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Two cars travelling towards each other on a straight road at velocity, $12$ $m / s$ and $20$ $m / s$ respectively. When they are $350$ $m$ apart, both driver apply their brakes and each car de-accelerates at $2$ $m / s^{2}$ until it stops.
$(a)$ How far apart will the car be after stopping.
$(b)$ Will the car collide to one another?

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Solution

$V_{A} = 12$ $m / s$
$V_{B} = 20$ $m / s$
$a = - 2$ $m / s^{2}$
$v^{2} - u^{2} = 2 a s$
$v = 0$ $m / s$ for both
$\Rightarrow - u^{2} = 2 a s$
$\Rightarrow s = \frac{- u^{2}}{2 a}$
Now putting data,
$s_{1} = 36$ $m$ ,
$s_{2} = 100$ $m$
$(a)$ But the distance between them is $350$ ; $350 - 136 = 214$ $m$
$(b)$ So, these are not going to collide.

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