Unit 2.5 – Graphical Representation of Motion

1. Displacement-Time Graph

• Definition: A graph that plots displacement ($s$) on the y-axis and time ($t$) on the x-axis.
• Interpretation:
  • Slope of the graph: Represents velocity.
    • Positive slope → Positive velocity (motion in the positive direction).
    • Negative slope → Negative velocity (motion in the negative direction).
    • Zero slope → Object is at rest.
  • Shape of the graph:
    • Straight line → Uniform velocity.
    • Curved line → Variable velocity.

• A horizontal line indicates the object is stationary (no displacement over time).
• A straight line with a positive slope indicates uniform motion in the positive direction.

2. Velocity-Time Graph

• Definition: A graph that plots velocity ($v$) on the y-axis and time ($t$) on the x-axis.
• Interpretation:
  • Slope of the graph: Represents acceleration.
    • Positive slope → Positive acceleration.
    • Negative slope → Negative acceleration (deceleration).
    • Zero slope → Constant velocity (no acceleration).
  • Area under the graph: Represents displacement.
    • Area above the x-axis → Positive displacement.
    • Area below the x-axis → Negative displacement.

• A horizontal line indicates constant velocity (zero acceleration).
• A straight line with a positive slope indicates uniformly accelerated motion.

3. Acceleration-Time Graph

• Definition: A graph that plots acceleration ($a$) on the y-axis and time ($t$) on the x-axis.
• Interpretation:
  • Shape of the graph:
    • Horizontal line → Constant acceleration.
    • Zero line → No acceleration (constant velocity).
    • Curved line → Variable acceleration.
  • Area under the graph: Represents change in velocity.

• A horizontal line at $a=0$ indicates no acceleration (object moves with constant velocity).
• A positive horizontal line indicates constant positive acceleration.

Quick Revision Points

• Displacement-Time Graph:
  • Slope = Velocity.
  • Straight line = Uniform velocity; Curved line = Variable velocity.
• Velocity-Time Graph:
  • Slope = Acceleration.
  • Area under the graph = Displacement.
• Acceleration-Time Graph:
  • Area under the graph = Change in velocity.
  • Horizontal line = Constant acceleration.

Previous Year Questions and Answers

• A straight line passing through the origin indicates uniform velocity.
• The slope of the graph gives the magnitude of the velocity.

• A horizontal line parallel to the time axis indicates constant velocity.
• The slope of the graph is zero, meaning there is no acceleration.

• A straight line with a positive slope indicates uniformly accelerated motion.
• The slope of the graph gives the magnitude of the acceleration.

• The area under a velocity-time graph gives displacement.
• If the area is above the time axis, it represents positive displacement; if below, it represents negative displacement.

• A horizontal line at $a=0$ indicates no acceleration.
• The object is moving with constant velocity.

Expected Questions

• A curved displacement-time graph indicates variable velocity.
• The slope of the graph changes with time, indicating changing velocity.

• A straight line with a negative slope indicates uniformly decelerated motion.
• The slope of the graph gives the magnitude of the deceleration.

• The area under an acceleration-time graph gives the change in velocity.

• A horizontal displacement-time graph indicates that the object is stationary (no motion).

• A curved velocity-time graph indicates variable acceleration.
• The slope of the graph changes with time, indicating changing acceleration.