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Q.
Give example of a motion where x >0, u < 0 a > 0 at a particular instant
Motion in a Straight Line
Solution:
Let us consider function of motion
$x ( t )= A + Be ^{-\gamma t}$
Where $\gamma$ and $A$, is a constant $B$ is a amplitude. $x ( t )$ is displacement at time $t$, where $A > B$ and $\gamma>0$
$v ( t )=\frac{ d x ( t )}{ dt }=0+(-\gamma) Be ^{-\gamma t }=-\gamma Be ^{-\gamma t}$
$a ( t )=\frac{ d }{ d t}[ v ( t )]=\frac{ d }{ dt }\left(-\gamma Bexp ^{-\gamma t }\right)=\left(\gamma B ^{2} \exp ^{-\gamma t }\right)$
From (i) $\therefore A>B$ so $x$ is always +ve i.e. $x>0$
From (ii) $v$ is always negative from (ii) $v<0$. From (iii) a is always again positive $a > O$.
As the value of $\gamma^{2} Be ^{-\gamma t}$ can varies from o to $+\infty$.