To determine the acceleration of the car at a specific time using the velocity equation \( v(t) = -t^2 + 15 \), we first need to find the acceleration, which is the derivative of the velocity function with respect to time.
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Differentiate the velocity function: \[ a(t) = \frac{dv}{dt} = \frac{d}{dt} (-t^2 + 15) = -2t \]
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Calculate the acceleration at \( t = 5 \) seconds: \[ a(5) = -2(5) = -10 \text{ mi/h}^2 \]
The negative sign indicates that the acceleration is in the opposite direction of the velocity, suggesting that the car is slowing down.
Thus, at 5 seconds, the car is slowing down at a rate of 10 mi/h².
The correct answer is: A. The car is slowing down at a rate of 10 mi/h².
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