Final answer:
A graph of speed versus time for a 12-second interval, starting 2 seconds before the brakes are applied and ending 1 second after the brakes are released, would display a constant speed of 12.0 m/s for the first 2 seconds, followed by a linear decrease in speed over the next 9 seconds until reaching 3.00 m/s. Finally, it remains constant at 3.00 m/s for the last 1 second.
Explanation:
Initially, the train travels south at a constant speed of 12.0 m/s. Before the brakes are applied, the speed remains constant for 2 seconds. After the brakes are applied, the train decelerates with a constant acceleration until it reaches a speed of 3.00 m/s after 9 seconds. During this period, the speed decreases linearly.
The speed versus time graph would show a horizontal line at 12.0 m/s for the first 2 seconds, indicating the constant speed. Afterward, a linear decrease in speed would be depicted over the subsequent 9 seconds, forming a diagonal line as the speed decreases from 12.0 m/s to 3.00 m/s. Finally, the graph would show a horizontal line at 3.00 m/s for the last 1 second, indicating that the speed remains constant once the train has stopped decelerating.
This graphical representation illustrates the train's speed behavior during the given time frame, showcasing the transition from constant speed to deceleration and eventually reaching and maintaining a new constant speed after the brakes are released.