Two trains initially separated byba distance d. One train moves with velocity v1 and the othet with velocity v2,such that v1>v2.Now the train moving with velocity v1 applies a constant retardation `a`. Prove that the hap between the two trains should be d>{(v1-v2)^2}÷2a so that the trsins do not collide.

Three identical balls are placed on a frictionless horizontal surface touching each other. They stick to each other because of adhesive. Another ball of same radius and mass m is placed over the void created by the three balls. Find the forces applied by the balls kept on the floor to each other if the system remains in equilibrium.

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

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