Two trains face each other on adjacent tracks. They are initially at rest, and their front ends are 34 m apart. The train on the left accelerates rightward at 1.18 m/s2. The train on the right accelerates leftward at 1.19 m/s2.

(a) How far does the train on the left travel before the front ends of the trains pass?

To find how far the train on the left travels before the front ends of the trains pass, we need to determine the time it takes for the front ends to meet.

Let's denote the distance traveled by the train on the left as "x" and the time it takes for the front ends to meet as "t".

We know that the initial distance between the front ends of the trains is 34 m.

The train on the left is accelerating at a rate of 1.18 m/s^2, so we can use the equation of motion:
x = vt + (1/2)at^2,
where "v" is the initial velocity (0 m/s) and "a" is the acceleration (1.18 m/s^2).

Similarly, the train on the right is accelerating at a rate of -1.19 m/s^2 (negative because it's in the opposite direction), so its equation of motion is:
(34 - x) = vt + (1/2)at^2.

Since the front ends of the trains meet when they are at the same position, we can set the two equations equal to each other:
vt + (1/2)at^2 = (34 - x).

Now we need to solve this equation for "t". Rearranging the equation, we get:
(1/2)at^2 + vt - (34 - x) = 0.

This is a quadratic equation in terms of "t". We can solve this using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a),
where a = (1/2)a for both terms, b = v for both terms, and c = -(34 - x) for both terms.

Substituting these values into the quadratic formula, we get:
t = (-v ± √(v^2 - 4a(34 - x))) / a.

Since the train is accelerating rightward, "v" and "a" are both positive values. We can ignore the negative solution for "t" as it doesn't make sense in this context.

After finding the value of "t", we can substitute it back into the equation x = vt + (1/2)at^2 to find "x".

Therefore, the steps to find how far the train on the left travels before the front ends of the trains pass are:
1. Set up equations of motion for both trains.
2. Equate the equations to find "t".
3. Use the quadratic formula to solve for "t".
4. Substitute the value of "t" back into the equation of motion for the train on the left to find "x".

Note: The values of velocity, acceleration, and distance traveled in this problem are not provided, so they need to be given to find the specific answer.