The Driver Of A Train Moving At A Speed v1 sights A Goods A Train A Distanced ahead Of Him On The Same Track Moving In The Same Direction With A Slower Speed v2. He Puts On A Brakes And Gives His Train A Constant Retardation A. Show That There Will Be No Collision If

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Question

The driver of a train moving at a speed v₁ sights a goods a train a distanced ahead of him on the same track moving in the same direction with a slower speed v₂. He Puts on a brakes and gives his train a constant retardation a. Show that there will be no collision if

None of these

easy

Solution

Correct option is

For no collision the speed on the train must be reduced to v₂ before the trains meet, i.e., the velocity of train relative to goods train v₁ – v₂ should become zero before the train meet.

Now if s is the displacement of train relative to goods train when it comes to rest relative to goods train due to application of brakes, we have from 3^rd equation of motion, i.e.,