Kinematics for NEET Physics
Master motion in one and two dimensions — equations, graphs, projectiles & relative velocity, explained for NEET aspirants.
🔍 Detailed concept explanation
📏 1. Scalars and vectors
Scalars: magnitude only (mass, speed, distance). Vectors: magnitude + direction (displacement, velocity, acceleration). Vector addition: triangle/parallelogram law, component method.
📐 2. Motion in a straight line
Distance vs displacement: Distance is path length (scalar), displacement is shortest length (vector). Speed = distance/time, velocity = displacement/time. Acceleration = rate of change of velocity.
📈 3. Equations of motion (constant acceleration)
v = u + at, s = ut + ½at², v² = u² + 2as, sn = u + a(2n‑1)/2 (distance in nth second). For free fall: a = g = 9.8 m/s² downward.
📊 4. Graphs in kinematics
Slope of position–time = velocity; slope of velocity–time = acceleration; area under velocity–time = displacement; area under acceleration–time = change in velocity.
🎯 5. Projectile motion
Two‑dimensional motion under gravity. Horizontal velocity constant, vertical acceleration = –g. Time of flight T = 2u sinθ/g, maximum height H = u² sin²θ/(2g), range R = u² sin2θ/g.
🚀 6. Relative velocity
Velocity of A relative to B: vAB = vA – vB. For two dimensions, vector subtraction. Used in river‑boat problems, rain‑man problems.
📋 Complete formula sheet
s = ut + ½at²
v² = u² + 2as
(sign depends on direction)
H = u² sin²θ/(2g)
R = u² sin2θ/g
| Quantity | Symbol / Formula |
|---|---|
| Displacement (nth second) | sn = u + (a/2)(2n‑1) |
| Average velocity (const a) | (u + v)/2 |
| Range on inclined plane | R = (2u² sin(θ-α) cosθ)/(g cos²α) |
✏️ Solved NEET-level examples
Example 1 (1D motion)
A car accelerates from rest at 2 m/s² for 5 s, then moves with constant velocity for 10 s, and then decelerates at 4 m/s² to stop. Find total distance.
Total distance = 25 + 100 + 12.5 = 137.5 m.
Example 2 (Projectile)
A projectile is thrown with speed 20 m/s at angle 30° from horizontal. Find its time of flight, maximum height, and range. (g = 10 m/s²)
Example 3 (Relative velocity)
Rain is falling vertically at 5 m/s. A woman runs horizontally at 2 m/s. Find the velocity of rain relative to her.
📈 Important graphs & key points
- s–t graph : slope → velocity; parabola for const acceleration
- v–t graph : slope → acceleration; area → displacement
- a–t graph : area → change in velocity
- Projectile path : parabola, symmetric about highest point
⭐ For uniform motion, s–t is straight line; for uniform acceleration, v–t is straight line.
⚡ Quick revision box
⚠️ Common mistakes to avoid
- Confusing distance and displacement (scalar vs vector)
- Using equations of motion for non‑uniform acceleration
- Sign errors in free fall (taking g = +9.8 upward instead of downward)
- In projectile, mixing up sin and cos components
- Forgetting that relative velocity is vector subtraction
- Not converting units (km/h to m/s: multiply by 5/18)
🧠 Exam strategy tips
- Draw clear diagrams with coordinate axes.
- For multi‑part motion, treat each segment separately.
- In projectile, resolve initial velocity into components.
- Memorize standard formulas (T, H, R) to save time.
- Practice graph‑based questions – they appear frequently.
❓ Frequently asked questions
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