A velocity-time graph shows an object’s velocity over time. The slope of the line represents its acceleration, and the area under the curve represents its displacement.

What are Velocity-Time Graphs?

A velocity-time graph plots an object’s velocity on the vertical (y) axis against time on the horizontal (x) axis. Each point on the graph represents the object’s velocity at a specific instant in time.

  • Vertical Axis (y-axis): Velocity (often denoted as $v$, measured in m/s, km/h, etc.)
  • Horizontal Axis (x-axis): Time (often denoted as $t$, measured in seconds, minutes, etc.)

Interpreting Velocity-Time Graphs

The shape and slope of a velocity-time graph tell us a lot about an object’s motion:

  • Horizontal Line: If the line is flat (horizontal), the object’s velocity is not changing. This means the object is moving at a constant velocity (and zero acceleration).
  • Straight Line with a Slope: If the line is straight but angled, the object’s velocity is changing at a constant rate. This means the object has constant acceleration.
  • Curved Line: If the line is curved, the object’s acceleration is changing. This indicates non-constant acceleration.

Slope of a Velocity-Time Graph

Just like with position-time graphs, the slope of a velocity-time graph holds crucial information.

For a velocity-time graph:

\[\text{Slope} = \frac{\text{Change in Velocity}}{\text{Change in Time}} = \frac{\Delta v}{\Delta t}\]

The change in velocity over the change in time is, by definition, acceleration.

Therefore, the slope of a velocity-time graph represents the object’s acceleration.

  • Steeper Slope: Indicates a greater acceleration (faster change in velocity).
  • Zero Slope (Horizontal): Indicates zero acceleration (constant velocity).
  • Positive Slope: Indicates positive acceleration (velocity is increasing in the positive direction, or decreasing in the negative direction).
  • Negative Slope: Indicates negative acceleration (velocity is decreasing in the positive direction, or increasing in the negative direction).

Area Under a Velocity-Time Graph

Another powerful feature of a velocity-time graph is the area between the line and the time axis.

The area under a velocity-time graph represents the displacement of the object.

  • Area above the x-axis (positive velocity): Represents positive displacement.
  • Area below the x-axis (negative velocity): Represents negative displacement.
  • Total Displacement: Is the sum of positive and negative areas.
  • Total Distance: Is the sum of the absolute values of all areas.

Interactive Velocity-Time Graph

Explore different motion scenarios and see how acceleration (slope) and displacement (area) are calculated.

Calculated Acceleration: --- m/s²

Calculated Displacement: --- m

Interactive Velocity-Time Graph Visualizer An interactive tool to visualize velocity-time graphs for different motion types, showing calculated acceleration and displacement. Time (s) Velocity (m/s) 0 20 -20 10 1 2 3 4 5 6 7 8 9 5 10 15 -5 -10 -15

Select a motion type to see its corresponding velocity-time graph, then calculate acceleration and displacement!

Key Features to Look For

When analyzing a velocity-time graph, pay attention to:

  • Starting Point: Where the line begins on the y-axis (velocity) at $t=0$.
  • Intersections with x-axis: Where the line crosses the x-axis (velocity = 0), indicating the object momentarily stops or changes direction.
  • Changes in Slope: Points where the line’s steepness or direction changes, indicating a change in acceleration.

Interactive Match: Velocity-Time Graph

Test your understanding of the key terms associated with velocity-time graphs.

Click a term and then its matching meaning. Match all pairs to complete!

Why This Matters?

Velocity-time graphs are fundamental because:

  • They provide a direct visual representation of an object’s acceleration.
  • They allow for the calculation of displacement, even for complex motions, by finding the area under the curve.
  • They are a crucial step in understanding kinematics and solving motion problems.

Audio Explanation

Prefer to listen? Here's a quick audio summary of velocity-time graphs.

💡 Quick Concept Check:

A velocity-time graph shows a straight line with a positive slope. What does this tell you about the object's motion?

Click to Reveal Answer
A straight line with a positive slope on a velocity-time graph means the velocity is increasing at a constant rate. Therefore, the object has **constant positive acceleration**.

Ready to put your understanding of velocity-time graphs into practice? Check out these related skills:

Practice Problems

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