Phys3011- Day 2

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

2-1 Position, Displacement, and Average Velocity

• 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.

Four Basic Types of Motion

• Motion along a Straight Line

• Linear Motion

• Circular Motion

• Projectile Motion

• Rotational Motion

Overall Focus of Chapter 2

• Solve problems specifically about motion along a straight line.

General Properties of Motion

• 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.

The Particle Model

• 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 and Displacement

Position

• 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

• 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).

Further Practice - Example Calculations

• 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.

Vector Nature of Displacement

• 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.

Questions on Displacement

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

Average Velocity

Definition

• 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

Definition and Example

• 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 Graphs

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

Understanding Position vs. Time Graphs

• Key Findings:

  • Linear position graphs indicate uniform motion (constant velocity).

  • The slope of the position graph corresponds to average velocity.

Instantaneous Velocity and Speed

Instantaneous 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 and Instantaneous Velocity Comparison

• Average Velocity: (v_x = \Delta x / \Delta t)

• Instantaneous Velocity: Rate of change of position, mathematically (v_x = dx/dt)

Instantaneous Speed

• 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.

Summary and Key Takeaways

• 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.