posted by Pat .
the engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant accelaration of -0.100 m/s2, while the freight train continues with constant speed. Take x=0 at the location of the front of the passenger train when the engineer applies the brake. (a) will the cows nearby witness a collision? (b) if so, where it take place? (c) on a single graph, sketch the positions of the frong of the passenger train and the back of the freight train.
With no braking, the trains would collide in t = 200/(25-15) = 20 sec.
At a decelerauon of 0.10m/sec.^2, the passenger train would come to a stop in Vf = 0 = 25 - 0.10t yielding t = 250 sec.
Since the time to impact is less than the time to the passenger train stopping, the two trains will collide when the freight train has traveled 300 m. and the passenger train has traveled 500m.