Sketch, plot and interpret distance-time and speed-time graphs

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IGCSE Physics - 1.2 Motion: Distance-Time and Speed-Time Graphs

IGCSE Physics 0625

Topic: 1.2 Motion

Objective: Sketch, plot and interpret distance-time and speed-time graphs

This section focuses on understanding and interpreting graphs that show how the distance of an object changes with time (distance-time graphs) and how its speed changes with time (speed-time graphs). These graphs are crucial for analyzing motion and determining various physical quantities.

1. Distance-Time Graphs

A distance-time graph plots the distance an object has traveled against the time elapsed. The horizontal axis represents time, and the vertical axis represents distance.

Typical Distance-Time Graph Shapes

  • Rest: A horizontal line at a constant distance. This indicates the object is not moving.
  • Uniform Speed: A straight line with a constant positive gradient. This indicates the object is moving at a constant speed.
  • Uniform Acceleration: A straight line with a positive constant gradient. This indicates the object is moving with constant positive acceleration.
  • Uniform Deceleration: A straight line with a negative constant gradient. This indicates the object is moving with constant negative acceleration.
  • Variable Speed: A curved line. This indicates the object's speed is changing over time.

Interpreting Distance-Time Graphs

  1. Speed: The gradient of the distance-time graph represents the speed of the object. A steeper gradient means a higher speed.
  2. Acceleration/Deceleration: A positive gradient indicates acceleration, and a negative gradient indicates deceleration.
  3. Displacement: The vertical distance from the starting point to the position of the object at a given time.
  4. Time taken for a certain distance: Read the time value corresponding to the given distance on the graph.
Graph Shape Speed Acceleration/Deceleration
Horizontal line 0 0
Straight line (positive gradient) Constant Positive
Straight line (negative gradient) Constant Negative
Curved line Variable Variable

2. Speed-Time Graphs

A speed-time graph plots the speed of an object against the time elapsed. The horizontal axis represents time, and the vertical axis represents speed.

Typical Speed-Time Graph Shapes

  • Constant Speed: A horizontal line at a constant speed.
  • Uniform Acceleration: A straight line with a positive constant gradient.
  • Uniform Deceleration: A straight line with a negative constant gradient.

Interpreting Speed-Time Graphs

  1. Acceleration/Deceleration: A positive gradient indicates acceleration, and a negative gradient indicates deceleration. The magnitude of the gradient indicates the rate of change of speed.
  2. Initial Speed: The speed at the starting point of the graph (time = 0).
  3. Final Speed: The speed at the end point of the graph.
  4. Time taken to reach a certain speed: Read the time value corresponding to the given speed on the graph.
  5. Distance covered during a certain time interval: The area under the speed-time graph represents the distance covered.

The area under a speed-time graph can be calculated as the area of a trapezium if the speed changes linearly with time.

Suggested diagram: A speed-time graph showing uniform acceleration.

Practice Questions

  1. A distance-time graph shows a straight line with a positive gradient. What can you conclude about the object's motion?
  2. A speed-time graph shows a straight line with a positive gradient. What can you conclude about the object's motion?
  3. Explain what the area under a speed-time graph represents.