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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A particle moves in a straight line with its position given by \( s(t) = 2t^3 - 5t^2 + 4t \). Find its velocity at \( t = 3 \) seconds.

📌 Velocity is the derivative of position: \( v(t) = rac{ds}{dt} = rac{d}{dt}(2t^3 - 5t^2 + 4t) \).

📌 Differentiate: \( v(t) = 6t^2 - 10t + 4 \).

📌 Evaluate at \( t = 3 \): \( v(3) = 6(3)^2 - 10(3) + 4 = 54 - 30 + 4 = 28 \).

📌 Solve for \( x \) in the equation \( 3^{2x+1} = 81 \).

📌 Rewrite 81 as a power of 3: \( 81 = 3^4 \).

📌 Set exponents equal: \( 2x + 1 = 4 \).

📌 Solve: \( 2x = 3 \), so \( x = rac{3}{2} \).

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