Motion and Rest

Fundamental Concepts

Motion

Motion is the change in position of an object over time.

An object is in motion if its position changes relative to a reference frame.

Characteristics of motion:

• Requires a reference frame (the point from which we measure)
• Involves change in position over time
• Can be described using distance and displacement
• Can be measured with speed or velocity

Rest

Rest is the state in which an object's position does not change relative to a reference frame.

An object is at rest if its position remains constant relative to a reference frame.

Important: Both motion and rest are relative concepts - they depend on the chosen reference frame.

Reference Frames

A reference frame is a coordinate system used as a basis for measuring the position, velocity, and other properties of objects.

Importance of Reference Frames

The same object can be in motion in one reference frame and at rest in another.

Ejemplo: A person sitting in a moving train is at rest relative to the train, but in motion relative to the ground (or a person standing outside).

Ejemplo: The Earth appears stationary to us because we use it as our reference frame. However, the Earth is moving around the Sun, which is moving around the galaxy, which is moving in the universe.

Types of Reference Frames

Inertial Reference Frame:

• A reference frame in which Newton's laws of motion apply
• No acceleration of the reference frame itself
• Example: ground, stationary observer

Non-inertial Reference Frame:

• A reference frame that is itself accelerating
• Newton's laws must be modified
• Example: accelerating car, rotating platform

Distance vs Displacement

These are two important but different concepts in describing motion.

Distance (d)

Distance is the total length of the path traveled by an object, regardless of direction. Characteristics:

• Scalar quantity (has magnitude only, no direction)
• Always positive
• Depends on the path taken
• Cannot be less than displacement
• Symbol: d

> [Ejemplo: If you walk from point A to point B (5 m), then back to point A, then to point C (3 m), the total distance traveled is: > d = 5 m + 5 m + 3 m = 13 m]

Displacement (Δx or s)

Displacement is the straight-line distance and direction from the initial position to the final position. Characteristics:

• Vector quantity (has magnitude and direction)
• Can be positive, negative, or zero
• Depends only on initial and final positions
• Takes the shortest path conceptually
• Symbol: Δx, s, or r

> [Ejemplo: If you walk from point A to point B (5 m east), then back to point A, then to point C (3 m west): > > Starting position: x_i = 0 > Final position: x_f = 3 m west = -3 m > > Displacement = -3 m - 0 = -3 m (3 m to the west) > > But distance traveled = 5 + 5 + 3 = 13 m]

Comparison Table

Describing Motion in One Dimension

Position (x)

Position is the location of an object relative to a reference point (origin).

• Symbol: x or x(t) if it changes with time
• Can be positive or negative
• Measured from origin (usually x = 0)

Time Interval (Δt)

Time interval is the elapsed time between two events.

Where:

• t_f = final time
• t_i = initial time

> [Ejemplo: If an event starts at t = 2 s and ends at t = 5 s: > Δt = 5 s - 2 s = 3 s]

Relative Motion

Relative motion is the motion of an object as observed from a particular reference frame.

Galilean Relativity

In classical mechanics (non-relativistic speeds), velocities add directly:

Where:

• v_AB = velocity of A relative to B
• v_AC = velocity of A relative to C
• v_CB = velocity of C relative to B

> [Ejemplo: > - A train moves at 20 m/s relative to the ground > - A person walks at 2 m/s relative to the train in the same direction > - The person's velocity relative to the ground = 20 + 2 = 22 m/s > > But if the person walks opposite to the train's motion: > - The person's velocity relative to the ground = 20 - 2 = 18 m/s]

Mathematical Description of Motion

For motion in one dimension, we can describe an object's position as a function of time: x(t)

Examples of Motion Functions

Stationary object: (Position doesn't change - object is at rest) Object moving at constant velocity: (Position = 2 m + 3 m/s × time) Object accelerating uniformly: (More complex motion with acceleration)

Key Takeaways

1. Motion and rest are relative - they depend on the reference frame chosen
2. Distance measures the path length - always positive, scalar
3. Displacement measures the straight-line change in position - can be positive/negative, vector
4. Reference frames are essential for describing motion accurately
5. Position, distance, and displacement are fundamental to understanding motion
6. Relative motion explains how different observers can measure different velocities for the same object