Lecture on Motion Graphs

Overview

• Discussion of three types of motion graphs: Position, Velocity, and Acceleration with respect to Time.
• Exploration of relationships between these graphs based on their slopes.

Key Concepts

1. Position vs Time Graph

• Position is on the y-axis and time is on the x-axis.
• The slope of the position vs time graph represents velocity.

2. Velocity vs Time Graph

• The slope of the velocity vs time graph represents acceleration.

Velocity Concepts

Average Velocity

• Calculated as displacement over time.
• Represented by the slope of a straight line between two points on a position vs time graph.

Instantaneous Velocity

• Velocity at a specific point in time.
• Determined by the slope of a tangent line on the position vs time graph at a given instant.

Acceleration Concepts

Average Acceleration

• Similar relationship as velocity to position.

Instantaneous Acceleration

• Determined by the tangent to the curve on the velocity vs time graph.

Types of Motion

1. Zero Speed

• Position Time Graph: Horizontal line signifying no change in position.
• Velocity Time Graph: Horizontal line at zero; velocity is constant at zero.
• Acceleration: Horizontal line at zero, indicating no acceleration.

2. Constant Speed

• Position Time Graph: Straight diagonal line; slope represents constant velocity.
• Velocity Time Graph: Horizontal line at a non-zero value, indicating constant velocity.
• Acceleration: Horizontal line at zero.

3. Constant Acceleration

• Velocity Time Graph: Diagonal line with a positive constant slope.
• Position Time Graph: Curved line, slope increasing as velocity increases.

4. Deceleration (Negative Acceleration)

• Velocity Time Graph: Diagonal line with a negative slope, starting higher up on the y-axis.
• Position Time Graph: Curved line, slope decreases over time until horizontal.

Applications

• These graphs are applicable to any motion scenario with described parameters.
• Example given: A block sliding down a ramp under constant acceleration will have the same graph characteristics as a car accelerating constantly.