Final answer:
To calculate the car's deceleration, the formula a = (Δv) / t was used. Deceleration is -9 mi/s² when a vehicle slows from 27 mi/s to 0 mi/s in 3 seconds. For SI unit consistency, one must convert miles to meters.
Step-by-step explanation:
The question involves calculating the acceleration of a vehicle that slows down from 27 mi/s to 0 mi/s in 3 seconds. Acceleration is defined as the rate of change of velocity. It can also involve deceleration, or negative acceleration, when an object is slowing down.
To calculate the acceleration, we use the formula:
a = (Δv) / t
where a is the acceleration, Δv is the change in velocity, and t is the time it takes for the change. In this case, the initial velocity vi is 27 mi/s, the final velocity vf is 0 mi/s, and the time t is 3 seconds.
Let's convert the velocity from miles per second to meters per second to be consistent with SI units:
1 mile = 1609.34 meters, so 27 mi/s = 27 * 1609.34 m/s.
Now, we calculate the change in velocity:
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- Δv = vf - vi
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- Δv = 0 mi/s - 27 mi/s
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- Δv = -27 mi/s
And plug the values into the formula to find the acceleration:
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- a = (-27 mi/s) / 3 s
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- a = -9 mi/s2
The answer is -9 mi/s2, indicating a deceleration since it is negative. Remember that the actual conversion into meters per second would be necessary to have the acceleration in SI units.