JEE Main Physics Kinematics 2027: Projectile Motion, Graphs & Relative Velocity
Kinematics is where JEE Physics is won or lost. Master motion graphs, relative velocity and projectiles with worked examples and the mistakes that cost marks.
Edurack
September 28, 2026
Two balls leave your hand at 30° and 60° with the same speed. Which one lands farther? If your first instinct is 'the steeper one goes higher, so farther', Kinematics still has something to teach you. This chapter is the foundation under Laws of Motion, Work-Energy and Rotation, so every hour here pays back many times.
In kinematics, the graph is the question. Read the slope and the area before you touch a formula.
Chapter at a Glance
| Snapshot | Detail |
|---|---|
| NTA unit | Unit 2 of 20 — Kinematics |
| Priority (trend-based) | High |
| Typical question style | Graph-based MCQs, projectile and river-boat numericals |
| Best first step | Read graphs first, then projectile and relative motion |
Priority reflects past-paper trends, not an official NTA weightage.
What the NTA Syllabus Covers
- Frame of reference, motion in a straight line, speed and velocity
- Uniform and non-uniform motion, average speed and instantaneous velocity
- Uniformly accelerated motion, velocity-time and position-time graphs, relative velocity
- Motion in a plane, projectile motion, uniform circular motion
Master These Topics
1. Straight-Line Motion and Graphs
For constant acceleration, three equations do the work: v = u + at, s = ut + ½at² and v² = u² + 2as. The distance covered in the nth second is u + a(2n − 1)/2.
Worked example: A ball is dropped from rest (g = 10 m/s²). Distance in the 3rd second = 0 + 10 × (2 × 3 − 1) / 2 = 25 m. For free fall from rest, distances in successive seconds are in the ratio 1 : 3 : 5 : 7.
Graph reading rules:
- Slope of a position-time graph is velocity.
- Slope of a velocity-time graph is acceleration.
- Area under a velocity-time graph is displacement. Area under an acceleration-time graph is change in velocity.
Trap: Displacement can be zero while distance is not. Area under a v-t graph counts area below the axis as negative for displacement, but positive for distance.
2. Projectile Motion: Two Independent Motions
A projectile is launched at speed u and angle θ. Horizontal velocity stays constant, while vertical motion is free fall.
- Time of flight:
T = 2u sinθ / g - Maximum height:
H = u² sin²θ / 2g - Range:
R = u² sin2θ / g
Worked example: u = 20 m/s at 30°, g = 10. Then T = 2 × 20 × 0.5 / 10 = 2 s. H = 400 × 0.25 / 20 = 5 m. R = 400 × sin60° / 10 ≈ 34.6 m.
That answers the opening puzzle: angles θ and (90° − θ) give the same range, so the 30° and 60° balls land at the same spot. Range is maximum at 45°. The 60° ball just spends longer in the air and climbs higher.
3. Relative Velocity and River-Boat Problems
Relative velocity of A with respect to B is v_A − v_B (as vectors). In river problems, the boat's velocity relative to ground is the vector sum of its velocity in still water and the river current.
Worked example: Boat speed in still water is 5 m/s, river flows at 3 m/s, width 100 m.
- Shortest time: point straight across. Time = 100 / 5 = 20 s. Drift downstream = 3 × 20 = 60 m.
- Shortest path (land directly opposite): aim upstream at angle θ with sinθ = 3/5. Ground speed = √(5² − 3²) = 4 m/s. Time = 100 / 4 = 25 s.
Notice the trade-off: minimum time and minimum drift cannot both be achieved.
4. Uniform Circular Motion
Speed is constant but velocity changes direction, so there is a centripetal acceleration a = v²/r = ω²r pointing to the centre. Angular speed ω = 2π/T, and v = ωr.
Common Traps to Avoid
- Using the range formula for a projectile that lands at a different height than it started.
- Confusing distance with displacement in graph area questions.
- Assuming minimum crossing time also gives minimum drift in river problems.
- Forgetting that acceleration in circular motion is non-zero even at constant speed.
60-Second Revision Sheet
v = u + at,s = ut + ½at²,v² = u² + 2as- Projectile:
T = 2u sinθ/g,H = u² sin²θ/2g,R = u² sin2θ/g - Same range for θ and 90° − θ; maximum range at 45°
- Centripetal acceleration
a = v²/r = ω²r
Your Study Plan
- Day 1: 1D motion and graph interpretation (20 problems).
- Day 2: projectile motion including inclined-plane projectiles.
- Day 3: relative velocity, river-boat and rain-man problems.
- Day 4: mixed timed test and error review.
Practice Kinematics Questions Free → (opens in a new tab)
Continue Your Physics Journey
- Previous chapter: Units & Measurements
- Next chapter: Laws of Motion
- All 20 JEE Main Physics chapters
- Complete JEE Main Syllabus 2027 guide
Frequently Asked Questions
Which Kinematics topic is asked most in JEE Main?
Projectile motion, graph interpretation and relative velocity appear most often, usually as one or two MCQs or a numerical.
Do I need calculus for Kinematics?
Basic differentiation and integration help with variable acceleration, for example when velocity is given as a function of time. The syllabus problems stay simple.