Quick Summary
Kinematics studies motion without considering its cause. This chapter covers scalar and vector quantities, motion in one and two dimensions, equations of motion, projectile motion, and relative velocity. It is a high-weightage chapter in NEET and JEE.
Key Concepts
- Kinematics: Description of motion (what, not why)
- Distance: Total path length (scalar)
- Displacement: Shortest path from start to end (vector)
- Speed: Distance per unit time (scalar)
- Velocity: Displacement per unit time (vector)
- Acceleration: Rate of change of velocity (vector)
Equations of Motion (Uniform Acceleration)
| Equation | Symbols |
|---|---|
| v = u + at | u = initial velocity, v = final velocity |
| s = ut + ½at² | s = displacement |
| v² = u² + 2as | a = acceleration, t = time |
| sₙ = u + a(2n−1)/2 | sₙ = displacement in nth second |
Conditions: These equations hold only when acceleration is constant and motion is in a straight line.
Motion Under Gravity
When a body is thrown vertically upward:
- At maximum height, v = 0
- Time to reach max height: t = u/g
- Maximum height: H = u²/2g
- Time to return to ground: T = 2u/g
When a body is dropped (u = 0):
- v = gt, h = ½gt², v² = 2gh
Projectile Motion
A body projected at angle θ with initial velocity u.
- Horizontal velocity: uₓ = u cosθ (constant)
- Vertical velocity at t: uᵧ = u sinθ − gt
- Time of flight: T = 2u sinθ / g
- Maximum height: H = u² sin²θ / 2g
- Horizontal range: R = u² sin2θ / g
- Maximum range occurs at θ = 45°: R_max = u²/g
Key Point
The path of projectile is a parabola. At maximum height, vertical component of velocity = 0, horizontal component = u cosθ.
Relative Velocity
If A moves with velocity v_A and B with v_B:
Velocity of A relative to B = v_A − v_B
Rain and Man Problem
If rain falls vertically with velocity v_r and man walks with velocity v_m, the man must tilt his umbrella at angle θ = tan⁻¹(v_m / v_r) in the forward direction.
Vectors — Quick Revision
- Addition: Triangle law, parallelogram law
- Dot product: A · B = AB cosθ (scalar)
- Cross product: |A × B| = AB sinθ (vector, direction by right-hand rule)
- Unit vector: magnitude = 1, shows direction only
Important Questions
One Mark
- Define displacement. How is it different from distance?
- What is the condition for maximum horizontal range in projectile motion?
- State the equations of motion (all three).
- Define uniform velocity.
- At what angle should a projectile be thrown for maximum range?
Short Answer (3 marks)
- Derive the expression for the range of a projectile on a horizontal plane.
- A car starts from rest and attains a velocity of 20 m/s in 10 s. Find its acceleration and distance covered.
- Explain the difference between average speed and instantaneous speed.
Long Answer (5 marks)
- Derive the three equations of motion using calculus (or graphically for lower level). Apply them to a numerical problem involving free fall.
- Explain projectile motion. Derive expressions for time of flight, maximum height, and horizontal range. Show that the trajectory is parabolic.
Common Mistakes
- Using equations of motion when acceleration is NOT uniform.
- Forgetting that horizontal velocity in projectile motion remains constant — only vertical velocity changes.
- Mixing up distance and displacement in multi-step problems.
Board Exam Tips
- Draw a clear velocity-time graph to visualise problems — it helps derive answers quickly.
- Projectile motion derivations (range, height, time of flight) appear as 5-mark questions.
- Numerical problems carry significant marks — practise at least 10 problems from each type.
- NEET: Master projectile motion and relative velocity — 1–2 questions appear every year.