To find the acceleration of the train, we can use the following formula:
acceleration = (final velocity - initial velocity) / time
Since the train starts from rest (initial velocity is 0 m/s), the formula simplifies to:
acceleration = final velocity / time
We need to find the final velocity of the train. To do that, we can use another formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Given that the distance traveled by the train is 25 meters and the time is 45.50 seconds, we can rearrange the formula to solve for the final velocity:
25 = 0 + (0.5 * acceleration * 45.50^2)
Simplifying:
25 = 0.5 * acceleration * 2070.25
Dividing both sides by 0.5 * 2070.25:
acceleration = 25 / (0.5 * 2070.25)
acceleration ≈ 0.024 m/s²
Therefore, the acceleration of the train is approximately 0.024 m/s².