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Home » Nur wenn $ P \Rightarrow Q $ wahr **fÃ¼r alle $ x $**. - Sterling Industries

Nur wenn $ P \Rightarrow Q $ wahr fÃ¼r alle $ x $. - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 #### 14.31

📌 A car accelerates uniformly from rest to 60 m/s in 10 seconds, then maintains constant speed for 20 seconds, and finally decelerates uniformly to rest in 5 seconds. What is the total distance traveled?

📌 Acceleration phase: \( a = \frac{60}{10} = 6 \, \text{m/s}^2 \); distance \( = \frac{1}{2} \times 6 \times 10^2 = 300 \, \text{m} \).

📌 Constant speed: \( d = 60 \times 20 = 1200 \, \text{m} \).

📌 Deceleration phase: \( a = \frac{-60}{5} = -12 \, \text{m/s}^2 \); distance \( = 60 \times 5 + \frac{1}{2}(-12)(5^2) = 300 - 150 = 150 \, \text{m} \).

📌 Total distance \( = 300 + 1200 + 150 = 1650 \, \text{m} \).

📌 A cone with height 12 cm and base radius 5 cm is filled with water. The water flows out through a small hole at the bottom at a rate proportional to the square root of the water height. If the outflow rate is \( k\sqrt{h} \), where \( k = 0.2 \, \text{cm}^{1.5}/\text{min} \), what is the height of water after 10 minutes?

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