Motion and Force: Detailed Concepts

Introductory Overview

• Motion: Refers to the change in position of a body with respect to time.
• Rest and Motion: Relative concepts; whether a body is at rest or in motion depends on the reference point.
• Example: A bus driver and a passenger inside the bus—a static observer sees both in motion, but they appear stationary relative to each other.

Distance and Displacement

• Distance: (Scalar Quantity) Total path length covered by a body without considering direction.
• Displacement: (Vector Quantity) Straight-line distance between initial and final positions, with direction.
• Illustration: Walking different paths (route1, route2) between points A and B but displacement remains same if start and end points are same.

Speed and Velocity

• Speed: Distance covered per unit time; scalar quantity. Formula: Speed = Distance / Time.
• Velocity: Displacement per unit time; vector quantity. Formula: Velocity = Displacement / Time.

Types of Velocity

• Instantaneous Velocity: Velocity at a particular instant of time.
• Average Velocity: Total displacement divided by total time.
• Uniform Velocity: Velocity remains constant over time.
• Non-uniform Velocity: Velocity varies over time.

Acceleration

• Definition: Rate of change of velocity with respect to time. Formula: Acceleration = Δv / Δt.
• Positive Acceleration: Increase in velocity.
• Negative Acceleration (Deceleration): Decrease in velocity.
• Constant Acceleration: Acceleration is constant over time.
• Variable Acceleration: Acceleration changes over time.

Equations of Motion

1. v = u + at
2. s = ut + 0.5*at²
3. v² = u² + 2as*

• Applications: Solve for unknown variables (initial velocity, final velocity, distance covered, acceleration) using the equations.

Newton’s Laws of Motion

First Law (Law of Inertia)

• A body remains at rest or in uniform motion unless acted upon by an external force.
• Inertia: Resistance of a body to change its state of motion or rest.

Second Law

• Force is equal to the rate of change of momentum. Formula: F = ma where F is force, m is mass, a is acceleration.
• Momentum: Product of mass and velocity, a vector quantity. Formula: p = mv.

Third Law

• For every action, there is an equal and opposite reaction.
• Example: Kicking a ball; the ball exerts an equal and opposite force back.

Types of Collisions

• Elastic Collisions: Both momentum and kinetic energy are conserved.
• Inelastic Collisions: Momentum is conserved, but kinetic energy is not.

Concept of Terminal Velocity (Viscous Media)

• When a body falls through a viscous liquid, it eventually reaches a constant speed where the force of gravity is balanced by the viscous drag.
• Formula: Terminal Velocity ∝ radius²

Inclined Plane

• Used to elevate heavy objects with less force.
• Components of Weight: Parallel and perpendicular to the inclined plane.
• Trigonometric Relations: mg sin θ and mg cos θ used to resolve forces.
• Acceleration on Incline: a = g(sin θ − μ cos θ) where μ is the coefficient of friction.

Practical Application Problems

• Worked examples for understanding concepts related to forces acting on bodies, inclined planes, tension, and acceleration.

Study Tips

• Practice problems from various past papers and end-of-chapter questions to reinforce understanding and application of concepts.