Kinematics describes motion without asking what causes it — no forces, just position, velocity and acceleration and how they connect. It is the chapter that teaches you to read a graph and extract real physical meaning from its slope and area, a skill every later mechanics chapter assumes you already have.
Everything in this chapter reduces to three equations of motion, but the marks are rarely lost on the equations themselves — they are lost on knowing which equation to reach for and on reading graphs correctly. A velocity-time graph's slope is acceleration; its area is displacement. A position-time graph's slope is velocity. Students who treat these as separate rules, rather than the same underlying idea applied twice, end up guessing in the exam instead of reasoning.
Projectile motion and relative velocity are this chapter's second half, and they are really just the same one-dimensional equations applied along two perpendicular axes at once. Once you see that, projectile problems stop being a separate topic to memorise.
Equations of motion and projectile formulae
| Situation | Formula |
|---|---|
| First equation of motion | v = u + at |
| Second equation of motion | s = ut + ½at² |
| Third equation of motion | v² = u² + 2as |
| Distance in nth second | sn = u + a(2n−1)/2 |
| Time of flight (projectile) | T = 2u sinθ / g |
| Maximum height (projectile) | H = u² sin²θ / 2g |
| Horizontal range (projectile) | R = u² sin2θ / g |
| Maximum range angle | θ = 45° |
| Relative velocity | vAB = vA − vB |
Topics covered
- Distance and displacement — the scalar-vector distinction that underlies every later definition in this chapter
- Speed and velocity, average and instantaneous — the difference between average values over an interval and the instantaneous value at one instant
- The three equations of motion — derivation from first principles using calculus and graphically, not just memorised as formulae
- Motion under gravity — applying the same three equations with a = −g, including the up-and-down symmetry of the motion
- Position-time and velocity-time graphs — reading slope and area correctly for uniform and non-uniform motion
- Projectile motion — splitting motion into independent horizontal and vertical components
- Horizontal projectile and projectile from a height — the two projectile variants that differ from the standard case
- Relative velocity in one and two dimensions — including relative velocity of rain with respect to a moving observer, a classic exam scenario
Why this chapter matters
In NEET and JEE, kinematics is one of the highest-yield chapters in the entire syllabus, because its formulae recur inside almost every other mechanics question — a Laws of Motion problem nearly always needs an equation of motion buried inside it. Graph-reading questions are also a NEET staple, and they are pure speed once the slope-and-area logic is automatic.
For Class 11 boards, expect at least one full numerical built on the equations of motion and one graph-based question in every paper. Projectile motion numericals are also a near-certain inclusion.
Mistakes students make in this chapter
- Using the equations of motion when acceleration isn't constant. All three equations assume uniform acceleration — they silently give a wrong answer otherwise, and exams sometimes test exactly this.
- Ignoring the sign of g. Taking upward as positive means g is negative throughout — students who switch signs partway through a projectile problem get the height and range wrong.
- Treating horizontal and vertical projectile motion as connected. They are completely independent — horizontal velocity never changes during projectile flight, and mixing the two axes is the most common projectile error.
- Confusing slope and area on a v-t graph. Slope gives acceleration, area gives displacement — swapping these under exam pressure is extremely common.
- Forgetting relative velocity is a vector subtraction. Direction matters as much as magnitude, especially in two-dimensional relative velocity problems like rain-and-observer questions.
Worked example: a full projectile calculation
- Resolve the initial velocity into components. This is the single step that makes every projectile problem work — the horizontal and vertical motions are then completely independent:uₓ = u cos30° = 20 × 0.866 = 17.32 m/su_y = u sin30° = 20 × 0.5 = 10 m/s
- Find the time of flight from the vertical motion alone. The ball rises, stops, and falls back symmetrically, so the total time is twice the time to reach the top:T = 2u_y/g = 2(10)/10 = 2 s
- Find the maximum height, again from the vertical motion only, using v² = u² − 2gh with v = 0 at the top:H = u_y²/2g = 100/20 = 5 m
- Find the range from the horizontal motion. There is no horizontal acceleration, so the horizontal velocity never changes and distance is simply speed times time:R = uₓ × T = 17.32 × 2 = 34.6 m
- Cross-check with the range formula to confirm the answer — the two routes must agree:R = u²sin2θ/g = 400 × sin60°/10 = 34.6 m ✓
- Answer the last part using that formula. Range depends on sin2θ, and sin2θ is unchanged if θ is replaced by (90° − θ), because sin(180° − x) = sin x:θ = 60° gives the same range (sin120° = sin60°)
What the notes contain
The PDF derives all three equations of motion from calculus and graphically, works through the full projectile motion derivation step by step, and includes labelled diagrams of every standard graph type with worked examples of extracting values from each. A dedicated section walks through relative velocity in two dimensions with the geometry drawn out.
How to use this: build the concept from these notes first, then do one quick NCERT pass before the exam for exact wording and diagram labels, and spend whatever time is left on previous year questions.
Questions
Are the three equations of motion derived or just given in this PDF?
Both. They are derived properly using calculus and shown graphically, so you understand where they come from rather than memorising them blind — which also means you'll recognise instantly when they don't apply.
Does this cover relative velocity of rain and a moving man?
Yes, with the full vector diagram worked through, since this exact scenario appears repeatedly in NEET and board papers.
What's the maximum range angle in projectile motion and why?
45°, because range is proportional to sin2θ, which is maximum when 2θ = 90°. The full reasoning is worked through in the PDF.
Is this enough for NEET on its own?
Use it to build the concept, then do a quick NCERT pass for exact wording before your exam, and spend the rest of your time on previous year questions.
All other chapters
Every chapter of Class 11 and Class 12 Physics, Chemistry and Biology — each with its own notes and PDF.