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in Physical World and Measurement by (50 points)
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If volume of water in a tank increases with time as per the equation, \( V = t ^{3}- t ^{2}+2 \) where volume is in litre and time is in second, then rate of change of volume at \( t=3 sec \) will be:- 

(1) \( 20 l / s \) 

(2) \( 21 l / s \) 

(3) \( 22 l/s \) 

(4) \( 23 l / s \)

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1 Answer

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by (53.3k points)

Correct option is (2) \( 21 \,l/s\)

Given Volume

\(V = t^3 - t^2 + 2\)

\(\left(\frac{dV}{dt}\right) = 3t^2 - 2t\)

at \(t = 3\)

\(\left(\frac{dV}{dt}\right) = 27 - 6\)

\(\frac{dv}{dt} = 21 \,l/s\)

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