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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
  1. 13 m / sec
  2. None of these
  3. 14 m / sec
  4. 15 m / sec


Solution

The correct option is D 15 m / sec
Here 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=0x=(αβ)

For x = (αβ),d2Tdx2is + ve i.e., > 0

T has minima for x=αβ.

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