Solving 1-D Motion Problem: Collision & Speed Calculation for Two Trains

[hb1]

(a) A red train traveling at 71.8 km/h and a green train traveling at 143.6 km/h are headed toward one another along a straight, level track. When they are 950.9 m apart, each engineer sees the other's train and applies the brakes. The brakes decelerate each train at the rate of 1.017 m/s2. Is there a collision?

I got the answer: yes.

Second part of the problem (where I'm stumped):

(b) If so, what is the speed of each train at impact?

For simplicity's sake, I tried adding the distances each train would travel if it were heading in the positive x direction (positive velocity, negative acceleration) to get 950.9 m. In other words, I wrote:

V-naught-R * t + 1/2 * a * t^2 + V-naught-G * t + 1/2 * a * t^2 = 950.9

Then I tried to solve the quadratic equation for t, but I get imaginary numbers.. so there must be something wrong with my equation. HELP!

Edit: Sorry, this should probably be in the high school forum.

 

[StatusX]

Check your math again, but if you keep getting imaginary numbers, that would make sense only if the trains don't actually collide, so you should check your work in the first part.

 

[hb1]

No, my dad figured it out. The reason I was getting imaginary numbers is because the red train is already stopped when the collision occurs. Whoever set the problem up is creative. But I'm not amused.