How to look for and calculate terminal velocity on an x vs t graph

Answer 1

To find the terminal velocity on an x vs t graph, follow these steps:

1. Look for a region where the graph becomes a horizontal line or levels off. This represents the object reaching its terminal velocity. Terminal velocity is the maximum velocity an object can attain while falling through a fluid (like air or a liquid), where the gravitational force is balanced by the drag force.

2. Once you have identified the region where the graph levels off, locate the corresponding time value (t = t₁) where the velocity becomes constant.

3. Calculate the terminal velocity by finding the slope of the line before the level-off point. The slope represents the acceleration of the object during free fall before it reaches the terminal velocity. Use the formula:

v = (x₂ - x₁) / (t₂ - t₁)

Where v is the initial acceleration.

4. Repeat the same calculation for multiple points/lines before the leveling-off region.

5. Take the average value of the calculated slopes to find the approximate terminal velocity of the object.

Note: It's important to understand that this method assumes a linear relationship between distance and time before reaching terminal velocity. In reality, the relationship can be more complex for objects subject to varying forces and fluid dynamics.