Motion in a Straight Line - Result Question 22
23. A particle moves along a straight line OX. At a time $t$ (in seconds) the distance $x$ (in metres) of the particle from O is given by $x=40+12 t-t^{3}$. How long would the particle travel before coming to rest?
[2006]
(a) $40 m$
(b) $56 m$
(c) $16 m$
(d) $24 m$
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Answer:
Correct Answer: 23. (b)
Solution:
$ \begin{equation*} \text{ (b) } x=40+12 t-t^{3} \tag{d} \end{equation*} $
$v=\frac{d x}{d t}=12-3 t^{2}$
For $v=0 ; t=\sqrt{\frac{12}{3}}=2 sec$
So, after 2 seconds velocity becomes zero.
Value of $x$ in 2 secs $=40+12 \times 2-2^{3}$
$ =40+24-8=56 m $
