Velocity with constant acceleration is a fundamental concept in physics that describes how the speed and direction of an object change over time when subjected to a constant accelerating force. This concept is crucial in understanding various phenomena, from the motion of vehicles to the fall of objects under gravity.

The relationship between velocity, initial velocity, acceleration, and time is expressed by the following equation:

\[ v = v_0 + at \]

Where:

- \(v\) is the final velocity (m/s)
- \(v_0\) is the initial velocity (m/s)
- \(a\) is the acceleration (m/s²)
- \(t\) is the time interval (s)

Let's calculate the final velocity of a car that starts from rest and accelerates at 3 m/s² for 10 seconds:

- Identify the known values:
- Initial velocity (\(v_0\)) = 0 m/s (starting from rest)
- Acceleration (\(a\)) = 3 m/s²
- Time (\(t\)) = 10 s

- Apply the velocity formula: \[ v = v_0 + at \]
- Substitute the known values: \[ v = 0 + (3 \text{ m/s²})(10 \text{ s}) \]
- Perform the calculation: \[ v = 30 \text{ m/s} \]

Let's visualize the velocity, acceleration, and time relationship with our example:

This visual representation shows:

- The x-axis represents time, from 0 to 10 seconds
- The y-axis represents velocity, from 0 to 30 m/s
- The green line shows the linear increase in velocity over time
- The red point indicates the final velocity (30 m/s) at 10 seconds

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