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

43 When a high-speed passenger train traveling at $161 \text{ km/h}$ 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 $D = 676 \text{ m}$ ahead (Fig. 2-20). The locomotive is moving at $29.0 \text{ km/h}$. 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.