Two trucks are moving in a straight line towards each other at initial velocities `u_(1)` and `u_(2)` and with constant retardations `a_(1)` and `a_(2)`. If the initial separation between them is `d`, find the minimum value of `d` for no collision.

Explanation

`u_(1//2)=u_(1)+u_(2)`
`a_(1//2)=a_(1)+a_(2)`
Now truck `2` is at rest, truck `1` is moving under constant retardation `(a_(1)+a_(2))` with initial velocity `(u_(1)+u_(2))`. The truck will stop after trevelling a distance `s`.
`v^(2)=u^(2)+2as`
`0=(u_(1)+u_(2))^(2)-2(a_(1)+a_(2))s`
`s=((u_(1)+u_(2))^(2))/(2(a_(1)+a_(2)))`
For no collision,
`sled`
`dges`
`dge((u_(1)+u_(2))^(2))/(2(a_(1)+a_(2)))`
`d_(min)=((u_(1)+u_(2))^(2))/(2(a_(1)+a_(2)))`