Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 43

When a high-speed passenger train traveling at 161 km/h rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance \( D = 676 \) m ahead (Fig. 2.17). The locomotive is moving at 29.0 km/h. The engineer of the high-speed train immediately applies the brakes. (a) What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided? (b) Assume that the engineer is at \( x = 0 \) when, at \( t = 0 \), he first spots the locomotive. Sketch \( x(t) \) curves for the locomotive and high-speed train for the cases in which a collision is just avoided and is not quite avoided.