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 $0.3 m / s^{2} a n d 0.2 m / s^{2}$ respectively, then the time they take to pass each other will be

5 sec

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10 sec

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15 sec

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20 sec

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Solution

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, $s = s_{1} + s_{2} = 100 + 125 = 225$
$\Rightarrow 225 = 20 t + \frac{1}{2} \times 0.5 \times t^{2} \Rightarrow 0.5 t^{2} + 40 t - 450 = 0$

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

$∴$ t=10 sec (Taking +ve value).

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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/s2 and 0.2m/s2 respectively, then the time they take to pass each other will be

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/s2. As, s=s1+s2=100+125=225 ⇒225=20t+12×0.5×t2⇒0.5t2+40t−450=0 ⇒t=40±√1600+4×(0.5)×4501=−40±50 ∴ t=10 sec (Taking +ve value).

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 $0.3 m / s^{2} a n d 0.2 m / s^{2}$ respectively, then the time they take to pass each other will be