#### opus

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**1. The problem statement, all variables and given/known data**

When a train traveling at 161 km/h rounds a bend, the engineer sees that a locomotive has entered onto the track from the side and is a distance D=676m ahead. The locomotive is moving at 29 km/h. The engineer of the high speed train immediately applies the brakes.

What must the magnitude of the resulting constant deceleration be if a collision is to be just avoided?

**2. Relevant equations**

All constant acceleration equations of motion.

**3. The attempt at a solution**

My approach currently is to take ##v=v_0 + at## for the train, solve for t, and plug that expression in for t into the position function for the train. I do this because I don't know anything about time, and it isn't mentioned in the problem.

So I get the position function for the train is equal to ##x_2=x_0 + \frac{-v_1^2 + v_2^2}{2a}##, solving for a, I get ##a=\frac{-v_1^2 + v_2^2}{2(x_2-x_1)}##.

Now here is my next step, and I'm unsure on it's validity. It has given me the incorrect solution, but I'm trying to figure out what part is wrong with this.

Since we want to know the deceleration magnitude that the train must have to not collide with the locomotive, we can say that when they are at the same position, their speeds must be equal. For this reason, I have taken the ##v_2## in my equation, and substituted in the velocity of the locomotive for ##v_2## I then plug in the value of the initial speed for the train, and 676 meters for ##x_2-x_1## So it looks like:

##a_{train}=\frac{-(44.72~m/s)^2+(8.05 m/s)^2}{2(676~m)}##

This gives me an incorrect solution, but not a drastically unreasonable one. I get 1.43 m/s and the correct solution is 0.994 m/s.

So where in my reasoning, have I made an error?

Thank you.