The question: When a high-speed passenger train traveling at vP = 55 m/srounds a

Question

The question:

When a high-speed passenger train traveling at vP = 55 m/srounds a bend, the engineer is shocked to see that a locomotive hasimproperly entered onto the track from a siding and is a distance D= 1000 m ahead (see figure). The locomotive is moving at vL = 9m/s. The engineer of the passenger train immediately applies thebrakes. Assume that an x axis extends in the direction of motion.What must be the constant acceleration along that axis if acollision is to be just avoided?

It has to deal with two velocities and I can't figure out whichformula to use. Any help would be rated highly thank you.

Explanation / Answer

u = 55 km/h, v = 9 km/h, D = 1000 m, find a. relative to the locomotive, the train's initial velocity is u - v,final velocity = 0, deceleration = a, displacement = D, so 0 - (u - v)2 = 2*(-a)*D a = (u - v)2/(2D) NOTE: Make sure to convert to m/s

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