Question

Two trains one of length $100\text{m}$ and another of length $125\text{m}$, are moving in mutually opposite directions along parallel lines, meet each other, each with speed $100\text{m/s}$. If their accelerations are $0.3{\text{m/s}}^2$ and $0.2{\text{m/s}}^2$ respectively, then the time they take to pass each other will be

• A. $5s$
• B. $10s$
• C. $15s$
• D. $20s$

Answer 1

The correct option is B $10s$

Relative velocity of one train w.r.t. other
$=10+10=20m/s.$
Relative acceleration $=0.3+0.2=0.5m/s^2$
If trains cross each other, then from $s=ut+\frac{1}{2}a{t}^2$
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).