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:

  1. (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 $