Final answer:
The train decelerates from 35 m/s to 0 m/s in 12.6 s. By using the formula for acceleration (a = ∆v/∆t) the deceleration calculated is -2.78 m/s². Hence, the correct answer is B. -2.78 m/s². Option B is correct.
Step-by-step explanation:
To calculate the train's acceleration, we need to use the formula a = ∆v/∆t, where a is the acceleration, ∆v is the change in velocity, and ∆t is the change in time. The train decelerates from an initial velocity of 35 m/s to a final velocity of 0 m/s in a time span of 12.6 seconds. This means the change in velocity (∆v) is v_final - v_initial = 0 - 35 m/s = -35 m/s, indicating a decrease in speed.
To find the deceleration (which is negative acceleration), we use the formula: ∆v/∆t, which is: -35 m/s / 12.6 s = -2.78 m/s². Deceleration is negative because the train is slowing down, so the correct answer is B. -2.78 m/s².
To find the train's acceleration, we can use the formula:
acceleration = change in velocity / time taken
Given that the train's initial velocity is 35 m/s and it comes to a stop in 12.6 s, the change in velocity is 35 m/s and the time taken is 12.6 s. Thus, the acceleration is:
acceleration = 35 m/s / 12.6 s = - 2.78 m/s²
Therefore, the train's acceleration is - 2.78 m/s².