Distance-Time Graphs

Introduction

• Distance-time graphs visualize how far something has traveled over a period of time.
• They help in understanding different parts of a journey.

Key Concepts

Gradient and Speed

• Gradient of the line at any point on a distance-time graph indicates the speed of the object.
  • Formula: Gradient = Change in Distance / Change in Time = Speed
• Straight Line:
  • Represents constant speed.
  • Example: Traveling 20 meters in 2 seconds results in a speed of 10 meters per second (20/2).
• Flat Line:
  • Indicates the object is stationary.
  • Gradient and speed are zero.
• Curved Line:
  • Shows changing speed; acceleration or deceleration.
  • Steeper slope indicates increasing speed (acceleration).
  • Decreasing slope shows decreasing speed (deceleration).

Calculating Speed

• Constant Speed (Straight Line):
  • Calculate speed by dividing the total change in distance by the total change in time.
• Changing Speed (Curved Line):
  • Draw a tangent at the specific point on the curve.
  • Tangent: A straight line that has the same gradient as the curve at that point.
  • Calculate the gradient of the tangent by selecting two points on the tangent.
  • Example: If the change in distance is 12 meters and the change in time is 3 seconds, speed = 4 meters per second (12/3).

Summary

• Straight Lines: Constant speeds
• Flat Lines: Object is stationary
• Curved Lines: Changing speeds
• Finding Speed at a Point:
  • For straight lines, use the gradient formula.
  • For curves, draw a tangent and calculate its gradient.

Conclusion

• Distance-time graphs are crucial for understanding motion.
• Practice by determining speeds from various sections of the graph.

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