🧠 Introduction
Kinematics is the branch of mechanics that deals with the motion of objects without considering the causes of motion (i.e., forces). It includes concepts of displacement, velocity, acceleration, and equations of motion.
⚙️ Motion
Definition: A body is said to be in motion if it changes its position with respect to time.
Types of Motion:
- Translatory Motion – All parts of the body move the same distance.
- Rotational Motion – Body rotates about an axis.
- Oscillatory Motion – To and fro motion (e.g., pendulum).
📏 Basic Terms in Kinematics
| Term | Symbol | SI Unit | Definition |
|---|---|---|---|
| Distance | s | meter (m) | Total path length travelled |
| Displacement | meter (m) | Change in position (vector) | |
| Speed | v | m/s | Rate of change of distance |
| Velocity | m/s | Rate of change of displacement | |
| Acceleration | m/s | Rate of change of velocity |
Scalar vs Vector Quantities
- Scalars: Only magnitude (e.g., speed, distance).
- Vectors: Magnitude + direction (e.g., velocity, displacement).
🧾 Types of Motion
1. Uniform Motion
- Equal displacements in equal intervals of time.
- Velocity is constant.
2. Non-Uniform Motion
- Unequal displacements in equal intervals.
- Velocity is not constant.
3. Uniformly Accelerated Motion
- Acceleration is constant.
- Applies in many NEET problems (free fall, projectile).
🧮 Equations of Motion (For Uniform Acceleration)
Where:
- = Initial velocity
- = Final velocity
- = Acceleration
- = Displacement
- = Time
⏱️ Graphical Representation
1. Displacement-Time Graph
- Slope = velocity
2. Velocity-Time Graph
- Slope = acceleration
- Area under curve = displacement
3. Acceleration-Time Graph
- Area under curve = change in velocity
🧲 Relative Velocity
Definition: The velocity of one object with respect to another.
Case 1: Objects moving in same direction
Case 2: Opposite directions
🛰️ Motion in 2D (Projectile Motion)
- Two independent motions:
- Horizontal (uniform)
- Vertical (accelerated)
Important Formulas
- Time of flight (T):
- Maximum height (H):
- Horizontal Range (R):
Where = initial velocity, = angle of projection
🎯 Problem Solving Strategy
- Identify known and unknown quantities.
- Use proper signs (+/-) with direction.
- Choose the correct kinematic formula.
- Draw motion graphs if needed.
- Use dimensional analysis for verification.
📘 Example Problems
- A car accelerates from rest at 2 m/s. Find its speed after 5 s.
- A stone is thrown upward at 20 m/s. Find time to reach max height.
- A train travels 100 m in 4 s with uniform acceleration. Starting from rest, find the acceleration.
📚 Revision Checklist
🔁 Common Mistakes to Avoid
- Mixing up displacement and distance
- Ignoring direction (sign convention)
- Using wrong formula without checking conditions
- Confusing velocity with speed