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 1.80 s and the second in 1.66 s. find the constant acceleration of the train.

The average velocity can be calculated using the formula:

v = d / t

For the 1st car, the velocity is calculated as:

v1 = 8.60 m / 1.80 s = 4.78 m / s

While that of the 2nd car is:

v2 = 8.60 m / 1.66 s = 5.18 m / s

Now we can solve for the acceleration using the formula:

v2^2 = v1^2 + 2 a d

Rewriting in terms of a:

a = (v2^2 - v1^2) / 2 d

a = (5.18^2 - 4.78^2) / (2 * 8.6)

a = 0.23 m/s

Therefore the train has a constant acceleration of about 0.23 meters per second.