Question

A train 300 m long is moving on a straight track with a speed of 82.8 km/h. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 17.5 km/h. Assuming constant acceleration, determine how long the train blocked the crossing.

Answer 1

To calculate how long the train blocked the crossing, one must first find the train's acceleration during deceleration and then use it to compute the time it took to decelerate fully, which represents how long the train occupied the crossing.

Step-by-step explanation:

To determine how long the train blocked the crossing, we first need to calculate the acceleration of the train while it is decelerating. We can use the formula

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance covered. In this case, the distance is the length of the train (300 m), the initial velocity (u) is 82.8 km/h (which converts to 23 m/s), and the final velocity (v) is 17.5 km/h (which converts to 4.86 m/s).

Once we have the acceleration, we can use the formula

v = u + at

to find the time t the train takes to decelerate. This will give us the time during which the train blocks the crossing because it represents the time taken for the entire length of the train to pass the crossing point after deceleration has begun.