Question
Two trains on the same line are approaching each other with velocity u1, and u2When there is distance of x between them, both apply brakes and brakes give the retardation of at1 and a2. Prove that it is just possible to avoid the collision if

Solution
Let u1, be velocity of train A and a1, be retardation.
Let x, be the distance travelled by the train A before it comes at rest.

Using the third equation of motion,

Similarly, if x2 is the distance travelled by train B before it comes at rest then

Collision can be avoided, if the total distance travelled by both the trains is x.
i.e.
Let x, be the distance travelled by the train A before it comes at rest.

Using the third equation of motion,

Similarly, if x2 is the distance travelled by train B before it comes at rest then

Collision can be avoided, if the total distance travelled by both the trains is x.
i.e.
