To compute the acceleration at the moment the train speed reaches 50.0 km/h, we can use the formula for centripetal acceleration:
a = (v^2) / r
where
a = acceleration
v = velocity
r = radius of the curve
First, let's convert the velocities from km/h to m/s, since the formula requires the velocity to be in m/s:
v1_initial = 90.0 km/h = 90.0 * (1000 m / 3600 s) = 25.0 m/s
v2_final = 50.0 km/h = 50.0 * (1000 m / 3600 s) = 13.9 m/s
Now, let's calculate the initial centripetal acceleration using the initial velocity v1_initial and the radius r:
a_initial = (v1_initial^2) / r = (25.0 m/s)^2 / 150 m = 4.17 m/s^2
Since it is mentioned that the train continues to slow down at the same rate, the acceleration remains constant as the train slows down. Therefore, the acceleration when the train reaches 50.0 km/h is the same as the initial acceleration:
a_final = a_initial = 4.17 m/s^2
So, the acceleration at the moment the train speed reaches 50.0 km/h is 4.17 m/s^2.