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Home » The \( n \)-th term is \( a_n = S_n - S_n-1 \). - Ready Digital AB

The \( n \)-th term is \( a_n = S_n - S_n-1 \). - Ready Digital AB

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 At \( t = 30 \), \( S(30) = 10e^{-0.075} + 20(1 - e^{-0.075}) \approx 14.31 \) kg.

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

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