Question

Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their accelerations are $0.3m/s^{2}and0.2m/s^2$ respectively, then the time they take to pass each other will be

• A. 5 sec
• B. 10 sec
• C. 15 sec
• D. 20 sec

Answer 1

The correct option is B

10 sec

Relative velocity of one train w.r.t other = 10 + 10=20 m/s.
Relative accerleration =0.3+0.2=0.5 $m/s^2$.
As, $s=s_1+s_2=100+125=225$
$\Rightarrow 225=20t+\frac{1}{2}\times 0.5\times t^2\Rightarrow 0.5t^2+40t-450=0$

$\Rightarrow t=\frac{40\pm \sqrt{1600+4\times \left(0.5\right)\times 450}}{1}=-40\pm 50$

$\therefore$ t=10 sec (Taking +ve value).