A particle moves according to the law $s=t^{3}-6 t^{2}+9 t+25 .$ The displacement of

A particle moves according to the law $s=t^{3}-6 t^{2}+9 t+25 .$ The displacement of
  1. 0 units
  2. -27 units
  3. 27 units
  4. 9 units

Solution

Given $s=t^{3}-6 t^{2}+9 t+25$ ....(1) $\begin{array}{l}v=\frac{d s}{d t}=3 t^{2}-12 t+9 \\ \frac{d v}{d t}=6 t-12\end{array}$ Given $6 t-12=0 \Rightarrow t=2$ $\therefore$ from $(1), s=(2)^{3}-6 \times 4+18+25=27$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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