Final answer:
Using the given maximum possible braking force and the mass of the train, the calculated stopping distance exceeds the available distance before the obstacle, indicating the train cannot be stopped in time to avoid a collision.
Step-by-step explanation:
To determine if the train can be stopped in time, we can utilize the work-energy principle or kinematic equations. To check whether the train can stop before hitting the truck, we calculate the minimum stopping distance using the formula: Stopping distance = (initial velocity squared) / (2 × deceleration). The deceleration (a) can be found using the formula F = m × a, where F is the maximum possible braking force and m is the mass of the train. Substituting the given values: Deceleration (a) = F / m = 84000 N / 55200 kg = 1.52 m/s². Now, calculate the stopping distance: Stopping distance = (26.8 m/s) ² / (2 × 1.52 m/s²) = 239.68 m. This stopping distance is greater than the available distance of 184 m. Therefore, the engineer cannot stop the train in time to avoid hitting the truck.