Motion In A Straight Line Ques 16
16. The position $x$ of a particle with respect to time $t$ along $x$-axis is given by $x=9 t^{2}-t^{3}$ where $x$ is in metres and $t$ in second. What will be the position of this particle when it achieves maximum speed along the $+ve$ $x$ direction?
[2007]
(a) $54 $ $m$
(b) $81 $ $m$
(c) $24 $ $m$
(d) $32 $ $m$.
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Answer:
Correct Answer: 16.(a)
Solution:
- (a) Speed $v=\frac{d x}{d t}=\frac{d}{d t}(9 t^{2}-t^{3})=18 t-3 t^{2}$
For maximum speed its acceleration should be zero,
Acceleration $\frac{d v}{d t}=0 \Rightarrow 18-6 t=0 \Rightarrow t=3$
At $t=3$ its speed is max
$\Rightarrow x _{\text{max }}=81-27=54 $ $m$
Position of any point is completely expressed by two factors its distance from the observer and its direction with respect to observer.
That is why position is characterised by a vector known as position vector.
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