Motion Graphs - Velocity-Time Graph

Introduction

• Velocity-time graphs are graphical representations used to describe the motion of an object concerning its velocity over time.
• These graphs help us understand how an object's velocity changes as it moves.

Gradient and Acceleration

• The gradient (slope) of a velocity-time graph at a specific time provides valuable information about the object's acceleration at that moment.
• Acceleration is a measure of how an object's velocity changes over time.

Calculating Acceleration

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

Displacement from Area

• The area under a velocity-time graph represents the displacement of the object.
• To find displacement from the graph, calculate the area enclosed by the graph and the time axis.
• This method works for both positive and negative displacements.

Interpreting the Graphs

• Constant Positive Velocity Graph: A horizontal line indicates constant positive velocity.
• Constant Positive Acceleration Graph: A straight line with a positive gradient represents constant positive acceleration.
• Constant Negative Acceleration Graph: A straight line with a negative gradient represents constant negative acceleration.
• Initial Conditions: Note the initial displacement and initial velocity on the graph, which may affect the motion.

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Motion Graphs - Velocity-Time Graph

Key Points

• Velocity-time graphs show how an object's velocity changes with time.
• The gradient at a specific time provides information about the object's acceleration at that time.
• Acceleration calculations involve finding the change in velocity and dividing it by the change in time.
• Displacement can be determined by calculating the area under the velocity-time graph.
• Different types of motion are represented by various graph shapes and initial conditions.

Summary

• Velocity-time graphs help us visualise and analyse an object's motion by showing how velocity changes with time.
• The gradient of the graph provides information about acceleration.
• Acceleration calculations involve finding the change in velocity and dividing it by the change in time.
• Displacement can be determined by calculating the area under the graph.
• Different types of motion are represented by distinct graph patterns and initial conditions.