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Question

# A particle is moving in a straight line according to the formula s = t2 + 8t + 12. If s be measured in metre and t be measured in second, then the average velocity of the particle in third second is

A
14 m / sec
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B
13 m / sec
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C
15 m / sec
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D
None of these
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Solution

## The correct option is C 15 m / secHere number of batches =Nx and time per batch (α=βx2) second ∴ Total processing time T=(Nx)(α+βx2)=N(αx+βx) second For fast processing T must be least, ∴ dTdx=N(−αx2+β);d2Tdx2=2Nαx3 For maxima or minima of T, dTdx=0⇒x=√(αβ) For x = √(αβ),d2Tdx2is + ve i.e., > 0 ∴T has minima for x=√αβ.

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