Graphical Analysis of Acceleration

Key Concepts

• Average Acceleration: The change in velocity over a time interval.
• Instantaneous Acceleration: The acceleration of an object at a specific point in time.

Graph Description

• The graph has:
  • Time Axis: Horizontal axis representing time.
  • Velocity Axis: Vertical axis representing velocity.
• Velocity Equation: Describes how velocity changes over time.

Points of Interest

• Initial Time (TI): Starting point of observation.
• Initial Velocity (VI): Velocity at the starting time.
• Final Time (TF): Ending point of observation.
• Final Velocity (VF): Velocity at the ending time.

Finding Average Acceleration

• Connect Initial and Final Points: Draw a line connecting the initial (TI, VI) and final (TF, VF) points on the graph.
• Slope Calculation: The slope of this line represents the average acceleration.
  • Formula: Average acceleration = ( \frac{VF - VI}{TF - TI} )

Finding Instantaneous Acceleration

• Tangent Line: Draw a tangent at the point of interest on the curve.
• Slope of Tangent: The slope of the tangent line gives the instantaneous acceleration.

Summary

• To find average acceleration, measure the slope of the line connecting initial and final points.
• To find instantaneous acceleration, measure the slope of the tangent line at a specific point on the curve.