On a winter night, a train was coming from Agra to Delhi at a slow speed. The train was almost full to its capacity as people were visiting the Taj Mahal, suddenly the driver sighted another train at some distance ahead of him moving in the same direction on the same track but with lower speed. He applied the brakes to slow down his train and averted a major rail accident. The driver of the train was awarded for the same.

(i) Show that there will be no collision if the first train is moving with velocity v1 and velocity of other train is v2, if d > (v1 -v2)2 / 2a.

(ii) Determine the relative velocity of two objects moving with same velocity in the same directions.

(iii) What is the abilities of driver which you will appreciate?

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