceleration is opposite to velocity — if v > 0 and object decelerates, a < 0. Substituting incorrect signs is the most common error in NEET kinematics.
Download Study Notes — Equation of Kinematics
PDF · Cheat Sheet · MCQ Set · PYQSubtopics in Equation of Kinematics
2-Column TableRapid Revision — Equation of Kinematics
Concept → Trap → Example1) Motion with Zero Acceleration
Uniform velocity: v = u, s = utWhen acceleration = 0: velocity is constant throughout the motion (v = u). Displacement formula: s = ut (distance = speed × time, signed for direction). NCERT: 'When particle moves with zero acceleration' — both magnitude and direction of velocity remain unchanged. This is uniform motion in a straight line.
- v = u = constant (velocity does not change). No change in speed OR direction.
- s = ut (displacement equals initial velocity multiplied by time). For positive u and t: positive displacement in the direction of motion.
- The v-t graph is horizontal (slope = 0 = acceleration). The x-t graph is a straight line with constant positive slope = u.
2) Motion with Constant Acceleration
Five SUVAT equationsNCERT: 'These are the various relations between u, v, a, t and s for the particle moving with uniform acceleration.' Five equations: (1) v = u + at. (2) s = ut + ½at². (3) v² = u² + 2as. (4) s = ½(u+v)t. (5) sₙ = u + (a/2)(2n−1). Condition: 'Acceleration is said to be constant when both the magnitude and direction of acceleration remain constant.'
- Equation (1) v = u + at: relates velocity to time. Use when s is not needed and t is involved.
- Equation (2) s = ut + ½at²: relates displacement to time. Use when v is not needed (or not given).
- Equation (3) v² = u² + 2as: relates velocity to displacement without time. Use when t is not given and not needed.
- Equation (4) s = ½(u+v)t: displacement from average velocity when both initial and final velocities are known.
- Equation (5) sₙ = u + (a/2)(2n−1): displacement in the nth second alone (not total displacement from t = 0).
US Curriculum Gaps — Equation of Kinematics for NEET
US AP Physics students may find these specific aspects of kinematic equations tested differently in NEET.The nth-second formula sₙ = u + (a/2)(2n−1) is not a standard US AP Physics 1 topic
US AP Physics 1 covers the four standard SUVAT equations (v = u+at; s = ut+½at²; v² = u²+2as; s = ½(u+v)t) but does NOT commonly test the nth-second formula sₙ = u + (a/2)(2n−1). This formula gives displacement in the nth second specifically (not total displacement from t = 0). NEET tests this formula directly, often asking for displacement in the 3rd, 5th, or 10th second — values that require sₙ directly, not computing sₙ = s(n) − s(n−1) the long way.
- sₙ = u + (a/2)(2n−1): n is an integer identifying the second (n = 1 for the 1st second).
- sₙ is the displacement in that second only — not the cumulative displacement from t = 0.
- Derivation: sₙ = s(n) − s(n−1) = [un + ½an²] − [u(n−1) + ½a(n−1)²] = u + (a/2)(2n−1).
- NEET pattern: ratio of distances in 1st, 3rd, 5th seconds of free fall from rest: s₁:s₃:s₅ = 1:5:9 (odd-number ratio).
The odd-number ratio for free-fall distances is a classic NEET pattern not explicitly taught in US AP courses
From rest (u = 0) under constant acceleration a, the distances covered in successive equal time intervals are in the ratio 1:3:5:7:... (odd natural numbers). This follows directly from the nth-second formula with u = 0: sₙ = (a/2)(2n−1) → s₁:s₂:s₃:... = 1:3:5:... NEET tests this ratio pattern multiple times — recognising it immediately saves time. The ratio 1:2:3:4... (for cumulative distances) is also tested — total distance in 1st, 2nd, 3rd seconds from rest: s₁:s₁₊₂:s₁₊₂₊₃ = 1:4:9 (squares).
- Distances in successive equal time intervals (from rest, constant a): s₁:s₂:s₃:... = 1:3:5:7:... (odd numbers).
- Cumulative distances from rest after 1, 2, 3, ... equal intervals: S₁:S₂:S₃:... = 1:4:9:16:... (perfect squares).
- This ratio uniquely identifies uniform acceleration from rest in NEET graphs and match-the-following questions.
NEET-Style Practice Questions — Equation of Kinematics
4 NEET-style practice questionsPractice Problems — Equation of Kinematics
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Physics — Equation of Kinematics Revision Checklist
Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.
Frequently Asked Questions — Equation of Kinematics
Notes · Downloads · Revision · Important QuestionsWhat are the conditions for the equations of kinematics to be valid?
What does sₙ in the nth-second formula represent, and how is it different from total displacement?
Why do the kinematic equations give the displacement (not distance) in equation (2)?
What is the stopping distance formula and when is it used?
Why is it that for a body starting from rest under uniform acceleration, the distances in successive equal time intervals are in the ratio 1:3:5:7:...?
Which equation of kinematics should I use when time is not given and not required?
How do I solve a problem where two bodies start at different times and the question asks when they meet?
Can the kinematic equations be used for free-fall under gravity?
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