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



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 3rd equation of motion, i.e.,



The train will not collide if




A passenger is standing ‘d’  away from a bus. The bus being to move with constant acceleration a. To catch the bus, the passenger runs at a constant speed v towards the bus. What must be the minimum speed of the passenger so that he may catch the bus?