First slide

Relative velocity in 1-d

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 acceleration are 0.3 m/s² and 0.2 m/s², respectively, then the time they take to pass each other will be

Moderate

A

5s
B

10s
C

15s
D

20s

Solution

Relative velocity of one train w.r.t. other $= 10 + 10 = 20 m / s$
$Relative acceleration = 0.3 + 0.2 = 0.5 m / s^{2}$
$If trains cross each other, then from s = u t + \frac{1}{2} a t^{2}$
$\begin{array}{l} As, s = s_{1} + s_{2} = 100 + 125 = 225 \\ \Rightarrow 225 = 20 t + \frac{1}{2} \times 0.5 \times t^{2} \Rightarrow 0.5 t^{2} + 40 t - 450 = 0 \\ \Rightarrow t = - \frac{40 \pm \sqrt{1600 + 4 . (005) \times 450}}{1} = - 40 \pm 50 \\ ∴ t = 10 sec (Taking +ve value). \end{array}$

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