Lecture Notes: Velocity-Time Graphs

Overview

• Focus: Understanding velocity-time graphs, which show how an object's velocity changes over time.
• Comparison: Velocity-time graphs are similar to distance-time graphs but distinct. It's crucial to identify the graph type correctly in exams.

Velocity-Time Graph Characteristics

• Axes:
  • Y-axis: Velocity
  • X-axis: Time
• Gradient: The gradient of the curve represents acceleration.
  • Formula: Change in velocity / Change in time = Acceleration

Types of Gradients

• Constant Positive Gradient: Indicates constant acceleration.
• Constant Negative Gradient: Indicates constant deceleration.
• Flat Sections: Gradient is 0, indicating constant velocity.
  • Example: If velocity is 3 meters/second in a flat section, it remains constant.
• Increasing Gradient: Curve gets steeper, indicating increasing acceleration.

Calculating Acceleration and Velocity

• Use the formula for acceleration to find values during constant acceleration/deceleration.
  • Example: Change in velocity = 3 m/s, change in time = 2 s, acceleration = 1.5 m/s².
• Identifying constant velocity by checking the velocity on the y-axis for flat sections.

Finding Distance Traveled

• Area Under the Curve: Represents the distance traveled.
  • Split the area into simple shapes (e.g., triangles and rectangles) for easier calculation.
  • Example Calculation:
    • Area of triangle: 1/2 * base * height = 3 meters.
    • Area of rectangle: base * height = 6 meters.
    • Total distance in 4 seconds: 9 meters.
• Note: Area under velocity-time graphs results in distance (meters), not area (meters²).*

Curved Parts of the Graph

• Estimation Method: Counting squares under the curve with a given grid.
  • Example: Each square = 1 meter of distance.
  • Count full and partial squares to estimate total area.

Conclusion

• Understanding velocity-time graphs requires careful examination of gradients, flat sections, and areas under curves.
• Practice identifying graph types to avoid confusion on exams.

• Reminder: Share this knowledge with peers and educators if helpful.