Position Time Graph and Average Velocity

Introduction

• Understanding position-time graph.
• Calculating average velocity between different time intervals.

Key Concepts

• Average Velocity: Defined as ( \frac{x_f - x_i}{t_f - t_i} )
  • ( x_f ): Final position
  • ( x_i ): Initial position
  • ( t_f ): Final time
  • ( t_i ): Initial time

Calculation Examples

Interval 0 to 2 Seconds

• Position at t=2s: 5
• Position at t=0s: 0
• Average velocity: ( \frac{5 - 0}{2 - 0} = 2.5 ) m/s (positive direction)
  • Positive slope -> Moving along positive x-axis

Interval 2 to 3 Seconds

• Final Position: t=3s, position=3
• Initial Position: t=2s, position=5
• Average velocity: ( \frac{3 - 5}{3 - 2} = -2 ) m/s
  • Negative slope -> Moving in the opposite direction

Interval 3 to 5 Seconds

• Position remains constant at 3
• Average velocity: 0 m/s (particle at rest)

Interval 5 to 6 Seconds

• Final Position: t=6s, position=0
• Initial Position: t=5s, position=3
• Average velocity: ( \frac{0 - 3}{6 - 5} = -3 ) m/s
  • More downhill -> Higher negative average velocity

Interval 7 to 8 Seconds

• Final Position: t=8s, position=0
• Initial Position: t=7s, position=-3
• Average velocity: ( \frac{0 - (-3)}{8 - 7} = 3 ) m/s
  • Positive slope -> Moving in the forward direction

Interval 0 to 5 Seconds

• Final Position: t=5s, position=3
• Initial Position: t=0s, position=0
• Average velocity: ( \frac{3 - 0}{5 - 0} = 0.6 ) m/s
  • Moving along positive x-axis

Summary of Motion

• Moved forward 5 meters in first interval.
• Moved backward from 5m to 3m.
• Stayed at rest from 3s to 5s.
• Moved from 3m to -3m.
• Returned to origin from -3m.

Conclusion

• Described how to find average velocity from a position-time graph.
• Next steps: Plotting velocity-time graph and finding acceleration-time graph from velocity-time graph.

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