Motion Graphs - Displacement-Time Graph

Introduction

• Displacement-time graphs are graphical representations used to describe the motion of an object over time.
• These graphs provide valuable insights into an object's velocity and displacement as it moves.

Gradient and Velocity

• The gradient (slope) of a displacement-time graph at a specific time is a crucial parameter.
• It tells us about the object's velocity at that particular moment.

Calculating Velocity

• To calculate the velocity of an object using a displacement-time graph, use the following formula:
  • Velocity (v) = Change in Displacement (Δs) / Change in Time (Δt)
  • Δs is the difference in displacement between two points on the graph.
  • Δt is the difference in time between the same two points.

Interpreting the Gradient

• The steeper the gradient of the graph at a point, the greater the velocity at that instant.
• A horizontal line on the graph (zero gradient) represents a stationary object (zero velocity).
• A straight line with a positive gradient indicates constant positive velocity.
• A straight line with a negative gradient indicates constant negative velocity (motion in the opposite direction).

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Motion Graphs - Displacement-Time Graph

Key Points

• Displacement-time graphs show how an object's displacement changes with time.
• The gradient at a specific time provides the velocity at that time.
• Calculating velocity from the graph involves finding the change in displacement and dividing it by the change in time.
• Different slopes on the graph represent different velocities, including zero velocity for a horizontal line.
• The direction of motion (positive or negative) can be determined from the gradient's sign.

Summary

• Displacement-time graphs are useful tools for visualising and understanding an object's motion.
• The gradient of the graph at a given time reveals the object's velocity at that moment.
• Velocity calculations involve finding the change in displacement and dividing it by the change in time.
• The slope of the graph indicates the magnitude and direction of the object's velocity.