Train collision problem, speed at impact

[kazo0]

1. A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward each other along a straight, level track. When they are 950 m apart, each engineer sees the other’s train and applies the brakes. The brakes slow each train at the rate of 1.0 m/s2. Is there a collision? If so, answer yes and give the speed of the red train and the speed of the green train at impact, respectively. If not, answer no and give the separation between the trains when they stop.

I was able to find that the trains would indeed collide, I don't know how to find out the last part, what their speeds are at the instant that they collide. Can anyone help me out?

Thanks

Homework Equations

i used the equation V^2 = Vo^2 + 2((delta)x)

The Attempt at a Solution

I was able to find that the trains would indeed collide, I don't know how to find out the last part, what their speeds are at the instant that they collide. Can anyone help me out?

Thanks

 

[Delphi51]

Write equations for the distance each train travels up to time t after the brakes are applied. By setting the total of the two distances to 950 m, you should be able to solve for the time of the collision. Then you can use velocity formulas for the two trains to find their speeds at that time.

 

[tomcue]

To find the speeds of the trains at impact, we can use the equation for final velocity (V) in terms of initial velocity (Vo), acceleration (a), and displacement (Δx):

V^2 = Vo^2 + 2aΔx

For the red train, we have Vo = 72 km/h, a = -1.0 m/s^2 (since the brakes are slowing the train down), and Δx = 950 m. Converting the units to meters and seconds, we get:

V^2 = (20 m/s)^2 + 2(-1.0 m/s^2)(950 m)
V^2 = 400 m^2/s^2 - 1900 m^2/s^2
V^2 = -1500 m^2/s^2

Taking the square root of both sides, we get the speed of the red train at impact:

V = -38.7 m/s = -139.3 km/h (since the speed is negative, this means the train is moving in the opposite direction)

For the green train, we have Vo = 144 km/h, a = -1.0 m/s^2, and Δx = 950 m. Converting the units, we get:

V^2 = (40 m/s)^2 + 2(-1.0 m/s^2)(950 m)
V^2 = 1600 m^2/s^2 - 1900 m^2/s^2
V^2 = -300 m^2/s^2

Taking the square root, we get the speed of the green train at impact:

V = -17.3 m/s = -62.3 km/h (again, the negative sign indicates the train is moving in the opposite direction)

Therefore, the speeds of the trains at impact are -139.3 km/h for the red train and -62.3 km/h for the green train. This means that the red train was traveling faster than the green train before the collision, but they both slowed down due to the brakes and ended up colliding at a slower speed.