The driver of a train travelling at 115 km/hour sees on the same track, 100 m infront of him' a slow train travelling in the same direction at 25 km/hour. The Ieast retardation that must be applied to faster train to avoid a collision is

The relative velocity of faster train with respect to slow train is given by
$\begin{array}{l}\mathrm{u}=115-25=90\mathrm{km}/ \mathrm{hour}\\ =90\times \frac{5}{18}=25\mathrm{m}/\sec \end{array}$
Distance (s) between two trains = 100 m.
If the collision is to be avoided, the relative velocity should be zero. Thus
$\begin{array}{l}{\mathrm{v}}^2-{\mathrm{u}}^2=2\mathrm{as}\\ 0-(25{)}^2=2\mathrm{a}\times 100 \mathrm{or} -625=200\mathrm{a}\end{array}$
$\therefore \mathrm{a}=-\frac{625}{200}=-3\cdot 125\mathrm{m}/{\mathrm{s}}^2$
So, the retardation should be 3.125 m/s²