Liz rushes down onto a subway platform to find her train already departing. She stops and watches the cars go by. Each car is 8.60 m long. The first moves past her in 2.05 s and the second in 1.82 s. Find the constant acceleration of the train.

To find the constant acceleration of the train, we can use the equation:

a = (v_f - v_i) / t

where:
a is the acceleration,
v_f is the final velocity of the train,
v_i is the initial velocity of the train, and
t is the time taken.

First, we need to find the initial and final velocities of the train.

The initial velocity (v_i) can be found using the formula:

v_i = (2 * d) / t

where:
d is the length of the train.

Given that each car is 8.60 m long and the first car moves past Liz in 2.05 s, we can calculate the initial velocity:

v_i = (2 * 8.60 m) / 2.05 s
v_i = 8.60 m / 1.025 s
v_i = 8.39 m/s (rounded to two decimal places)

Similarly, we can calculate the final velocity (v_f) for the second car:

v_f = (2 * 8.60 m) / 1.82 s
v_f = 8.60 m / 0.91 s
v_f = 9.45 m/s (rounded to two decimal places)

Now, we can calculate the acceleration (a):

a = (v_f - v_i) / t
a = (9.45 m/s - 8.39 m/s) / 1.82 s
a = 1.06 m/s^2 (rounded to two decimal places)

Therefore, the constant acceleration of the train is 1.06 m/s^2.