How do you interpret velocity vs time graphs in physics?

Interpreting Velocity vs Time Graphs

A velocity vs time graph shows how an object's velocity changes over time. The horizontal axis (x-axis) represents time ($t$), and the vertical axis (y-axis) represents velocity ($v$). These graphs are fundamental in kinematics for analyzing motion.

Key Points

• Slope: The slope of the graph at any point gives the object's acceleration.
• Area under the curve: The area between the graph and the time axis represents the object's displacement over that time interval.

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Worked Example

Problem:
A car moves in a straight line. Its velocity vs time graph is a straight line from $v = 0$ m/s at $t = 0$ s to $v = 10$ m/s at $t = 5$ s.
Find:

1. The car's acceleration.
2. The displacement after 5 seconds.

Step 1: Find the Acceleration

The graph is a straight line, so acceleration is constant and equals the slope:

$$ a = \frac{Delta v}{Delta t} = \frac{10,\text{m/s} - 0,\text{m/s}}{5,\text{s} - 0,\text{s}} = \frac{10}{5} = 2,\text{m/s}^2 $$

Step 2: Find the Displacement

Displacement is the area under the velocity-time graph. Here, it's a triangle:

$$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5,\text{s} \times 10,\text{m/s} = 25,\text{m} $$

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Takeaways

• The slope of a velocity vs time graph gives acceleration.
• The area under the curve gives displacement.
• A straight, sloped line means constant acceleration; a horizontal line means constant velocity.