Question

Two cars A and B are moving towards each other on a straight road with velocity 10 m/sec. and 12 m/sec. respectively. When they are 160 m apart, each car decelerates at $2{\text{m/sec}}^2$ until they stop in order to avoid collision. Calculate the distance (in $m$) between them when they come to rest.

Answer 1

Let $s_1$ and $s_2$ be the distance covered by the cars after they begin to decelerate.
For car I,
$v=u+at$ (By first equation of motion)
$\Rightarrow 0=10–2t$
$\therefore t=5\text{s}$
i.e., after $5\text{s}$ car I will stop.
$\therefore$ Distance travelled before car I stop
$s_1=10\times 5-\frac{1}{2}\times 2\times 25=25\text{m}$
For car II,
Applying $v=u+at$
$\Rightarrow 0=12–2t$
$\therefore t=6\text{s}$
$\therefore s_2=12\times 6-\frac{1}{2}\times 2\times 36=36\text{m}$
$\therefore$ Distance between them when they come to rest $=\{160–(25+36\left)\right\}=99\text{m}$