JEE Mains 2026 Revision Capsule – Kinematics (1D, 2D, Projectile, Relative Motion)
Kinematics describes motion using algebra and geometry. No forces, no energy—just pure positional logic. This capsule focuses only on what JEE Mains actually asks and nothing extra.
1. Core Ideas Students Must Master
Graph interpretation, projectile motion, relative velocity (rain–man, boat–river), and vector components are the backbone of this chapter.
2. Essential Formulas (Zero Fluff)
1D Motion
\( v = u + at \)
\( s = ut + \frac{1}{2}at^2 \)
\( v^2 = u^2 + 2as \)
Average velocity (constant acceleration): \( v_{avg} = \frac{u+v}{2} \)
Projectile Motion
Horizontal: \( x = (u\cos\theta)t \)
Vertical: \( y = (u\sin\theta)t - \frac{1}{2}gt^2 \)
Time of flight: \( T = \frac{2u\sin\theta}{g} \)
Range: \( R = \frac{u^2\sin2\theta}{g} \)
Maximum height: \( H = \frac{u^2\sin^2\theta}{2g} \)
Velocity Vector at Any Time
\( \vec{v} = (u\cos\theta)\hat{i} + (u\sin\theta - gt)\hat{j} \)
3. Relative Motion (Boat–River, Rain–Man)
Relative velocity formula: \( \vec{v}_{AB} = \vec{v}_A - \vec{v}_B \)
Drift of boat: (river speed × time)
Angle of apparent rain: \( \tan\alpha = \frac{\text{horizontal}}{\text{vertical}} \)
4. Motion Graphs (High-Scoring)
Position–Time (x–t): slope = velocity
Velocity–Time (v–t): slope = acceleration, area = displacement
Acceleration–Time (a–t): area = change in velocity
Curved line → variable acceleration, kink → sudden velocity change
5. PYQ Patterns to Keep in Fingertips
- Use symmetry when projectile lands at same height.
- Chasing/meeting problems → use relative velocity.
- Boat crosses shortest time → go perpendicular to river.
- Graphs crossing time axis → velocity changes sign.
Quick Revision Summary
Kinematics is geometry wearing a physics hat—treat velocity as slope, area as displacement, and vectors as honest arrows.
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