Motion In A Straight Line Ques 17
17. 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: 17.(b)
Solution:
- (b) $x=40+12 t-t^{3} $
$v=\frac{d x}{d t}=12-3 t^{2}$
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 $
BETA
