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 acceleration are 0.3 m/s^{2} and 0.2 m/s^{2} respectively, then the time they take to pass each other will be
Text Solution
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Relative velocity of one train w.r.t . other
=10+10=20 m / s .
Relative acceleration =0.3+0.2=0.5 m / s 2
If trains cross each other then from \(s = ut + \frac{1}{2} at^{2}\)
As, S = S_{1} + S_{2} = 100 + 125 = 225
⇒ ⇒ \(225 = 20t + \frac{1}{2} \times 0.5 \times t^{2}\) ⇒ ⇒ 0.5t^{2} + 40t - 450 = 0
⇒ ⇒ \(t = \frac{40 \pm \sqrt{1600 - 4 \cdot (0.05) \times 450}}{1}\) \(= -40 \pm 50\)
∴ ∴ \(t = 10 \text{ sec}\) (Taking +ve value).
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