1. Tardigrade
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  4. The relation between time t and distance x for a moving body is given as t=m x2+n x, where m and n are constants. The retardation of the motion is: (When v stands for velocity)

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Q. The relation between time $t$ and distance $x$ for a moving body is given as $t=m x^{2}+n x$, where $m$ and $n$ are constants. The retardation of the motion is: (When $v$ stands for velocity)

JEE MainJEE Main 2021Motion in a Straight Line

Solution:

$t=m x^{2}+n x$
$\frac{1}{v}=\frac{d t}{d x}=2 m x+n$
$v=\frac{1}{2 m x+n}$
$\frac{d v}{d t}=-\frac{2 m}{(2 m x+n)^{2}}\left(\frac{d x}{d t}\right)$
$a=-(2 m) v^{3}$