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  4. A car moving with speed v on a straight road can be stopped with in distance d on applying brakes. If same car is moving with speed 3v and brakes provide half retardation, then car will stop after travelling distance

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Q. A car moving with speed $v$ on a straight road can be stopped with in distance $d$ on applying brakes. If same car is moving with speed $3v$ and brakes provide half retardation, then car will stop after travelling distance

Motion in a Straight Line

Solution:

$d_{s}=\frac{u^{2}}{2 a}$
$d_{s} \propto u^{2} \Rightarrow \frac{d_{s}}{d_{s}'}-\frac{u^{2}}{u^{'2}}$
$u'=3 v$
$u=v$
So, $\frac{d_{s}}{d_{s}'}=\frac{v^{2}}{9 v^{2}}$
$\Rightarrow d_{s}'=9 d_{s}$
$\Rightarrow d_{s}'=9 d$