Phys3011- Day 2

Day 2,3 Motion along Straight Line (Chapter 2)

Learning Outcomes: After studying this section, you will be able to:
- Recognize motion of an object as if it were a point-like particle if all parts move in the same direction and rate.
- Identify a particle's position on a scaled axis (x-axis).
- Understand the relationship between displacement and initial/final positions.
- Calculate average velocity from displacement and time intervals.
- Analyze average speed concerning total distance and time interval.
- Read graphs of particle position and determine average velocity between specific times.

Motion is confined to a straight line (vertical, horizontal, slanted).
Forces causing motion will be addressed in Chapter 5; focus here is solely on motion itself and changes.
- Discussion includes whether the object speeds up, slows down, stops, or reverses.
The object is treated as a particle if every part moves in the same direction and rate.

In modeling motion, treat the object's mass as concentrated at a single point (particle).
This simplifies representations in motion diagrams to single dots instead of the entire object.

Position: Identifies the location of an object in relation to a reference point (origin).
- Utilizes coordinates marked on an axis, e.g., x (m).

Displacement: Change in position, represented as Δx = x2 - x1.
- Defined as final position minus initial position.
- Can be positive or negative depending on direction.
- Example: Moving from x_initial = 5 m to x_final = 12 m results in a displacement of Δx = 12 m - 5 m = 7 m (positive direction).

Example: Maria starts at position x = 23 m and undergoes a displacement Δx = -50 m.
- Final Position Calculation: x_final = 23 m - 50 m = -27 m.

Displacement is a vector quantity indicating both magnitude and direction.
- Positive sign (+) indicates direction (east/north), negative sign (−) indicates opposite direction (west/south).
- Example: A displacement of Δx = -4 m has a magnitude of 4 m.

Determine which displacements shown in scenarios are positive or negative based on their direction relative to the x-axis.

Average Velocity (v_avg): Describes how fast an object is moving and is a vector quantity.
- Formula: v_avg = Δx / Δt = (x2 - x1) / (t2 - t1) where units are m/s.

Average Speed: Total distance covered divided by the time interval.
- Average speed is always positive (no direction involved).
- Example: Moving from x = 3 m to x = -3 m in 2 seconds results in average velocity = -3 m/s; average speed = 3 m/s.

Position vs. Time Graph: Visual representation of an object's position against time.

Key Findings:
- Linear position graphs indicate uniform motion (constant velocity).
- The slope of the position graph corresponds to average velocity.

Instantaneous Velocity: Velocity at a specific moment derived from average velocity by minimizing time intervals.
Related to the slope of the position-time graph at that instant.

Average Velocity: (v_x = \Delta x / \Delta t)
Instantaneous Velocity: Rate of change of position, mathematically (v_x = dx/dt)

Instantaneous Speed: Absolute value of instantaneous velocity (always positive).
- Example: A velocity of +5 m/s and -5 m/s reflects the same speed of 5 m/s.

Understanding motion involves calculating displacement, velocity, and recognizing vector nature.
The chapter emphasizes conceptualizing motion along a straight line, distinguishing between average and instantaneous measures.