# 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.

Sep 23, 2017

See the approach below...

#### Explanation:

Here each train should have a final velocity of $0 m {s}^{-} 1$
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 ${s}_{1} + {s}_{2} \le s$
or,${v}_{1}^{2} / \left(2 {r}_{1}\right) + {v}_{2}^{2} / \left(2 {r}_{2}\right) \le s$