To determine the time it takes for the train to pass the crossing, we can calculate the time taken for the train to slow down from 84.2 km/h to 16.4 km/h.
First, let's convert the speeds from km/h to m/s for consistent units:
Speed of the train initially (V1) = 84.2 km/h = 84.2 * (1000/3600) = 23.4 m/s
Speed of the train finally (V2) = 16.4 km/h = 16.4 * (1000/3600) = 4.6 m/s
Now, let's use the formula for acceleration:
a = (V2 - V1) / t
Where:
a = acceleration
V1 = initial velocity
V2 = final velocity
t = time taken
Rearrange the formula to solve for t:
t = (V2 - V1) / a
Since the acceleration is constant, we can calculate it using the formula:
a = (V2 - V1) / t
Substituting the values:
t = (4.6 - 23.4) / a
To find the acceleration (a), we can use the formula:
a = (V2 - V1) / t1,
where t1 is the time taken for the train to initially slow down.
The initial velocity of the train (V1) is 23.4 m/s,
the final velocity (V2) is 0 m/s since the train comes to a stop,
and we need to find the time taken (t1).
Using the formula:
a = (V2 - V1) / t1
0 = (0 - 23.4) / t1
Now solving for t1:
t1 = (0 - 23.4) / 0 = undefined (division by zero)
This calculation shows that the train would theoretically take infinite time to come to a complete stop.
Therefore, the train never stops completely. It just slows down and continues moving, indicating that the train never blocked the crossing.