Two trains along the same straight rails moving with constant speed $60 k m / h r$ and $30 k m / h r$ respectively towards each other. If at time $t = 0$ , the distance between them is $90 k m$ , the time when they collide is:

$1 h r$

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$2 h r$

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$3 h r$

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$4 h r$

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Solution

The correct option is A
$1 h r$

Step 1: Given
Speed of first train: $V_{1} = 60 k m / h r$
Speed of second $V_{2} = 30 k m / h r$
Distance between the trains at $t = 0$ : $D = 90 k m$
Step 2: Formula Used
$T i m e t a k e n = \frac{R e l a t i v e d i s p l a c e m e n t}{R e l a t i v e v e l o c i t y}$
Step 3: Find the time when the trains collide
Calculate the relative velocity of the trains by subtracting the velocity of second train (negative vector) from first train, as they are moving in same direction.
$V_{r e l} = V_{1} - V_{2} = 60 - (- 30) = 90 k m / h r$
Calculate the time of collision using the formula. The distance will be relative displacement of the trains.
$T i m e t a k e n = \frac{R e l a t i v e d i s p l a c e m e n t}{R e l a t i v e v e l o c i t y} = \frac{90 k m}{90 k m / h r} = 1 h r$
Hence, the trains will collide after $1 h r$ . option A is correct.

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Two trains along the same straight rails moving with constant speed 60km/hr and 30km/hr respectively towards each other. If at time t=0, the distance between them is 90km, the time when they collide is:

Two trains along the same straight rails moving with constant speed $60 k m / h r$ and $30 k m / h r$ respectively towards each other. If at time $t = 0$ , the distance between them is $90 k m$ , the time when they collide is: