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Home » Car KE = 0.5×1000×400 = 200,000 J - 500apps

Car KE = 0.5×1000×400 = 200,000 J - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 If the velocity of an object is given by \( v(t) = 3t^2 + 2t \), what is its acceleration at \( t = 4 \) seconds?

📌 Acceleration is the derivative of velocity, \( a(t) = \frac{d}{dt}(3t^2 + 2t) = 6t + 2 \).

📌 At \( t = 4 \), \( a(4) = 6(4) + 2 = 24 + 2 = 26 \) m/s².

📌 #### 26 m/s²Question: A climate policy analyst is evaluating the distribution of 6 distinct urban green energy initiatives into 3 identical community districts. How many distinct ways can this be done if each district must receive at least one initiative?

📌 Solution: The problem requires partitioning 6 distinguishable initiatives into 3 non-empty indistinct subsets. This is given by the Stirling numbers of the second kind, $ S(6, 3) $. The formula for $ S(n, k) $ is $ \frac{1}{k!} \sum_{i=0}^{k} (-1)^{k-i} \binom{k}{i} i^n} $. Plugging in $ n=6 $ and $ k=3 $:

📌 S(6, 3) = \frac{1}{6} \left( 3^6 - 3 \cdot 2^6 + 3 \cdot 1^6 \right) = \frac{1}{6} (729 - 192 + 3) = \frac{540}{6} = 90.

📌 Thus, the number of ways is $\boxed{90}$.

📌 Question: A hydrologist is modeling groundwater flow through 7 distinct soil layers. How many distinct sequences of 4 layers can be selected and ordered for analysis if the operation "pump water" is applied to exactly 2 of them?

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