To determine how long the train blocked the crossing, we need to calculate the time it takes for the train to come to a complete stop from its initial speed of 80.1 km/h.
Step 1: Convert the speeds from km/h to m/s.
The initial speed of the train is 80.1 km/h, which is (80.1 * 1000) / 3600 = 22.25 m/s.
The final speed of the last car is 16.9 km/h, which is (16.9 * 1000) / 3600 = 4.69 m/s.
Step 2: Calculate the deceleration (negative acceleration) of the train.
Since the train is slowing down, the acceleration is negative. We can use the following formula to calculate the deceleration:
acceleration = (final speed - initial speed) / time
Rearranging the formula gives us:
time = (final speed - initial speed) / acceleration
In this case, the final speed is 0 m/s (since the train comes to a stop) and the initial speed is 22.25 m/s. Therefore, the deceleration can be calculated as:
deceleration = (final speed - initial speed) / time
0 - 22.25 = -22.25 m/s
Step 3: Calculate the time it takes for the train to come to a complete stop.
Using the formula from step 2, we can find the time:
time = (final speed - initial speed) / acceleration
time = (0 - 22.25) / -22.25
time = 1 second
Step 4: Calculate the distance traveled during the deceleration.
To find the distance traveled during the deceleration, we can use the following formula:
distance = initial speed * time + (1/2) * acceleration * (time^2)
In this case, the initial speed is 22.25 m/s, the time is 1 second, and the acceleration is -22.25 m/s^2. Plugging these values into the formula, we get:
distance = 22.25 * 1 + (1/2) * (-22.25) * (1^2)
distance = 22.25 - 11.125
distance = 11.125 meters
Step 5: Calculate the time the train blocked the crossing.
The train's length is given as 400 meters, and during the deceleration, it traveled a distance of 11.125 meters. Therefore, the time the train blocked the crossing can be calculated using the formula:
time_blocked = (total distance - distance traveled during deceleration) / initial speed
Plugging in the values, we get:
time_blocked = (400 - 11.125) / 22.25
time_blocked = 18.022 seconds
Therefore, the train blocked the crossing for approximately 18.022 seconds.