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 720 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, give (a) the speed of the red train, (b) the speed of the green train, and (c) the separation between the trains when they collide (0 m).
If not, give (a) the speed of the red train (0 m/s), (b) the speed of the green train (0 m/s), and (c) the separation between the trains when they stop.

To determine if there will be a collision between the red and green trains, we need to calculate the time taken for them to collide or come to a stop.

Let's calculate the time taken for both trains to stop using the given information:

For the red train:
Initial speed of the red train (u1) = 72 km/h = 20 m/s (since 1 km/h = 1000 m/3600 s)
Acceleration of the red train (a1) = -1.0 m/s^2 (negative because it's decelerating)
Final velocity of the red train (v1) = 0 m/s

Using the equation: v1 = u1 + a1 * t1 (where t1 is the time taken for the red train to stop)
0 = 20 + (-1.0) * t1
20 = t1

Therefore, it will take the red train 20 seconds to stop.

Similarly, for the green train:
Initial speed of the green train (u2) = 144 km/h = 40 m/s (since 1 km/h = 1000 m/3600 s)
Acceleration of the green train (a2) = -1.0 m/s^2
Final velocity of the green train (v2) = 0 m/s

Using the equation: v2 = u2 + a2 * t2 (where t2 is the time taken for the green train to stop)
0 = 40 + (-1.0) * t2
40 = t2

Therefore, it will take the green train 40 seconds to stop.

Now, let's calculate the separation between the trains when they stop:

The distance traveled by the red train (s1) during its deceleration can be calculated using the equation: s1 = u1 * t1 + 0.5 * a1 * t1^2
s1 = 20 * 20 + 0.5 * (-1.0) * 20^2
s1 = 400 - 200
s1 = 200 m

Similarly, the distance traveled by the green train (s2) can be calculated:
s2 = 40 * 40 + 0.5 * (-1.0) * 40^2
s2 = 1600 - 800
s2 = 800 m

Since the trains were initially 720 m apart, the total separation between the trains when they stop is:
Total separation = s1 + s2 + initial separation
Total separation = 200 + 800 + 720
Total separation = 1720 m

As the separation between the trains when they stop is more than 0 m, there won't be a collision between them. Therefore, the answers are:

(a) The speed of the red train is 0 m/s.
(b) The speed of the green train is 0 m/s.
(c) The separation between the trains when they stop is 1720 m.