The passenger train is traveling at 100 mi/hr when the driver makes the turn. The locomotive train is on the same tracks as the passenger train and moving towards it at 18 mi/hr. The distance between the two trains is 0.28 mi.
Adding the velocities of the two trains, the net velocity with which the passenger train is approaching the locomotive is 118 mi/hr. The distance between them is 0.28 mi within which the passenger train has to stop to avoid a collision.
Let the acceleration required be A.
Using the formula v^2 - u^2 = 2*a*s
=> 0 - 118^2 = 2*A*0.28
=> A = -118^2/2*0.28
=> A = -24864.2 mi/hr^2
The deceleration due to the brakes should be 24864.2 mi/hr^2 to avoid a collision.