Question

What will be the condition of no collision between the two trains?

Two trains are coming towards each other along the same line with velocity `u_1` and `u_2` respectively. When the distance between them is `s`, both drivers apply breaks to create retardation `r_1` and `r_2` respectively.

Answer 1

See the approach below...

Explanation:

Here each train should have a final velocity of `0 ms^-1`
Hence,the traveled distance by train `A` is...
`v_1^2=0^2+2r_1s_1=>s_1=v_1^2/(2r_1`
As like in second case ,`v_2^2=0^2+2r_2s_2=>s_2=v_1^2/(2r_2`
Here,the relation in the distance might be `s_1+s_2 <=s`
or,`v_1^2/(2r_1)+v_2^2/(2r_2)<=s`