Final answer:
The acceleration of the train as it slows down from 45 m/s east to 15 m/s east over 12 seconds is -2.5 m/s². The negative sign indicates a deceleration.
Step-by-step explanation:
To find the acceleration of the train as it slows down, we can use the formula for constant acceleration, which is a = (v - u) / t, where v is the final velocity, u is the initial velocity, and t is the time taken to change the velocity. In this instance, the train's initial velocity (u) is 45 m/s east and its final velocity (v) is 15 m/s east, with the time of deceleration (t) being 12 s.
Plugging in the values: a = (15 m/s - 45 m/s) / 12 s = -30 m/s / 12 s = -2.5 m/s². The negative sign indicates that the acceleration is in the opposite direction of motion, which means it is a deceleration.