The change in velocity is calculated by subtracting the initial velocity from the final velocity: Δv = vf - vi. However, if you know the acceleration and the time interval, there's another way to calculate it.
Here's a breakdown of the methods:
1. Using Initial and Final Velocities:
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Formula: Δv = vf - vi
- Δv = change in velocity
- vf = final velocity
- vi = initial velocity
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Explanation: This is the most straightforward way. Simply subtract the object's starting velocity from its ending velocity. The result indicates how much and in what direction the velocity changed.
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Example: A car accelerates from 10 m/s to 25 m/s. The change in velocity is 25 m/s - 10 m/s = 15 m/s.
2. Using Acceleration and Time:
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Formula: Δv = a * t
- Δv = change in velocity
- a = acceleration (constant)
- t = time interval
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Explanation: This method works when the acceleration is constant (uniform). Multiply the acceleration by the time interval over which it occurs.
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Derivation: This formula is derived from the final velocity formula: vf = vi + a t. Rearranging, we get Δv = vf - vi = (vi + a t) - vi = a * t.
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Example: A rocket accelerates at a constant rate of 5 m/s² for 10 seconds. The change in velocity is 5 m/s² * 10 s = 50 m/s.
Summary:
| Method | Formula | Conditions | Example |
|---|---|---|---|
| Final - Initial Velocity | Δv = vf - vi | Always applicable | A ball slows down from 15 m/s to 5 m/s. Δv = 5 m/s - 15 m/s = -10 m/s (the negative sign indicates a decrease in velocity). |
| Acceleration x Time | Δv = a * t | Constant (uniform) acceleration | A cyclist accelerates at 2 m/s² for 8 seconds. Δv = 2 m/s² * 8 s = 16 m/s. |
The change in velocity is a vector quantity, meaning it has both magnitude (how much the velocity changed) and direction. Pay attention to the signs (positive or negative) to indicate the direction of the change.
