A particle moving from a fixed point on a straight line travels a distance S metres in t sec . If S=t^3-t^2-t+3 , then the distance (in mts) travelled by the particle when it comes to rest is

Correct answer: (C) 2. S=t^3-t^2-t+3 v=(d S)/(d t)=3 t-2 t-1 v=0 ⇒(t-1)(3 t+1) ⇒ t=1 ∴ S=1-1-1+3=2

Q109 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics

A particle moving from a fixed point on a straight line travels a distance $S$ metres in $t \mathrm{sec}$. If $S=t^3-t^2-t+3$, then the distance (in mts) travelled by the particle when it comes to rest is

A
5
B
4
Correct answer
C
2
D
3

Solution

$S=t^3-t^2-t+3$ $\begin{aligned} & v=\frac{d S}{d t}=3 t-2 t-1 \\ & v=0 \Rightarrow(t-1)(3 t+1) \Rightarrow t=1 \\ & \therefore \quad S=1-1-1+3=2\end{aligned}$

Hence, the correct answer is option: 'C'.

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