Two trans one t ravelling at 54 kmph and the other at 72 kmph are headed towards one another along a straingt track. When they are `1//2` km apart, both drivers simultaneously seee the other train and apply their brakes. If each train is decelerated at the rate of `1 m//s^(2)`, will there be a collision ?

Explanation

Velocity of the first train is 54 kmph`=15(m)/(s)`
Distance travelled by the first train before coming to rest
`s_(1)=(u^(2))/(2a)=(225)/(2)=112.5m`
Velocity of the second train is `72 kmph = 20 m//s` Distance t ravelled by the second train before coming to rest
`s_(2)=(u^(2))/(2a)=(400)/(2)=200m`
Total distance travelled by the two trains before coming to rest `= s_(1)+s_(2)=112.5+200=312.5m` Because the initial distance of separation is 500 m which is greater than 312.5 m, there will be no collision between the two trains.