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Velocity-Time Graph Area Calculator

Run the Velocity-Time Area Calculator MicroSim Fullscreen

Description

This MicroSim demonstrates the fundamental relationship that the area under a velocity-time curve equals displacement. Students can select different motion scenarios and adjust the time interval to see how the shaded area corresponds to the change in position.

Key Concepts

  • Positive area (above the time axis) = positive displacement (motion in + direction)
  • Negative area (below the time axis) = negative displacement (motion in - direction)
  • Net displacement = positive area - negative area
  • For rectangles: Area = velocity × time
  • For triangles: Area = ½ × base × height

Scenarios

  1. Constant Positive Velocity: Rectangle - simple v × t
  2. Constant Negative Velocity: Rectangle below axis - negative displacement
  3. Acceleration from Rest: Triangle - ½ × t × v
  4. Deceleration to Stop: Trapezoid - average velocity × time
  5. Speed Up Then Slow Down: Two triangles forming a peak
  6. Direction Reversal: Area both above and below axis

Learning Objectives

After using this MicroSim, students should be able to:

  1. Calculate displacement from the area under a v-t curve
  2. Distinguish between positive and negative areas
  3. Apply geometric formulas (rectangle, triangle, trapezoid) for area calculation
  4. Understand that net displacement accounts for direction changes