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## Homework Statement

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?

## Homework Equations

v

_{0passenger}=25 m/s

x

_{0freight}=200m

## The Attempt at a Solution

When the collision takes place, x

_{passenger}=x

_{freight}

v

_{0passenger}*t +½*a*t

^{2}=x

_{0freight}+v

_{freight}*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 x

I choose t=22.54s because "it happens earlier"

Now x

_{0freight}+v_{freight}*t= 200m+(15m/s)*22.54s≈540m
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