To find the acceleration of the plane, we can use the formula for acceleration, which is given by:
\[ a = \frac{\Delta v}{\Delta t} \]
where:
- \( a \) is the acceleration,
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the change in time.
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Convert the time from minutes to hours: \( 3 \) minutes = \( \frac{3}{60} \) hours = \( 0.05 \) hours
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Initial velocity (\( v_i \)): \( 600 \) km/h
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Final velocity (\( v_f \)): \( 70 \) km/h
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Calculate the change in velocity (\( \Delta v \)): \[ \Delta v = v_f - v_i = 70 , \text{km/h} - 600 , \text{km/h} = -530 , \text{km/h} \]
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Calculate the acceleration (\( a \)): \[ a = \frac{\Delta v}{\Delta t} = \frac{-530 , \text{km/h}}{0.05 , \text{h}} = -10600 , \text{km/h}^2 \]
So, the acceleration of the plane is \(-10600 , \text{km/h}^2\). This negative sign indicates a reduction in speed, confirming that it is deceleration.