How to find average velocity from a velocity-time graph?
Understand the Problem
The question is asking how to calculate average velocity using a velocity-time graph. This involves analyzing the graph to determine the total displacement and the total time taken, and then using the formula for average velocity.
Answer
\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}}
Answer for screen readers
The average velocity is the total displacement divided by the total time.
Steps to Solve
- Identify the total displacement from the graph
To find the total displacement, calculate the area under the velocity-time graph. This involves summing up the areas of geometric shapes (like rectangles, triangles, etc.) under the graph:
$$ ext{Total Displacement} = ext{Area under the velocity-time graph}$$
- Determine the total time interval
Identify the total time duration by examining the x-axis (time axis) of the graph. This is the difference between the final and initial time.
$$ ext{Total Time} = t_{ ext{final}} - t_{ ext{initial}}$$
- Calculate the average velocity
The average velocity is the total displacement divided by the total time:
$$ ext{Average Velocity} = \frac{ ext{Total Displacement}}{ ext{Total Time}}$$
The average velocity is the total displacement divided by the total time.
More Information
The area under the curve in a velocity-time graph represents the total displacement, and dividing this by the total time gives the average velocity.
Tips
A common mistake is not calculating the area under the curve correctly. Ensure you correctly identify and sum the areas of all the geometric shapes (rectangles, triangles) under the velocity-time graph for an accurate displacement.
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