Collision - The engineer of a passenger train traveling at 25 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of -0.1 m/s^2, while the freight train continues with constant speed. Take x=0 as the location of the front of the passenger train when the engineer applies the brakes. (a) Will the cows nearby witness a collision? (b) If so, where will it take place?
The Attempt at a Solution
When the collision takes place, xpassenger=xfreight
v0passenger*t +½*a*t2=x0freight +vfreight*t
Solving this quadratic equation for t gives me t=22.54s AND t=177.459...s
I choose t=22.54s because "it happens earlier"
Now x0freight+vfreight*t= 200m+(15m/s)*22.54s≈540m