Two trains A and B which are 100 km apart are travelling towards each other on different tracks with the initial speed of 50 km/h for both. The train A accelerates at $20\,kmh^{-2}$ and the train B retards at the rate $20kmh^{-2}$ The distance covered by the train A when they cross each other is approximately :

Using the relative motion equation, the relative acceleration of train A with respect to train B is 20 - (-20) = 40 km/h^2. Since the initial relative speed is zero and the total distance to be covered is 100 km, we apply the kinematic formula s = ut + (1/2)at^2 to get 100 = 0 + (1/2)(40)t^2, yielding t = sqrt(5) hours. The distance covered by train A is found using the same formula: s_A = 50(sqrt(5)) + (1/2)(20)(5), which simplifies to 50(sqrt(5) + 1) km or approximately 162 km.

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